Download Hi-Res ImageDownload to MS-PowerPointCite This:Nano Lett. 2020, 20, 4, 2288-2295

Proximity Spin–Orbit Torque on a Two-Dimensional Magnet within van der Waals Heterostructure: Current-Driven Antiferromagnet-to-Ferromagnet Reversible Nonequilibrium Phase Transition in Bilayer CrI₃

Kapildeb Dolui
Kapildeb Dolui
Department of Physics and Astronomy, University of Delaware, Newark, Delaware 19716, United States
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Marko D. Petrović
Marko D. Petrović
Department of Physics and Astronomy, University of Delaware, Newark, Delaware 19716, United States
More by Marko D. Petrović

Klaus Zollner
Klaus Zollner
Institute for Theoretical Physics, University of Regensburg, Regensburg 93040, Germany
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Petr Plecháč
Petr Plecháč
Department of Mathematical Sciences, University of Delaware, Newark, Delaware 19716, United States
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Jaroslav Fabian
Jaroslav Fabian
Institute for Theoretical Physics, University of Regensburg, Regensburg 93040, Germany
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, and

Branislav K. Nikolić*
Branislav K. Nikolić
Department of Physics and Astronomy, University of Delaware, Newark, Delaware 19716, United States
*Email: [email protected]
More by Branislav K. Nikolić
http://orcid.org/0000-0002-5793-7764

Cite this: Nano Lett. 2020, 20, 4, 2288–2295

Publication Date (Web):March 4, 2020

https://doi.org/10.1021/acs.nanolett.9b04556

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Abstract

The recently discovered two-dimensional magnetic insulator CrI₃ is an intriguing case for basic research and spintronic applications since it is a ferromagnet in the bulk but an antiferromagnet in bilayer form, with its magnetic ordering amenable to external manipulations. Using the first-principles quantum transport approach, we predict that injecting unpolarized charge current parallel to the interface of the bilayer-CrI₃/monolayer-TaSe₂ van der Waals (vdW) heterostructure will induce spin–orbit torque and thereby drive the dynamics of magnetization on the first monolayer of CrI₃ in direct contact with TaSe₂. By combining the calculated complex angular dependence of spin–orbit torque with the Landau-Lifshitz-Gilbert equation for classical dynamics of magnetization, we demonstrate that current pulses can switch the direction of magnetization on the first monolayer to become parallel to that of the second monolayer, thereby converting CrI₃ from antiferromagnet to ferromagnet while not requiring any external magnetic field. We explain the mechanism of this reversible current-driven nonequilibrium phase transition by showing that first monolayer of CrI₃ carries current due to evanescent wave functions injected by metallic transition metal dichalcogenide TaSe₂, while concurrently acquiring strong spin–orbit coupling via such a proximity effect, whereas the second monolayer of CrI₃ remains insulating. The transition can be detected by passing vertical read current through the vdW heterostructure, encapsulated by a bilayer of hexagonal boron nitride and sandwiched between graphite electrodes, where we find a tunneling magnetoresistance of ≃240%.

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Introduction

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The recent discovery of two-dimensional (2D) magnets derived from layered van der Waals (vdW) materials(1,2) has opened new avenues for basic research on low-dimensional magnetism(3,4) and potential applications in spintronics.(5−9) Their magnetic phases can substantially differ from those in conventional bulk magnetic materials due to large structural anisotropy, which makes different signs and magnitudes of intralayer J_intra and interlayer J_inter exchange coupling between localized magnetic moments possible. For example, J_intra and J_inter are ferromagnetic and antiferromagetic, respectively, between magnetic moments on Cr atoms within the bilayer of CrI₃, which eventually becomes an antiferromagnetic insulator with Néel temperature T_N ≃ 61 K.(2) Hence, antiferromagnet spins have an opposite orientation in the two monolayers, whereas monolayer, trilayer, and bulk CrI₃ are ferromagnetic. Thus, the bilayer of CrI₃ can also be viewed as two monolayer ferromagnets that are antiferromagnetically coupled to each other. The monolayer CrI₃ circumvents the Mermin-Wagner theorem,(10) where thermal fluctuations destroy long-range magnetic order in 2D, by exhibiting strong uniaxial perpendicular magnetic anisotropy (PMA) that removes rotational invariance and effectively makes it a realization of the Ising model.(3) The PMA is also required for high-density device applications.

The layer and stacking order(11,12) dependence of electronic and spin structure as a new knob, together with possibilities for external manipulation via gating, straining, and coupling to other 2D materials within vdW heterostructures, allows for dramatic changes of magnetic ordering of 2D magnets, which is not possible with conventional bulk magnetic materials. For example, very recent experiments(13−15) have demonstrated antiferromagnet (AFM) to ferromagnet (FM) phase transition in the bilayer of CrI₃ by applying an external electric field via gate voltage or by electrostatic doping. While these effects offer potential building blocks(16) for an ultralow-dissipation nonvolatile memory, at present, they employ cumbersome external magnetic fields that cannot be generated on the nanoscale as required for integration with other elements of a circuit. Furthermore, to read the change of magnetic state of such a device within a circuit, it is still required to pass a current through it,(17) as demonstrated recently using unconventional magnetic tunnel junctions where bilayer CrI₃ functions as the spin-filter sandwiched between metallic electrodes (such as graphene) with current flowing perpendicular to the interface.(18−21)

An alternative for magnetization switching is to inject a current through 2D magnet and drive its magnetization dynamics via spin torque, as exemplified by very recent experiments(8,9) on spin–orbit torque (SOT)(22,23) driven magnetization dynamics in Fe₃GeTe₂/Pt heterostructures. However, the layers employed in these experiments were much thicker than the ultimate limit envisaged using vdW heterostructures composed of just a few atomically thin layers. They are flat and ensure highly transparent interfaces, so that drastically smaller energy consumption per switching cycle can be achieved. These experiments have also relied on Fe₃GeTe₂ being a metallic vdW ferromagnet,(3) so that the CrI₃ bilayer with an energy gap is at first sight not suitable for SOT-operated devices.

Here, we employ first-principle quantum transport framework, which combines(24−26) nonequilibrium Green functions (NEGFs)(27) for two-terminal devices with noncollinear density functional theory (ncDFT) calculations,(28,29) to predict that the AFM–FM nonequilibrium phase transition can be induced by SOT in the bilayer-CrI₃/monolayer-TaSe₂ vdW lateral heterostructure depicted in Figure 1 where unpolarized charge current is injected parallel to the interface. The monolayer of metallic TaSe₂ is chosen in 1H phase for which lattice mismatch between TaSe₂ and CrI₃ is as small as 0.1%, while inversion symmetry of TaSe₂ is broken to create large spin–orbit coupling (SOC).

Figure 1. Schematic view of the CrI₃/TaSe₂ vdW heterostructure consisting of an insulating antiferromagnetic bilayer of CrI₃ and a nonmagnetic metallic monolayer TMD TaSe₂. The unpolarized charge current is injected parallel to the interface by a small applied bias voltage V_b between the left and right macroscopic reservoirs. The current flows through the monolayer of TaSe₂ as well as through the first monolayer (see the Supporting Information) of CrI₃ due to evanescent wave functions injected into it by TaSe₂. The unit vectors of magnetizations on the two CrI₃ monolayers are denoted by m₁ and m₂. The heterostructure is assumed to be infinite in the xy-plane.

Both conventional spin-transfer torque (in the absence of SOC and in geometries with two FM layers with noncollinear magnetizations(24,30)) and SOT (in geometries with one FM layer but requiring interfacial or bulk SOC effects(24−26,31,32)) can be described microscopically and independently of a particular physical mechanism(22,26) as a consequence of the interaction between current-driven (CD) nonequilibrium spin density(33−35) of conduction electrons S_CD(r) and a nonzero exchange-correlation (XC) magnetic field B_XC(r)(28,29) present in equilibrium. Their cross product, S_CD(r) × B_XC(r), is local torque at some point in space r, so that the total torque is obtained by integration(24,25,30)

(1)While B_XC(r) is nonzero in both the monolayer and bilayer of CrI₃ due to long-range magnetic ordering, S_CD(r) appears only on the monolayer of CrI₃ that is in direct contact with the monolayer of TaSe₂, as demonstrated by Figure 2. This is due to the proximity effect where evanescent wave functions from TaSe₂ penetrate [Figures 2 and 3; also see the Supporting Information] up to the first monolayer of CrI₃ to make it a current carrier (see the Supporting Information for spatial profiles of local charge current density), while also bringing(36) SOC from TaSe₂ to ensure that S_CD(r) is not collinear to B_XC(r). The giant SOC hosted by TaSe₂ itself due to inversion symmetry breaking in ultrathin layers of transition metal dichalcogenides (TMDs)(37,38) is confirmed by large S_CD(r) within the spatial region of the TaSe₂ monolayer in Figure 2.

Figure 2. Current-driven nonequilibrium spin density S_CD = (S_CD^x,S_CD^y,S_CD^z) in the linear-response regime within a bilayer-CrI₃/monolayer-TaSe₂ vdW heterostructure for (a) m₁∥x̂; (b) m₁∥ŷ; (c) m₁∥ẑ. Vertical dashed lines indicate the position of each atomic plane. The area of the common rectangular supercell of the vdW heterostructure in Figure 1 is denoted by , where a = 6.85 Å is the lattice constant of bulk CrI₃. Shaded green areas represent rescaled S_CD^y in the spatial region of the first monolayer of CrI₃, which is in direct contact with the monolayer of TaSe₂.

Figure 3. First-principles-computed bands of the bilayer-CrI₃/monolayer-TaSe₂ vdW heterostructure with SOC turned on. We use Hubbard U = 2.0 eV and U = 0 eV for (a) and (c), respectively, in ncDFT + U calculations where the color corresponds to the equilibrium spin expectation value, (σ̂_z is the Pauli matrix) in the eigenstates |Ψ_k⟩ of ncDFT Hamiltonian (for the other two components, S_eq^x and S_eq^y, and their texture in k-space, see the Supporting Information). Panels (b) and (d) show the same band structures as (a) and (c), respectively, but with different colored symbols corresponding to projections onto different monolayers.

The SOT vector in eq 1, with its complex angular dependence [Figure 4] on the direction of magnetization (along the unit vector m₁ in Figure 1) of the first monolayer of CrI₃, is combined in a multiscale fashion(30,39) with the classical dynamics of magnetization governed by the Landau-Lifshitz-Gilbert (LLG) equation to demonstrate reversible switching of m₁ [Figure 5b and the accompanying movie in the Supporting Information] from the −z to +z direction by current pulses and, thereby, transition from the AFM to FM phase of the CrI₃ bilayer. The dynamics of m₁ can be detected by passing the vertical read current along the z-axis,(17) where we compute the tunneling magnetoresistance (TMR) of ≃240% [Figure 6] due to the AFM–FM transition of the CrI₃ bilayer. For such a scheme, we assume that the bilayer-CrI₃/monolayer-TaSe₂ vdW heterostructure is sandwiched between two metallic semi-infinite graphite electrodes along the z-axis with hexagonal BN (hBN) bilayers inserted between the leads and vdW heterostructure [inset of Figure 6].

Figure 4. Azimuthal (θ) and polar (φ) angle dependence of the magnitude of SOT component |T^o| (odd in m₁) for different orientations of the magnetization m₁ = (sin θ cosφ, sin θ sinφ, cos θ) on the first monolayer of CrI₃. The magnetization is rotated within the (a) xz-plane; (b) xy-plane; (c) yz-plane. Solid blue lines are fit to NEGF + ncDFT-computed SOT values (red dots) using eq 6 with fitting parameters from Table 1.

Figure 5. Classical dynamics of magnetizations (a, b) m₁(t) on the first monolayer of CrI₃ and (c, d) m₂(t) on the second monolayer of CrI₃. The two magnetizations are exchange coupled [eq 7], while according to Figure 2 only m₁(t) experiences SOT from Figure 4. The dynamics is obtained by solving two coupled LLG equations [eq 8] for m₁(t) and m₂(t). The bias voltage V_b = 0.2 V is dc in (a) and (c), while in (b) and (d) we use a sequence of short rectangular voltage pulses of the same amplitude with pulse duration δt_ON = 1.0 ps followed by a pause of δt_OFF = 100 ps during which no voltage is applied. A movie animating m₁(t) in panel (b) as well as m₂(t) in panel (d) is provided in the Supporting Information.

Figure 6. TMR vs angle θ between magnetizations m₁ and m₂ on two monolayers of CrI₃ in Figure 1 for vertical read current(17) flowing perpendicularly (i.e., along the z-axis in Figure 1) through the bilayer-CrI₃/monolayer-TaSe₂ vdW heterostructure. The heterostructure is sandwiched between two semi-infinite graphite leads with (red squares) and without (blue circles) the bilayer of hBN inserted between the leads and the vdW heterostructure, as illustrated in the inset.

Methodology

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We employ the interface builder in the QuantumATK(40) package to construct a unit cell of the vdW heterostructure in Figure 1 while starting from experimental lattice constants of CrI₃ and TaSe₂ layers. In order to determine the interlayer distance between CrI₃ and TaSe₂, we perform DFT calculations with Perdew–Burke–Ernzerhof (PBE) parametrization of the generalized gradient approximation (GGA) for the XC functional, including Grimme D2(41) vdW corrections.

In addition, we employ ncDFT + U calculations using the Quantum ESPRESSO(42) package to examine how nonzero(43) Hubbard U affects the bands of the vdW heterostructures since nonzero U has been utilized before(44,45) as a cure for the band gap problem in CrI₃.(46) For this purpose, we use PBE parametrization of GGA for the XC functional; fully relativistic pseudopotentials with the projector augmented wave method(47) for describing electron–core interactions; energy cutoff of 550 Ry for the plane wave basis set; k-point sampling of 30 × 30 × 1 for self-consistent calculations. A comparison of the cases with U = 0 and U = 2.0 eV in Figure 3 shows that U ≠ 0 barely changes the band structure within the energy window of ±1 eV, with only the conduction band of CrI₃ experiencing a shift in energy of about ≃0.15 eV [Figure 3b,d] at the Γ point and energies around 0.5 eV. This is because Hubbard U acts(44,45) on d-orbitals of Cr whose bands are higher in energy. States near the Fermi level E – E_F = 0, which are responsible for charge and spin transport properties in the linear-response transport regime, are formed by a TaSe₂ monolayer [Figure 3b,d]. Due to the short-range of the proximity effect, only the bands of the first monolayer of CrI₃ hybridize with the bands of TaSe₂, such as spin-down bands near the K valley at energies of 0.5–0.8 eV [Figure 3a,b].

The NEGF + ncDFT formalism,(24,25,30) which combines self-consistent Hamiltonian from ncDFT calculations (with U = 0 based on Figure 3) with a nonequilibrium density matrix and current calculations from NEGF calculations, makes it possible to compute spin torque in an arbitrary device geometry at small or finite bias voltage. The single-particle Kohn–Sham (KS) Hamiltonian in ncDFT is given by

(2)where σ = (σ̂_x, σ̂_y, σ̂_z) is the vector of the Pauli matrices; V_ext(r), V_H(r), and V_XC(r) = δE_XC[n(r),μ(r)]/δn(r) are the external, Hartree, and XC potentials, respectively, and the XC magnetic field, B_XC(r) = δE_XC[n(r),μ(r)]/δμ(r), is the functional derivative with respect to the vector magnetization density μ(r). The extension of DFT to the case of spin-polarized systems is formally derived in terms of μ(r) and total electron density n(r), where in collinear DFT μ(r) points in the same direction at all points in space, while in ncDFT μ(r) can point in an arbitrary direction.(28,29)

The heterostructure in Figure 1 is split into the central region and left (L) and right (R) semi-infinite leads, all of which are composed of the same CrI₃/TaSe₂ trilayer. The self-energies of the leads Σ_L,R(E) and the Hamiltonian Ĥ_KS of the central region are obtained from ncDFT calculations within the QuantumATK package(40) using PBE parametrization of GGA for the XC functional; norm-conserving fully relativistic pseudopotentials of the type SG15-SO(40,48) for describing electron–core interactions; the SG15 (medium) numerical linear combination of atomic orbitals (LCAO) basis set.(48) Periodic boundary conditions are employed in the plane perpendicular to the transport direction with grids of 1 × 101 k-point (lateral device setup in Figure 1 for SOT calculations) and 25 × 25 k-point (vertical device setup in the inset of Figure 6 for TMR calculations). The energy mesh cutoff for the real-space grid is chosen as 100 hartree.

The lesser Green function (GF), G^<(E) = iG(E)[f_L(E)Γ_L(E) + f_R(E)Γ_R(E)]G^†(E), of NEGF formalism makes it possible to construct the nonequilibrium density matrix(27)

(3)in the steady state and elastic transport regime. Here, G = [EΛ – H_KS – Σ_L(E,V_L) – Σ_R(E,V_R)]⁻¹ is the retarded GF; f_L,R(E) = f(E – eV_L,R) is the shifted Fermi function of the macroscopic reservoirs into which semi-infinite leads terminate; V_b = V_L – V_R is the applied bias voltage between them; Γ_L,R(E) = i[Σ_L,R(E) – Σ_L,R^†(E)] is the level broadening matrix. For the lateral heterostructure [Figure 1], all matrices, H_KS, G, G^<, Γ_L,R and ρ_neq, depend on k_y, while for vertical the heterostructure [inset of Figure 6], they depend on (k_x,k_y). Due to the nonorthogonality of the LCAO basis set |ϕ_n⟩, we also use the overlap matrix Λ composed of elements ⟨ϕ_i|ϕ_j⟩.

The CD part of the nonequilibrium density matrix, ρ_CD(k_y) = ρ_neq(k_y) – ρ_eq(k_y), is obtained by subtracting the equilibrium density matrix ρ_eq(k_y) for V_L = V_R. This yields

(4)and SOT

(5)which we compute by performing trace in the LCAO basis [instead of in real space as in eq 1], and additional integration over the one-dimensional Brillouin zone (BZ) of length Ω_BZ is performed.

Nonequilibrium Spin Density

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The xy-plane averaged S_CD is plotted in Figure 2 for three representative orientations of the magnetization m₁∥{x̂, ŷ, ẑ} on the first monolayer of CrI₃. The nonequilibrium spin density is zero on the second monolayer of CrI₃, which confirms that evanescent wave functions originating from the metallic TaSe₂ monolayer and the spin–orbit proximity effect carried by them decay exponentially fast, so they are able to reach only the first monolayer of CrI₃. Independently of the orientation of m₁, the magnitude of S_CD within the first monolayer of CrI₃ is mainly dominated by its y-component, which is an order of magnitude smaller than S_CD within TaSe₂. Concurrently, the magnetic proximity effect from CrI₃ induces a small magnetization into the monolayer of TaSe₂ with magnetic moments on Ta and Se atoms being 0.008 and 0.001 μ_B, respectively, where μ_B is the Bohr magneton. In comparison, we compute magnetic moments on Cr and I atoms as μ_Cr = 3.43 μ_B and μ_I = 0.14 μ_B, respectively. The component S_CD^y within the TaSe₂ monolayer is insensitive to m₁, while S_CD^x remains negligible.

Unlike the surface of the topological insulator(35) or heavy metals where S_CD is confined to the plane in accord with the phenomenology of the standard inverse spin-galvanic (or Edelstein) effect,(33,34) TaSe₂ exhibits large out-of-plane componentS_CD^z ,which is sensitive to the orientation of m₁ and it is highly sought for SOT-operated device applications.(49) This can be traced to the large S_eq^z component of the spin texture in k-space for an isolated monolayer TaSe₂, which remains large when TaSe₂ is covered by the bilayer CrI₃ while also acquiring nontrivial in-plane components S_eq^x and S_eq^y (see the Supporting Information for more details).

Angular Dependence of SOT

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The SOT vector can be decomposed,(31,50)T = T^e + T^o, into odd (o) and even (e) components with respect to the magnetization m₁. They can be computed directly from eqs 4 and 5 by using the respective components of the nonequilibrium density matrix, ρ_CD = ρ_CD^e + ρ_CD^o, as introduced in refs (24and51). Due to the absence of the bulk in the case of the monolayer TaSe₂, the vdW heterostructure in Figure 1 does not generate vertical spin Hall current along the z-axis as one of the mechanisms for T^e. Other interfacially based mechanisms(26) for T^e ≠ 0 require the backscattering of electrons,(24,52−54) which is absent in the ballistic transport regime we assume, so we find T^e → 0.

The nonzero T^o component, computed from NEGF + ncDFT formalism as dots in Figure 4, can be fitted by a function defined as an infinite series(50)

(6)assuming that current flows along the x-axis as in Figure 1. Note that other expansions, such as in terms of orthonormal vector spherical harmonics, can also be employed to define the fitting function.(26) Here, τ_nα^o and τ_nβ^o are the fitting parameters, and p is the unit vector along the reference direction set by current-induced nonequilibrium spin density, such that T^o = 0 when m₁∥p. In simple systems, like the Rashba spin-split 2D electron gas(33) or metallic surface of the topological insulator(35) in contact with the FM layer, p∥ŷ (assuming injected current along x̂) is determined by symmetry arguments.(25) However, for more complicated systems, it has to be calculated, and we find p ≡ (θ = 88°, φ = 98°) instead of often naı̈vely assumed p ≡ (θ = 90°, φ = 90°)∥ŷ. The lowest order term τ_0α^o(p × m₁) in eq 6 is conventional field-like torque,(22) while higher terms can have properties of both field-like and damping-like torque(26) [the lowest order term τ_0α^em₁ × (p × m₁) in the expansion of T^e is conventional damping-like torque(50)]. The value of τ_0α^o, together with other non-negligible parameters in eq 6, is given in Table 1.

Table 1. Non-negligible Coefficients (in units of 10^–4 eV_b/□) in the Expansion of T^o in Equation 6 Are Obtained by Fitting (Solid Lines) NEGF + ncDFT-Computed Angular Dependence of SOT (Dots) in Figure 4 for Bilayer-CrI₃/Monolayer-TaSe₂ vdW Heterostructure

p(θ, φ)	τ_0α^o	τ_1α^o	τ_2α^o	τ_3α^o	τ_0β^o	τ_1β^o
(88°, 98°)	77.22	17.32	–30.32	13.54	–9.19	–6.88

SOT-Driven Classical Dynamics of Magnetization

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The effective anisotropic classical Heisenberg model(3) for magnetic moments m₁ and m₂ on Cr atoms within two monolayers of CrI₃ in Figure 1 is given by

(7)where the values for J₁₂ = −0.05 meV, as the interlayer AFM exchange coupling, and A_⊥ = 1.5 meV, as the PMA constant in the presence of TaSe₂ monolayer, are extracted from ncDFT calculations. They are close to the corresponding values obtained for the isolated CrI₃ bilayer in previous ncDFT calculations.(11,55)

We simulate the classical dynamics m₁(t) by solving the LLG equation

(8)where γ is the gyromagnetic ratio;

is the effective magnetic field due to interactions in the Hamiltonian in eq 7; λ₁ is the Gilbert damping parameter; SOT at an arbitrary direction of m₁ is given by eq 6 with parameters in Table 1. The LLG equation for m₂ is the same as eq 8, but with

and T^o ≡ 0 because no current flows through the second monolayer of CrI₃.

The computed trajectories m₁(t) are plotted in Figure 5a for dc bias voltage as well as for rectangular voltage pulses in Figure 5b. The trajectories m₂(t) are much simpler, m₂^z(t) ≈ 1 while m₂^x(t) and m₂^y(t) perform small oscillations around zero, as shown in Figure 5c,d for dc bias voltage or rectangular voltage pulses, respectively. The time evolutions m₁(t) and m₂(t) are also animated in the movie provided in the Supporting Information. For unpolarized charge current injected by dc bias, magnetization m₁ switches from being antiparallel to m₂ to a noncollinear direction within the yz-plane. The nonequilibrium and noncollinear configuration of m₁ and m₂ will go to a stable FM phase (both magnetizations pointing along the positive z-axis) when V_b is turned off and the system goes back to equilibrium. On the other hand, using voltage pulses leads to AFM–FM transition with reversal from m₁∥–ẑ to m₁∥+ẑ while magnetization of the second layer remains m₂∥+ẑ. Such current-induced FM phase is stable in-between two pulses, on the proviso that A_⊥ > |J₁₂| in eq 7, and can be reversed back to the AFM phase by the next pulse [Figure 5b and movie in the Supporting Information]. We assume different Gilbert damping parameters λ₁ = 0.01 > λ₂ = 0.0001 on two monolayers of CrI₃ due to the presence of the TaSe₂ monolayer, but the actual value λ₁ on the first monolayer of CrI₃ is likely smaller. Thus, we anticipate that the time needed to stabilize the FM phase would be on the order of ∼1 ns instead of ∼100 ps in Figure 5 (where λ₁ was tuned for such numerical convenience).

Since T^o forces precession of magnetization around the axis defined by p, magnetization reversal in the voltage pulse setup is achieved by fine-tuning the pulse duration δt_ON to half of the period of that precession. The Gilbert damping term, λ₁m₁ × dm₁/dt, does not play a role in this type of switching, although λ₁ together with the PMA constant is critical to stabilize the FM phase after the pulse is switched off, as shown in the movie in the Supporting Information. For instance, when Gilbert damping is set to zero, the magnetizations in both monolayers never fully align with the z-axis and instead continue to precess around it which renders the FM phase unstable. Note that more detailed LLG simulations would be required to simulate more than two magnetic moments and their inhomogeneous switching in a particular device geometry, as often observed experimentally in ferromagnet/heavy-metal heterostructures,(56) but our two-terminal device is homogeneous and translationally invariant within the xy-plane in Figure 1. Also, in the presence of disorder and thereby induced voltage drop across the central region,(25,26,53) we expect that T^e would become nonzero(54) and contribute to switching.

TMR as a Probe of AFM–FM Transition

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Finally, in analogy with the experiments(17) where SOT-driven magnetization switching has been probed by passing additional vertical read current through SOT devices operated by lateral current, we investigate the angular dependence of TMR for vertical current assumed to be injected between semi-infinite graphite leads along the z-axis sandwiching bilayer-CrI₃/monolayer-TaSe₂ [see inset in Figure 6 for illustration]. We define angular dependence of TMR as TMR(θ) = [R(θ) – R(0)]/R(0), where R(0) is the resistance of the FM phase with m₁∥ẑ∥m₂ and R(θ) is the resistance for angle θ between them. We compute

as the inverse of two-terminal conductance expressed in terms of the zero-bias transmission function via the standard Landauer-Büttiker formula.(27) The total transmission function per unit interfacial area is obtained by the integration of the k_y-resolved transmission function over the BZ,

, akin to eq 5. Thus, R(θ = 180°) corresponds to the AFM phase. Note that TMR(θ = 180°) recovers the conventional definition of TMR using only parallel and antiparallel configurations of the magnetizations. In Figure 6, we obtain TMR(θ = 180°) ≃ 240% when using additional hBN bilayers inserted between graphite leads and the vdW heterostructure. When hBN is removed, TMR drops to TMR(θ = 180°) ≃ 40%, while exhibiting a peculiar change of sign for the angles between θ = 0° and θ = 180° in accord with the experimental observation reported in ref (18) of few-layer-graphene/bilayer-CrI₃/few-layer-graphene junctions.

Supporting Information

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The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.nanolett.9b04556.

Movie, accompanying Figure 5a,b, animates the time evolution of magnetizations, m₁(t) and m₂(t) in Figure 1, driven by a sequence of rectangular voltage pulses (MP4)
Additional details for Figure 2, such as the spatial profile of local current density on different monolayers of the bilayer-CrI₃/monolayer-TaSe₂ vdW heterostructure, as well as for Figure 3, such as spin textures in the bilayer-CrI₃/monolayer-TaSe₂ vdW heterostructure vs spin textures in an isolated monolayer-TaSe₂ (PDF)

pdf
- nl9b04556_si_002.pdf (5.98 MB)
mp4 video
- nl9b04556_si_001.mp4 (3.0 MB)

The authors declare no competing financial interest.

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Acknowledgments

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K.D. and B.K.N. were supported by DOE Grant No. DE-SC0016380. M.D.P. and P.P. were supported by ARO MURI Award No. W911NF-14-0247. K.Z. and J.F. were supported the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) SFB 1277 (Project-ID 314695032), DFG SPP 1666, and the European Unions Horizon 2020 research and innovation program under Grant No. 785219. The supercomputing time was provided by XSEDE, which is supported by NSF Grant No. ACI-1053575.

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This article references 56 other publications.

1
Gong, C.; Li, L.; Li, Z.; Ji, H.; Stern, A.; Xia, Y.; Cao, T.; Bao, W.; Wang, C.; Wang, Y.; Qiu, Z. Q.; Cava, R. J.; Louie, S. G.; Xia, J.; Zhang, X. Discovery of intrinsic ferromagnetism in two-dimensional van der Waals crystals. Nature 2017, 546, 265, DOI: 10.1038/nature22060
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Discovery of intrinsic ferromagnetism in two-dimensional van der Waals crystals
Gong, Cheng; Li, Lin; Li, Zhenglu; Ji, Huiwen; Stern, Alex; Xia, Yang; Cao, Ting; Bao, Wei; Wang, Chenzhe; Wang, Yuan; Qiu, Z. Q.; Cava, R. J.; Louie, Steven G.; Xia, Jing; Zhang, Xiang
Nature (London, United Kingdom) (2017), 546 (7657), 265-269CODEN: NATUAS; ISSN:0028-0836. (Nature Publishing Group)
The realization of long-range ferromagnetic order in two-dimensional van der Waals crystals, combined with their rich electronic and optical properties, could lead to new magnetic, magnetoelec. and magneto-optic applications. In two-dimensional systems, the long-range magnetic order is strongly suppressed by thermal fluctuations, according to the Mermin-Wagner theorem; however, these thermal fluctuations can be counteracted by magnetic anisotropy. Previous efforts, based on defect and compn. engineering, or the proximity effect, introduced magnetic responses only locally or extrinsically. Here we report intrinsic long-range ferromagnetic order in pristine Cr2Ge2Te6 at. layers, as revealed by scanning magneto-optic Kerr microscopy. In this magnetically soft, two-dimensional van der Waals ferromagnet, we achieve unprecedented control of the transition temp. (between ferromagnetic and paramagnetic states) using very small fields (smaller than 0.3 T). This result is in contrast to the insensitivity of the transition temp. to magnetic fields in the three-dimensional regime. We found that the small applied field leads to an effective anisotropy that is much greater than the near-zero magnetocryst. anisotropy, opening up a large spin-wave excitation gap. We explain the obsd. phenomenon using renormalized spin-wave theory and conclude that the unusual field dependence of the transition temp. is a hallmark of soft, two-dimensional ferromagnetic van der Waals crystals. Cr2Ge2Te6 is a nearly ideal two-dimensional Heisenberg ferromagnet and so will be useful for studying fundamental spin behaviors, opening the door to exploring new applications such as ultra-compact spintronics.
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Huang, B.; Clark, G.; Navarro-Moratalla, E.; Klein, D. R.; Cheng, R.; Seyler, K. L.; Zhong, D.; Schmidgall, E.; McGuire, M. A.; Cobden, D. H.; Yao, W.; Xiao, D.; Jarillo-Herrero, P.; Xu, X. Layer-dependent ferromagnetism in a van der Waals crystal down to the monolayer limit. Nature 2017, 546, 270, DOI: 10.1038/nature22391
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Layer-dependent ferromagnetism in a van der Waals crystal down to the monolayer limit
Huang, Bevin; Clark, Genevieve; Navarro-Moratalla, Efren; Klein, Dahlia R.; Cheng, Ran; Seyler, Kyle L.; Zhong, Ding; Schmidgall, Emma; McGuire, Michael A.; Cobden, David H.; Yao, Wang; Xiao, Di; Jarillo-Herrero, Pablo; Xu, Xiaodong
Nature (London, United Kingdom) (2017), 546 (7657), 270-273CODEN: NATUAS; ISSN:0028-0836. (Nature Publishing Group)
Since the discovery of graphene, the family of two-dimensional materials has grown, displaying a broad range of electronic properties. Recent addns. include semiconductors with spin-valley coupling, Ising superconductors that can be tuned into a quantum metal, possible Mott insulators with tunable charge-d. waves, and topol. semimetals with edge transport. However, no two-dimensional crystal with intrinsic magnetism has yet been discovered; such a crystal would be useful in many technologies from sensing to data storage. Theor., magnetic order is prohibited in the two-dimensional isotropic Heisenberg model at finite temps. by the Mermin-Wagner theorem. Magnetic anisotropy removes this restriction, however, and enables, for instance, the occurrence of two-dimensional Ising ferromagnetism. Here we use magneto-optical Kerr effect microscopy to demonstrate that monolayer chromium triiodide (CrI3) is an Ising ferromagnet with out-of-plane spin orientation. Its Curie temp. of 45 K is only slightly lower than that of the bulk crystal, 61 K, which is consistent with a weak interlayer coupling. Moreover, our studies suggest a layer-dependent magnetic phase, highlighting thickness-dependent phys. properties typical of van der Waals crystals. Remarkably, bilayer CrI3 displays suppressed magnetization with a metamagnetic effect, whereas in trilayer CrI3 the interlayer ferromagnetism obsd. in the bulk crystal is restored. This work creates opportunities for studying magnetism by harnessing the unusual features of atomically thin materials, such as elec. control for realizing magnetoelectronics, and van der Waals engineering to produce interface phenomena.
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Gibertini, M.; Koperski, M.; Morpurgo, A. F.; Novoselov, K. S. Magnetic 2D materials and heterostructures. Nat. Nanotechnol. 2019, 14, 408– 419, DOI: 10.1038/s41565-019-0438-6
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3
Magnetic 2D materials and heterostructures
Gibertini, M.; Koperski, M.; Morpurgo, A. F.; Novoselov, K. S.
Nature Nanotechnology (2019), 14 (5), 408-419CODEN: NNAABX; ISSN:1748-3387. (Nature Research)
The family of two-dimensional (2D) materials grows day by day, hugely expanding the scope of possible phenomena to be explored in two dimensions, as well as the possible van der Waals (vdW) heterostructures that one can create. Such 2D materials currently cover a vast range of properties. Until recently, this family has been missing one crucial member: 2D magnets. The situation has changed over the past 2 years with the introduction of a variety of atomically thin magnetic crystals. Here we will discuss the difference between magnetic states in 2D materials and in bulk crystals and present an overview of the 2D magnets that have been explored recently. We will focus on the case of the two most studied systems-semiconducting CrI3 and metallic Fe3GeTe2-and illustrate the phys. phenomena that have been obsd. Special attention will be given to the range of new van der Waals heterostructures that became possible with the appearance of 2D magnets, offering new perspectives in this rapidly expanding field.
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Burch, K. S.; Mandrus, D.; Park, J.-G. Magnetism in two-dimensional van der Waals materials. Nature 2018, 563, 47– 52, DOI: 10.1038/s41586-018-0631-z
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Magnetism in two-dimensional van der Waals materials
Burch, Kenneth S.; Mandrus, David; Park, Je-Geun
Nature (London, United Kingdom) (2018), 563 (7729), 47-52CODEN: NATUAS; ISSN:0028-0836. (Nature Research)
The discovery of materials has often introduced new phys. paradigms and enabled the development of novel devices. Two-dimensional magnetism, which is assocd. with strong intrinsic spin fluctuations, has long been the focus of fundamental questions in condensed matter physics regarding our understanding and control of new phases. Here we discuss magnetic van der Waals materials: two-dimensional at. crystals that contain magnetic elements and thus exhibit intrinsic magnetic properties. These cleavable materials provide the ideal platform for exploring magnetism in the two-dimensional limit, where new phys. phenomena are expected, and represent a substantial shift in our ability to control and investigate nanoscale phases. We present the theor. background and motivation for investigating this class of crystals, describe the material landscape and the current exptl. status of measurement techniques as well as devices, and discuss promising future directions for the study of magnetic van der Waals materials.
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Cortie, D. L.; Causer, G. L.; Rule, K. C.; Fritzsche, H.; Kreuzpaintner, W.; Klose, F. Two-Dimensional Magnets: Forgotten History and Recent Progress towards Spintronic Applications. Adv. Funct. Mater. 2019, 0, 1901414, DOI: 10.1002/adfm.201901414
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Gong, C.; Zhang, X. Two-dimensional magnetic crystals and emergent heterostructure devices. Science 2019, 363, eaav4450, DOI: 10.1126/science.aav4450
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Li, H.; Ruan, S.; Zeng, Y.-J. Intrinsic Van Der Waals Magnetic Materials from Bulk to the 2D Limit: New Frontiers of Spintronics. Adv. Mater. 2019, 31, 1900065, DOI: 10.1002/adma.201900065
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Alghamdi, M.; Lohmann, M.; Li, J.; Jothi, P. R.; Shao, Q.; Aldosary, M.; Su, T.; Fokwa, B. P. T.; Shi, J. Highly Efficient SpinOrbit Torque and Switching of Layered Ferromagnet Fe₃GeTe₂. Nano Lett. 2019, 19, 4400– 4405, DOI: 10.1021/acs.nanolett.9b01043
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Highly Efficient Spin-Orbit Torque and Switching of Layered Ferromagnet Fe3GeTe2
Alghamdi, Mohammed; Lohmann, Mark; Li, Junxue; Jothi, Palani R.; Shao, Qiming; Aldosary, Mohammed; Su, Tang; Fokwa, Boniface P. T.; Shi, Jing
Nano Letters (2019), 19 (7), 4400-4405CODEN: NALEFD; ISSN:1530-6984. (American Chemical Society)
Among van der Waals (vdW) layered ferromagnets, Fe3GeTe2 (FGT) is an excellent candidate material to form FGT/heavy metal heterostructures for studying the effect of spin-orbit torques (SOT). Its metallicity, strong perpendicular magnetic anisotropy built in the single at. layers, relatively high Curie temp. (Tc ∼ 225 K), and electrostatic gate tunability offer a tantalizing possibility of achieving the ultimate high SOT limit in monolayer all-vdW nanodevices. In this study, we fabricate heterostructures of FGT/Pt with 5 nm of Pt sputtered onto the atomically flat surface of ∼15-23 nm exfoliated FGT flakes. The spin current generated in Pt exerts a damping-like SOT on FGT magnetization. At ∼2.5 × 1011 A/m2 c.d., SOT causes the FGT magnetization to switch, which is detected by the anomalous Hall effect of FGT. To quantify the SOT effect, we measure the second harmonic Hall responses as the applied magnetic field rotates the FGT magnetization in the plane. Our anal. shows that the SOT efficiency is comparable with that of the best heterostructures contg. three-dimensional (3D) ferromagnetic metals and much larger than that of heterostructures contg. 3D ferrimagnetic insulators. Such large efficiency is attributed to the atomically flat FGT/Pt interface, which demonstrates the great potential of exploiting vdW heterostructures for highly efficient spintronic nanodevices.
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Wang, X. Current-driven magnetization switching in a van der Waals ferromagnet Fe₃GeTe₂. Science Advances 2019, 5, eaay8897, DOI: 10.1126/sciadv.aay8897
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Mermin, N. D.; Wagner, H. Absence of Ferromagnetism or Antiferromagnetism in One- or Two-Dimensional Isotropic Heisenberg Models. Phys. Rev. Lett. 1966, 17, 1133– 1136, DOI: 10.1103/PhysRevLett.17.1133
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Absence of ferromagnetism or antiferromagnetism in one- or two-dimensional isotropic Heisenberg models
Mermin, N. David; Wagner, Hans
Physical Review Letters (1966), 17 (22), 1133-6CODEN: PRLTAO; ISSN:0031-9007.
It is rigorously proved that at any nonzero temp., a 1- and 2-dimensional isotropic spin-S Heisenberg model with finite-range exchange interaction can be neither ferromagnetic nor antiferromagnetic. The method of proof is capable of excluding a variety of types of ordering in 1 and 2 dimensions.
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Sivadas, N.; Okamoto, S.; Xu, X.; Fennie, C. J.; Xiao, D. Stacking-Dependent Magnetism in Bilayer CrI₃. Nano Lett. 2018, 18, 7658– 7664, DOI: 10.1021/acs.nanolett.8b03321
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Stacking-Dependent Magnetism in Bilayer CrI3
Sivadas, Nikhil; Okamoto, Satoshi; Xu, Xiaodong; Fennie, Craig. J.; Xiao, Di
Nano Letters (2018), 18 (12), 7658-7664CODEN: NALEFD; ISSN:1530-6984. (American Chemical Society)
We report the connection between the stacking order and magnetic properties of bilayer CrI3 using first-principles calcns. We show that the stacking order defines the magnetic ground state. By changing the interlayer stacking order, one can tune the interlayer exchange interaction between antiferromagnetic and ferromagnetic. To measure the predicted stacking-dependent magnetism, we propose using linear magnetoelec. effect. Our results not only gives a possible explanation for the obsd. antiferromagnetism in bilayer CrI3 but also have direct implications in heterostructures made of two-dimensional magnets.
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Jiang, P.; Wang, C.; Chen, D.; Zhong, Z.; Yuan, Z.; Lu, Z.-Y.; Ji, W. Stacking tunable interlayer magnetism in bilayer CrI₃. Phys. Rev. B: Condens. Matter Mater. Phys. 2019, 99, 144401, DOI: 10.1103/PhysRevB.99.144401
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Stacking tunable interlayer magnetism in bilayer CrI3
Jiang, Peiheng; Wang, Cong; Chen, Dachuan; Zhong, Zhicheng; Yuan, Zhe; Lu, Zhong-Yi; Ji, Wei
Physical Review B (2019), 99 (14), 144401CODEN: PRBHB7; ISSN:2469-9969. (American Physical Society)
Diverse interlayer tunability of phys. properties of two-dimensional layers mostly lies in the covalent-like quasibonding that is significant in electronic structures but rather weak for energetics. Such characteristics result in various stacking orders that are energetically comparable but may significantly differ in terms of electronic structures, e.g., magnetism. Inspired by several recent expts. showing interlayer antiferromagnetically coupled CrI3 bilayers, we carried out first-principles calcns. for CrI3 bilayers. We found that the antiferromagnetic coupling results from a different stacking order with the C2/m space group symmetry, rather than the graphene-like one with R3 as previously believed. Moreover, we demonstrated that the intra- and interlayer couplings in CrI3 bilayer are governed by two different mechanisms, namely ferromagnetic superexchange and direct-exchange interactions, which are largely decoupled because of their significant difference in strength at the strong- and weak-interaction limits. This allows the much weaker interlayer magnetic coupling to be more feasibly tuned by stacking orders solely. Given the fact that interlayer magnetic properties can be altered by changing crystal structure with different stacking orders, our work opens a paradigm for tuning interlayer magnetic properties with the freedom of stacking order in two-dimensional layered materials.
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Huang, B.; Clark, G.; Klein, D. R.; MacNeill, D.; Navarro-Moratalla, E.; Seyler, K. L.; Wilson, N.; McGuire, M. A.; Cobden, D. H.; Xiao, D.; Yao, W.; Jarillo-Herrero, P.; Xu, X. Electrical control of 2D magnetism in bilayer CrI₃. Nat. Nanotechnol. 2018, 13, 544– 548, DOI: 10.1038/s41565-018-0121-3
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13
Electrical control of 2D magnetism in bilayer CrI3
Huang, Bevin; Clark, Genevieve; Klein, Dahlia R.; MacNeill, David; Navarro-Moratalla, Efren; Seyler, Kyle L.; Wilson, Nathan; McGuire, Michael A.; Cobden, David H.; Xiao, Di; Yao, Wang; Jarillo-Herrero, Pablo; Xu, Xiaodong
Nature Nanotechnology (2018), 13 (7), 544-548CODEN: NNAABX; ISSN:1748-3387. (Nature Research)
Controlling magnetism via elec. fields addresses fundamental questions of magnetic phenomena and phase transitions1-3, and enables the development of elec. coupled spintronic devices, such as voltage-controlled magnetic memories with low operation energy4-6. Previous studies on dil. magnetic semiconductors such as (Ga,Mn)As and (In,Mn)Sb have demonstrated large modulations of the Curie temps. and coercive fields by altering the magnetic anisotropy and exchange interaction2,4,7-9. Owing to their unique magnetic properties10-14, the recently reported two-dimensional magnets provide a new system for studying these features15-19. For instance, a bilayer of chromium triiodide (CrI3) behaves as a layered antiferromagnet with a magnetic field-driven metamagnetic transition15,16. Here, we demonstrate electrostatic gate control of magnetism in CrI3 bilayers, probed by magneto-optical Kerr effect (MOKE) microscopy. At fixed magnetic fields near the metamagnetic transition, we realize voltage-controlled switching between antiferromagnetic and ferromagnetic states. At zero magnetic field, we demonstrate a time-reversal pair of layered antiferromagnetic states that exhibit spin-layer locking, leading to a linear dependence of their MOKE signals on gate voltage with opposite slopes. Our results allow for the exploration of new magnetoelec. phenomena and van der Waals spintronics based on 2D materials.
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Jiang, S.; Li, L.; Wang, Z.; Mak, K. F.; Shan, J. Controlling magnetism in 2D CrI₃ by electrostatic doping. Nat. Nanotechnol. 2018, 13, 549– 553, DOI: 10.1038/s41565-018-0135-x
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Controlling magnetism in 2D CrI3 by electrostatic doping
Jiang, Shengwei; Li, Lizhong; Wang, Zefang; Mak, Kin Fai; Shan, Jie
Nature Nanotechnology (2018), 13 (7), 549-553CODEN: NNAABX; ISSN:1748-3387. (Nature Research)
The at. thickness of two-dimensional materials provides a unique opportunity to control their elec.1 and optical2 properties as well as to drive the electronic phase transitions3 by electrostatic doping. The discovery of two-dimensional magnetic materials4-10 has opened up the prospect of the elec. control of magnetism and the realization of new functional devices11. A recent expt. based on the linear magneto-elec. effect has demonstrated control of the magnetic order in bilayer CrI3 by elec. fields12. However, this approach is limited to non-centrosym. materials11,13-16 magnetically biased near the antiferromagnet-ferromagnet transition. Here, we demonstrate control of the magnetic properties of both monolayer and bilayer CrI3 by electrostatic doping using CrI3-graphene vertical heterostructures. In monolayer CrI3, doping significantly modifies the satn. magnetization, coercive force and Curie temp., showing strengthened/weakened magnetic order with hole/electron doping. Remarkably, in bilayer CrI3, the electron doping above ∼2.5 × 1013 cm-2 induces a transition from an antiferromagnetic to a ferromagnetic ground state in the absence of a magnetic field. The result reveals a strongly doping-dependent interlayer exchange coupling, which enables robust switching of magnetization in bilayer CrI3 by small gate voltages.
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Jiang, S.; Shan, J.; Mak, K. F. Electric-field switching of two-dimensional van der Waals magnets. Nat. Mater. 2018, 17, 406– 410, DOI: 10.1038/s41563-018-0040-6
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Electric-field switching of two-dimensional van der Waals magnets
Jiang, Shengwei; Shan, Jie; Mak, Kin Fai
Nature Materials (2018), 17 (5), 406-410CODEN: NMAACR; ISSN:1476-1122. (Nature Research)
Controlling magnetism by purely elec. means is a key challenge to better information technol.1. A variety of material systems, including ferromagnetic (FM) metals2-4, FM semiconductors5, multiferroics6-8 and magnetoelec. (ME) materials9,10, have been explored for the elec.-field control of magnetism. The recent discovery of two-dimensional (2D) van der Waals magnets11,12 has opened a new door for the elec. control of magnetism at the nanometer scale through a van der Waals heterostructure device platform13. Here we demonstrate the control of magnetism in bilayer CrI3, an antiferromagnetic (AFM) semiconductor in its ground state12, by the application of small gate voltages in field-effect devices and the detection of magnetization using magnetic CD (MCD) microscopy. The applied elec. field creates an interlayer p.d., which results in a large linear ME effect, whose sign depends on the interlayer AFM order. We also achieve a complete and reversible elec. switching between the interlayer AFM and FM states in the vicinity of the interlayer spin-flip transition. The effect originates from the elec.-field dependence of the interlayer exchange bias.
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16
Locatelli, N.; Cros, V.; Grollier, J. Spin-torque building blocks. Nat. Mater. 2014, 13, 11– 20, DOI: 10.1038/nmat3823
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Spin-torque building blocks
Locatelli, N.; Cros, V.; Grollier, J.
Nature Materials (2014), 13 (1), 11-20CODEN: NMAACR; ISSN:1476-1122. (Nature Publishing Group)
The discovery of the spin-torque effect has made magnetic nanodevices realistic candidates for active elements of memory devices and applications. Magnetoresistive effects allow the read-out of increasingly small magnetic bits, and the spin torque provides an efficient tool to manipulate - precisely, rapidly and at low energy cost - the magnetic state, which is in turn the central information medium of spintronic devices. By keeping the same magnetic stack, but by tuning a device's shape and bias conditions, the spin torque can be engineered to build a variety of advanced magnetic nanodevices. Here we show that by assembling these nanodevices as building blocks with different functionalities, novel types of computing architecture can be envisaged. We focus in particular on recent concepts such as magnonics and spintronic neural networks.
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17
Zhou, J.; Qiao, J.; Duan, C.-G.; Bournel, A.; Wang, K. L.; Zhao, W. Large Tunneling Magnetoresistance in VSe₂/MoS₂ Magnetic Tunnel Junction. ACS Appl. Mater. Interfaces 2019, 11, 17647– 17653, DOI: 10.1021/acsami.9b02493
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17
Large Tunneling Magnetoresistance in VSe2/MoS2 Magnetic Tunnel Junction
Zhou, Jiaqi; Qiao, Junfeng; Duan, Chun-Gang; Bournel, Arnaud; Wang, Kang L.; Zhao, Weisheng
ACS Applied Materials & Interfaces (2019), 11 (19), 17647-17653CODEN: AAMICK; ISSN:1944-8244. (American Chemical Society)
Two-dimensional (2D) van der Waals (vdW) materials provide the possibility of realizing heterostructures with coveted properties. Here, we report a theor. investigation of the vdW magnetic tunnel junction (MTJ) based on VSe2/MoS2 heterojunction, where the VSe2 monolayer acts as a ferromagnet with room-temp. ferromagnetism. We propose the concept of spin-orbit torque (SOT) vdW MTJ with reliable reading and efficient writing operations. The nonequil. study reveals a large tunneling magnetoresistance of 846% at 300 K, identifying significantly its parallel and antiparallel states. Thanks to the strong spin Hall cond. of MoS2, SOT is promising for the magnetization switching of VSe2 free layer. Quantum-well states come into being and resonances appear in MTJ, suggesting that the voltage control can adjust transport properties effectively. The SOT vdW MTJ based on VSe2/MoS2 provides desirable performance and exptl. feasibility, offering new opportunities for 2D spintronics.
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18
Song, T.; Cai, X.; Tu, M. W.-Y.; Zhang, X.; Huang, B.; Wilson, N. P.; Seyler, K. L.; Zhu, L.; Taniguchi, T.; Watanabe, K.; McGuire, M. A.; Cobden, D. H.; Xiao, D.; Yao, W.; Xu, X. Giant tunneling magnetoresistance in spin-filter van der Waals heterostructures. Science 2018, 360, 1214– 1218, DOI: 10.1126/science.aar4851
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18
Giant tunneling magnetoresistance in spin-filter van der Waals heterostructures
Song, Tiancheng; Cai, Xinghan; Tu, Matisse Wei-Yuan; Zhang, Xiaoou; Huang, Bevin; Wilson, Nathan P.; Seyler, Kyle L.; Zhu, Lin; Taniguchi, Takashi; Watanabe, Kenji; McGuire, Michael A.; Cobden, David H.; Xiao, Di; Yao, Wang; Xu, Xiaodong
Science (Washington, DC, United States) (2018), 360 (6394), 1214-1218CODEN: SCIEAS; ISSN:0036-8075. (American Association for the Advancement of Science)
Magnetic multilayer devices that exploit magnetoresistance are the backbone of magnetic sensing and data storage technologies. Here, the authors report multiple-spin-filter magnetic tunnel junctions (sf-MTJs) based on van der Waals (vdW) heterostructures in which atomically thin chromium triiodide (CrI3) acts as a spin-filter tunnel barrier sandwiched between graphene contacts. The authors demonstrate tunneling magnetoresistance that is drastically enhanced with increasing CrI3 layer thickness, reaching a record 19,000% for magnetic multilayer structures using four-layer sf-MTJs at low temps. Using magnetic CD measurements, the authors attribute these effects to the intrinsic layer-by-layer antiferromagnetic ordering of the atomically thin CrI3. The work reveals the possibility to push magnetic information storage to the atomically thin limit and highlights CrI3 as a superlative magnetic tunnel barrier for vdW heterostructure spintronic devices.
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Klein, D. R.; MacNeill, D.; Lado, J. L.; Soriano, D.; Navarro-Moratalla, E.; Watanabe, K.; Taniguchi, T.; Manni, S.; Canfield, P.; Fernández-Rossier, J.; Jarillo-Herrero, P. Probing magnetism in 2D van der Waals crystalline insulators via electron tunneling. Science 2018, 360, 1218– 1222, DOI: 10.1126/science.aar3617
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19
Probing magnetism in 2D van der Waals crystalline insulators via electron tunneling
Klein, D. R.; MacNeill, D.; Lado, J. L.; Soriano, D.; Navarro-Moratalla, E.; Watanabe, K.; Taniguchi, T.; Manni, S.; Canfield, P.; Fernandez-Rossier, J.; Jarillo-Herrero, P.
Science (Washington, DC, United States) (2018), 360 (6394), 1218-1222CODEN: SCIEAS; ISSN:0036-8075. (American Association for the Advancement of Science)
Magnetic insulators are a key resource for next-generation spintronic and topol. devices. The family of layered metal halides promises varied magnetic states, including ultrathin insulating multiferroics, spin liqs., and ferromagnets, but device-oriented characterization methods are needed to unlock their potential. Here, the authors report tunneling through the layered magnetic insulator CrI3 as a function of temp. and applied magnetic field. The authors elec. detect the magnetic ground state and interlayer coupling and observe a field-induced metamagnetic transition. The metamagnetic transition results in magnetoresistances of 95, 300, and 550% for bilayer, trilayer, and tetralayer CrI3 barriers, resp. The authors further measure inelastic tunneling spectra for their junctions, unveiling a rich spectrum consistent with collective magnetic excitations (magnons) in CrI3.
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Wang, Z.; Gutiérrez-Lezama, I.; Ubrig, N.; Kroner, M.; Gibertini, M.; Taniguchi, T.; Watanabe, K.; Imamoglu, A.; Giannini, E.; Morpurgo, A. F. Very large tunneling magnetoresistance in layered magnetic semiconductor CrI₃. Nat. Commun. 2018, 9, 2516, DOI: 10.1038/s41467-018-04953-8
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Very large tunneling magnetoresistance in layered magnetic semiconductor CrI3
Wang Zhe; Gutierrez-Lezama Ignacio; Ubrig Nicolas; Gibertini Marco; Giannini Enrico; Morpurgo Alberto F; Wang Zhe; Gutierrez-Lezama Ignacio; Ubrig Nicolas; Gibertini Marco; Morpurgo Alberto F; Kroner Martin; Imamoglu Atac; Taniguchi Takashi; Watanabe Kenji
Nature communications (2018), 9 (1), 2516 ISSN:.
Magnetic layered van der Waals crystals are an emerging class of materials giving access to new physical phenomena, as illustrated by the recent observation of 2D ferromagnetism in Cr2Ge2Te6 and CrI3. Of particular interest in semiconductors is the interplay between magnetism and transport, which has remained unexplored. Here we report magneto-transport measurements on exfoliated CrI3 crystals. We find that tunneling conduction in the direction perpendicular to the crystalline planes exhibits a magnetoresistance as large as 10,000%. The evolution of the magnetoresistance with magnetic field and temperature reveals that the phenomenon originates from multiple transitions to different magnetic states, whose possible microscopic nature is discussed on the basis of all existing experimental observations. This observed dependence of the conductance of a tunnel barrier on its magnetic state is a phenomenon that demonstrates the presence of a strong coupling between transport and magnetism in magnetic van der Waals semiconductors.
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Song, T.; Tu, M. W.-Y.; Carnahan, C.; Cai, X.; Taniguchi, T.; Watanabe, K.; McGuire, M. A.; Cobden, D. H.; Xiao, D.; Yao, W.; Xu, X. Voltage Control of a van der Waals Spin-Filter Magnetic Tunnel Junction. Nano Lett. 2019, 19, 915– 920, DOI: 10.1021/acs.nanolett.8b04160
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Voltage Control of a van der Waals Spin-Filter Magnetic Tunnel Junction
Song Tiancheng; Cai Xinghan; Cobden David H; Xu Xiaodong; Tu Matisse Wei-Yuan; Yao Wang; Carnahan Caitlin; Xiao Di; Taniguchi Takashi; Watanabe Kenji; McGuire Michael A; Xu Xiaodong
Nano letters (2019), 19 (2), 915-920 ISSN:.
Atomically thin chromium triiodide (CrI3) has recently been identified as a layered antiferromagnetic insulator, in which adjacent ferromagnetic monolayers are antiferromagnetically coupled. This unusual magnetic structure naturally comprises a series of antialigned spin filters, which can be utilized to make spin-filter magnetic tunnel junctions with very large tunneling magnetoresistance (TMR). Here we report voltage control of TMR formed by four-layer CrI3 sandwiched by monolayer graphene contacts in a dual-gated structure. By varying the gate voltages at fixed magnetic field, the device can be switched reversibly between bistable magnetic states with the same net magnetization but drastically different resistance (by a factor of 10 or more). In addition, without switching the state, the TMR can be continuously modulated between 17,000% and 57,000%, due to the combination of spin-dependent tunnel barrier with changing carrier distributions in the graphene contacts. Our work demonstrates new kinds of magnetically moderated transistor action and opens up possibilities for voltage-controlled van der Waals spintronic devices.
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Manchon, A.; Železný, J.; Miron, I. M.; Jungwirth, T.; Sinova, J.; Thiaville, A.; Garello, K.; Gambardella, P. Current-induced spin-orbit torques in ferromagnetic and antiferromagnetic systems. Rev. Mod. Phys. 2019, 91, 035004 DOI: 10.1103/RevModPhys.91.035004
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22
Current-induced spin-orbit torques in ferromagnetic and antiferromagnetic systems
Manchon, A.; Zelezny, J.; Miron, I. M.; Jungwirth, T.; Sinova, J.; Thiaville, A.; Garello, K.; Gambardella, P.
Reviews of Modern Physics (2019), 91 (3), 035004CODEN: RMPHAT; ISSN:1539-0756. (American Physical Society)
Spin-orbit coupling in inversion-asym. magnetic crystals and structures has emerged as a powerful tool to generate complex magnetic textures, interconvert charge and spin under applied current, and control magnetization dynamics. Current-induced spin-orbit torques mediate the transfer of angular momentum from the lattice to the spin system, leading to sustained magnetic oscillations or switching of ferromagnetic as well as antiferromagnetic structures. The manipulation of magnetic order, domain walls, and skyrmions by spin-orbit torques provides evidence of the microscopic interactions between charge and spin in a variety of materials and opens novel strategies to design spintronic devices with potentially high impact in data storage, nonvolatile logic, and magnonic applications. This paper reviews recent progress in the field of spin orbitronics, focusing on theor. models, material properties, and exptl. results obtained on bulk noncentrosym. conductors and multilayer heterostructures, including metals, semiconductors, and topol. insulator systems. Relevant aspects for improving the understanding and optimizing the efficiency of nonequil. spin-orbit phenomena in future nanoscale devices are also discussed.
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Ramaswamy, R.; Lee, J. M.; Cai, K.; Yang, H. Recent advances in spin-orbit torques: Moving towards device applications. Appl. Phys. Rev. 2018, 5, 031107 DOI: 10.1063/1.5041793
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Recent advances in spin-orbit torques: Moving towards device applications
Ramaswamy, Rajagopalan; Lee, Jong Min; Cai, Kaiming; Yang, Hyunsoo
Applied Physics Reviews (2018), 5 (3), 031107/1-031107/19CODEN: APRPG5; ISSN:1931-9401. (American Institute of Physics)
The ability of spintronic devices to utilize an elec. current for manipulating the magnetization has resulted in large-scale developments, such as magnetic random access memories and boosted the spintronic research area. In this regard, over the last decade, magnetization manipulation using spin-orbit torque has been devoted a lot of research attention as it shows a great promise for future ultrafast and power efficient magnetic memories. In this review, we summarize the latest advancements in spin-orbit torque research and highlight some of the tech. challenges for practical spin-orbit torque devices. We will first introduce the basic concepts and highlight the latest material choices for spin-orbit torque devices. Then, we will summarize the important advancements in the study of magnetization switching dynamics using spin-orbit torque, which are important from scientific as well as technol. aspects. The final major section focuses on the concept of external assist field-free spin-orbit torque switching which is a requirement for practical spin-orbit torque devices. (c) 2018 American Institute of Physics.
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Nikolić, B. K.; Dolui, K.; Petrovi, M.; Plecháč, P.; Markussen, T.; Stokbro, K. In Handbook of Materials Modeling; Andreoni, W., Ed.; Springer: Cham, 2018; pp 1– 35.
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25
Belashchenko, K. D.; Kovalev, A. A.; van Schilfgaarde, M. First-principles calculation of spin-orbit torque in a Co/Pt bilayer. Phys. Rev. Materials 2019, 3, 011401 DOI: 10.1103/PhysRevMaterials.3.011401
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First-principles calculation of spin-orbit torque in a Co/Pt bilayer
Belashchenko, K. D.; Kovalev, Alexey A.; van Schilfgaarde, M.
Physical Review Materials (2019), 3 (1), 011401CODEN: PRMHBS; ISSN:2475-9953. (American Physical Society)
The angular dependence of spin-orbit torque in a disordered Co/Pt bilayer is calcd. using a first-principles nonequil. Green's function formalism with an explicit supercell averaging over Anderson disorder. In addn. to the usual dampinglike and fieldlike terms, the odd torque contains a sizable planar Hall-like term (m·E)m×(z×m) whose contribution to current-induced damping is consistent with exptl. observations. The dampinglike and planar Hall-like torquances depend weakly on disorder strength, while the fieldlike torquance declines with increasing disorder. The torques that contribute to damping are almost entirely due to spin-orbit coupling on the Pt atoms, but the fieldlike torque does not require it.
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Belashchenko, K. D.; Kovalev, A. A.; van Schilfgaarde, M. Interfacial contributions to spin-orbit torque and magnetoresistance in ferromagnet/heavy-metal bilayers. Phys. Rev. B: Condens. Matter Mater. Phys. 2020, 101, 020407R, DOI: 10.1103/PhysRevB.101.020407
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27
Stefanucci, G.; van Leeuwen, R. Nonequilibrium Many-Body Theory of Quantum Systems: A Modern Introduction; Cambridge University Press: Cambridge, 2013.
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28
Capelle, K.; Vignale, G.; Györffy, B. L. Spin Currents and Spin Dynamics in Time-Dependent Density-Functional Theory. Phys. Rev. Lett. 2001, 87, 206403, DOI: 10.1103/PhysRevLett.87.206403
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Spin Currents and Spin Dynamics in Time-Dependent Density-Functional Theory
Capelle, K.; Vignale, G.; Gyorffy, B. L.
Physical Review Letters (2001), 87 (20), 206403/1-206403/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
We derive and analyze the equation of motion for the spin degrees of freedom within time-dependent spin-d.-functional theory (TD-SDFT). The results are (i) a prescription for obtaining many-body corrections to the single-particle spin currents from the Kohn-Sham equation of TD-SDFT, (ii) the existence of an exchange-correlation (xc) torque within TD-SDFT, (iii) a prescription for calcg., from TD-SDFT, the torque exerted by spin currents on the spin magnetization, (iv) a novel exact constraint on approx. xc functionals, and (v) the discovery of serious deficiencies of popular approxns. to TD-SDFT when applied to spin dynamics.
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Eich, F. G.; Gross, E. K. U. Transverse Spin-Gradient Functional for Noncollinear Spin-Density-Functional Theory. Phys. Rev. Lett. 2013, 111, 156401, DOI: 10.1103/PhysRevLett.111.156401
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29
Transverse spin-gradient functional for noncollinear spin-density-functional theory
Eich, F. G.; Gross, E. K. U.
Physical Review Letters (2013), 111 (15), 156401/1-156401/5CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
We present a novel functional for spin-d.-functional theory aiming at the description of noncollinear magnetic structures. The construction of the functional employs the spin-spiral-wave state of the uniform electron gas as ref. system. We show that the functional depends on transverse gradients of the spin magnetization; i.e., in contrast with the widely used local spin d. approxn., the functional is sensitive to local changes of the direction of the spin magnetization. As a consequence the exchange-correlation magnetic field is not parallel to the spin magnetization and a local spin torque is present in the ground state of the Kohn-Sham system. As a proof of principle, we apply the functional to a Chromium monolayer in the noncollinear 120°-Neel state.
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Ellis, M. O. A.; Stamenova, M.; Sanvito, S. Multiscale modeling of current-induced switching in magnetic tunnel junctions using ab initio spin-transfer torques. Phys. Rev. B: Condens. Matter Mater. Phys. 2017, 96, 224410, DOI: 10.1103/PhysRevB.96.224410
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31
Freimuth, F.; Blügel, S.; Mokrousov, Y. Spin-orbit torques in Co/Pt(111) and Mn/W(001) magnetic bilayers from first principles. Phys. Rev. B: Condens. Matter Mater. Phys. 2014, 90, 174423, DOI: 10.1103/PhysRevB.90.174423
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31
Spin-orbit torques in Co/Pt(111) and Mn/W(001) magnetic bilayers from first principles
Freimuth, Frank; Bluegel, Stefan; Mokrousov, Yuriy
Physical Review B: Condensed Matter and Materials Physics (2014), 90 (17), 174423/1-174423/10, 10 pp.CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
An applied elec. current through a space-inversion asym. magnet induces spin-orbit torques (SOTs) on the magnetic moments, which holds much promise for future memory devices. We discuss general Green's function expressions suitable to compute the linear-response SOT in disordered ferromagnets. The SOT can be decompd. into an even and an odd component with respect to magnetization reversal, where in the limit of vanishing disorder the even SOT is given by the const. Berry curvature of the occupied states, while the odd part exhibits a divergence with respect to disorder strength. Within this formalism, we perform first-principles d.-functional theory calcns. of the SOT in Co/Pt(111) and Mn/W(001) magnetic bilayers. We find the even and odd torque components to be of comparable magnitude. Moreover, the odd torque depends strongly on an addnl. capping layer, while the even torque is less sensitive. We show that the even torque is nearly entirely mediated by spin currents in contrast to the odd torque, which can contain an important contribution not due to spin transfer. Our results are in agreement with expts., showing that our linear-response theory is well-suited for the description of SOTs in complex ferromagnets.
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Mahfouzi, F.; Kioussis, N. First-principles study of the angular dependence of the spin-orbit torque in Pt/Co and Pd/Co bilayers. Phys. Rev. B: Condens. Matter Mater. Phys. 2018, 97, 224426, DOI: 10.1103/PhysRevB.97.224426
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33
Edelstein, V. M. Spin polarization of conduction electrons induced by electric current in two-dimensional asymmetric electron systems. Solid State Commun. 1990, 73, 233, DOI: 10.1016/0038-1098(90)90963-C
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34
Aronov, A. G.; Lyanda-Geller, Y. B. Nuclear electric resonance and orientation of carrier spins by an electric field. JETP Letters 1989, 50, 431
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35
Chang, P.-H.; Markussen, T.; Smidstrup, S.; Stokbro, K.; Nikolić, B. K. Nonequilibrium spin texture within a thin layer below the surface of current-carrying topological insulator Bi₂Se₃: A first-principles quantum transport study. Phys. Rev. B: Condens. Matter Mater. Phys. 2015, 92, 201406R, DOI: 10.1103/PhysRevB.92.201406
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35
Nonequilibrium spin texture within a thin layer below the surface of current-carrying topological insulator Bi2Se3: a first-principles quantum transport study
Chang, Po-Hao; Markussen, Troels; Smidstrup, Soeren; Stokbro, Kurt; Nikolic, Branislav K.
Physical Review B: Condensed Matter and Materials Physics (2015), 92 (20), 201406/1-201406/5CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
We predict that unpolarized charge current injected into a ballistic thin film of prototypical topol. insulator (TI) Bi2Se3 will generate a noncollinear spin texture S(r) on its surface. Furthermore, the nonequil. spin texture will extend into an ≃2-nm-thick layer below the TI surfaces due to penetration of evanescent wave functions from the metallic surfaces into the bulk of TI. Averaging S(r)over a few angstroms along the longitudinal direction defined by the current flow reveals a large component pointing in the transverse direction. In addn., we find an order of magnitude smaller out-of-plane component when the direction of injected current with respect to Bi and Se atoms probes the largest hexagonal warping of the Dirac-cone dispersion on the TI surface. Our anal. is based on an extension of the nonequil. Green's functions combined with d. functional theory (NEGF+DFT) to situations involving noncollinear spins and spin-orbit coupling. We also demonstrate how DFT calcns. with a properly optimized local orbital basis set can precisely match putatively more accurate calcns. with a plane-wave basis set for the supercell of Bi2Se3.
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Marmolejo-Tejada, J. M.; Chang, P.-H.; Lazić, P.; Smidstrup, S.; Stradi, D.; Stokbro, K.; Nikolić, B. K. Proximity band structure and spin textures on both sides of topological-insulator/ferromagnetic-metal Interface and their charge transport probes. Nano Lett. 2017, 17, 5626, DOI: 10.1021/acs.nanolett.7b02511
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Proximity band structure and spin textures on both sides of topological-insulator/ferromagnetic-metal interface and their charge transport probes
Marmolejo-Tejada, Juan Manuel; Dolui, Kapildeb; Lazic, Predrag; Chang, Po-Hao; Smidstrup, Soeren; Stradi, Daniele; Stokbro, Kurt; Nikolic, Branislav K.
Nano Letters (2017), 17 (9), 5626-5633CODEN: NALEFD; ISSN:1530-6984. (American Chemical Society)
The control of recently obsd. spintronic effects in topol.-insulator/ferromagnetic-metal (TI/FM) heterostructures is thwarted by the lack of understanding of band structure and spin textures around their interfaces. Here we combine d. functional theory with Green's function techniques to obtain the spectral function at any plane passing through atoms of Bi2Se3 and Co or Cu layers comprising the interface. Instead of naively assumed Dirac cone gapped by the proximity exchange field spectral function, we find that the Rashba ferromagnetic model describes the spectral function on the surface of Bi2Se3 in contact with Co near the Fermi level E0F, where circular and snowflake-like const. energy contours coexist around which spin locks to momentum. The remnant of the Dirac cone is hybridized with evanescent wave functions from metallic layers and pushed, due to charge transfer from Co or Cu layers, a few tenths of an electron-volt below E0F for both Bi2Se3/Co and Bi2Se3/Cu interfaces while hosting distorted helical spin texture wounding around a single circle. These features explain recent observation of sensitivity of spin-to-charge conversion signal at TI/Cu interface to tuning of E0F. Crucially for spin-orbit torque in TI/FM heterostructures, few monolayers of Co adjacent to Bi2Se3 host spectral functions very different from the bulk metal, as well as in-plane spin textures (despite Co magnetization being out-of-plane) due to proximity spin-orbit coupling in Co induced by Bi2Se3. We predict that out-of-plane tunneling anisotropic magnetoresistance in Cu/Bi2Se3/Co vertical heterostructure can serve as a sensitive probe of the type of spin texture residing at E0F.
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Zhu, Z. Y.; Cheng, Y. C.; Schwingenschlögl, U. Giant spin-orbit-induced spin splitting in two-dimensional transition-metal dichalcogenide semiconductors. Phys. Rev. B: Condens. Matter Mater. Phys. 2011, 84, 153402, DOI: 10.1103/PhysRevB.84.153402
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Giant spin-orbit-induced spin splitting in two-dimensional transition-metal dichalcogenide semiconductors
Zhu, Z. Y.; Cheng, Y. C.; Schwingenschlogl, U.
Physical Review B: Condensed Matter and Materials Physics (2011), 84 (15), 153402/1-153402/5CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
Fully relativistic first-principles calcns. based on d. functional theory are performed to study the spin-orbit-induced spin splitting in monolayer systems of the transition-metal dichalcogenides MoS2, MoSe2, WS2, and WSe2. All these systems are identified as direct-band-gap semiconductors. Giant spin splittings of 148-456 meV result from missing inversion symmetry. Full out-of-plane spin polarization is due to the two-dimensional nature of the electron motion and the potential gradient asymmetry. By suppression of the Dyakonov-Perel spin relaxation, spin lifetimes are expected to be very long. Because of the giant spin splittings, the studied materials have great potential in spintronics applications.
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Ge, Y.; Liu, A. Y. Effect of dimensionality and spin-orbit coupling on charge-density-wave transition in 2H-TaSe₂. Phys. Rev. B: Condens. Matter Mater. Phys. 2012, 86, 104101, DOI: 10.1103/PhysRevB.86.104101
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Effect of dimensionality and spin-orbit coupling on charge-density-wave transition in 2H-TaSe2
Ge, Yizhi; Liu, Amy Y.
Physical Review B: Condensed Matter and Materials Physics (2012), 86 (10), 104101/1-104101/7CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
A first-principles investigation of the charge-d.-wave (CDW) instability in bulk and single-layer 2H-TaSe2 is presented, focusing on the origin of the CDW instability, the role of the interlayer interactions, and the effect of spin-orbit coupling. While interlayer interactions and spin-orbit coupling have a nontrivial effect on the electronic structure and Fermi surface, the CDW instability is predicted to remain robust, with little or no change in the ordering wave vector. This is in contrast to the closely related 2H-NbSe2 material, where the CDW wave vector depends on dimensionality. The results are analyzed in terms of the interplay between the momentum dependence of the electron-phonon coupling and that of the electronic response function.
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Petrović, M. D.; Popescu, B. S.; Bajpai, U.; Plecháč, P.; Nikolić, B. K. Spin and Charge Pumping by a Steady or Pulse-Current-Driven Magnetic Domain Wall: A Self- Consistent Multiscale Time-Dependent Quantum-Classical Hybrid Approach. Phys. Rev. Appl. 2018, 10, 054038 DOI: 10.1103/PhysRevApplied.10.054038
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Spin and Charge Pumping by a Steady or Pulse-Current-Driven Magnetic Domain Wall: A Self-Consistent Multiscale Time-Dependent Quantum-Classical Hybrid Approach
Petrovic, Marko D.; Popescu, Bogdan S.; Bajpai, Utkarsh; Plechac, Petr; Nikolic, Branislav K.
Physical Review Applied (2018), 10 (5), 054038CODEN: PRAHB2; ISSN:2331-7019. (American Physical Society)
We introduce a multiscale framework that combines a time-dependent nonequil. Green-function (TDNEGF) algorithm, scaling linearly in the no. of time steps and describing quantum-mech. the conduction electrons in the presence of time-dependent fields of arbitrary strength or frequency, with classical time evolution of localized magnetic moments described by the Landau-Lifshitz-Gilbert (LLG) equation. The TDNEGF+LLG framework can be applied to a variety of problems where current-driven spin torque induces the dynamics of magnetic moments as the key resource for next-generation spintronics. Previous approaches to such nonequil. many-body systems (like the steady-state-NEGF+LLG framework) neglect noncommutativity of a quantum Hamiltonian of conduction electrons at different times and, therefore, the impact of time-dependent magnetic moments on electrons leading to the pumping of spin and charge currents. The pumped currents can, in turn, self-consistently affect the dynamics of magnetic moments themselves. Using the magnetic domain wall (DW) as an example, we predict that its motion will pump time-dependent spin and charge currents (on top of the unpolarized dc charge current injected through normal-metal leads to drive the DW motion), where the latter can be viewed as a realization of quantum charge pumping due to the time dependence of the Hamiltonian and the left-right symmetry breaking of the two-terminal device structure. The conversion of ac components of spin current, whose amplitude increases (decreases) as the DW approaches (recedes from) the normal-metal lead, into ac voltage via the inverse spin Hall effect offers a tool to precisely track the DW position along magnetic nanowire. We also quantify the DW transient inertial displacement due to its acceleration and deceleration by pulse current and the entailed spin and charge pumping. Finally, TDNEGF+LLG as a nonperturbative (i.e., numerically exact) framework allows us to establish the limits of validity of the so-called spin-motive force (SMF) theory for pumped charge current by time-dependent magnetic textures-the perturbative anal. formula of SMF theory becomes inapplicable for large frequencies (but unrealistic in a magnetic system) and, more importantly, for increasing noncollinearity when the angles between neighboring magnetic moments exceed approx. 10o.
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QuantumATK 2019.3; https://www.synopsys.com/silicon/quantumatk.html.
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41
Grimme, S. Semiempirical GGA-type density functional constructed with a long-range dispersion correction. J. Comput. Chem. 2006, 27, 1787– 1799, DOI: 10.1002/jcc.20495
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Semiempirical GGA-type density functional constructed with a long-range dispersion correction
Grimme, Stefan
Journal of Computational Chemistry (2006), 27 (15), 1787-1799CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
A new d. functional (DF) of the generalized gradient approxn. (GGA) type for general chem. applications termed B97-D is proposed. It is based on Becke's power-series ansatz from 1997 and is explicitly parameterized by including damped atom-pairwise dispersion corrections of the form C6·R-6. A general computational scheme for the parameters used in this correction has been established and parameters for elements up to xenon and a scaling factor for the dispersion part for several common d. functionals (BLYP, PBE, TPSS, B3LYP) are reported. The new functional is tested in comparison with other GGAs and the B3LYP hybrid functional on std. thermochem. benchmark sets, for 40 noncovalently bound complexes, including large stacked arom. mols. and group II element clusters, and for the computation of mol. geometries. Further cross-validation tests were performed for organometallic reactions and other difficult problems for std. functionals. In summary, it is found that B97-D belongs to one of the most accurate general purpose GGAs, reaching, for example for the G97/2 set of heat of formations, a mean abs. deviation of only 3.8 kcal mol-1. The performance for noncovalently bound systems including many pure van der Waals complexes is exceptionally good, reaching on the av. CCSD(T) accuracy. The basic strategy in the development to restrict the d. functional description to shorter electron correlation lengths scales and to describe situations with medium to large interat. distances by damped C6·R-6 terms seems to be very successful, as demonstrated for some notoriously difficult reactions. As an example, for the isomerization of larger branched to linear alkanes, B97-D is the only DF available that yields the right sign for the energy difference. From a practical point of view, the new functional seems to be quite robust and it is thus suggested as an efficient and accurate quantum chem. method for large systems where dispersion forces are of general importance.
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Giannozzi, P. QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials. J. Phys.: Condens. Matter 2009, 21, 395502, DOI: 10.1088/0953-8984/21/39/395502
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QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials
Giannozzi Paolo; Baroni Stefano; Bonini Nicola; Calandra Matteo; Car Roberto; Cavazzoni Carlo; Ceresoli Davide; Chiarotti Guido L; Cococcioni Matteo; Dabo Ismaila; Dal Corso Andrea; de Gironcoli Stefano; Fabris Stefano; Fratesi Guido; Gebauer Ralph; Gerstmann Uwe; Gougoussis Christos; Kokalj Anton; Lazzeri Michele; Martin-Samos Layla; Marzari Nicola; Mauri Francesco; Mazzarello Riccardo; Paolini Stefano; Pasquarello Alfredo; Paulatto Lorenzo; Sbraccia Carlo; Scandolo Sandro; Sclauzero Gabriele; Seitsonen Ari P; Smogunov Alexander; Umari Paolo; Wentzcovitch Renata M
Journal of physics. Condensed matter : an Institute of Physics journal (2009), 21 (39), 395502 ISSN:.
QUANTUM ESPRESSO is an integrated suite of computer codes for electronic-structure calculations and materials modeling, based on density-functional theory, plane waves, and pseudopotentials (norm-conserving, ultrasoft, and projector-augmented wave). The acronym ESPRESSO stands for opEn Source Package for Research in Electronic Structure, Simulation, and Optimization. It is freely available to researchers around the world under the terms of the GNU General Public License. QUANTUM ESPRESSO builds upon newly-restructured electronic-structure codes that have been developed and tested by some of the original authors of novel electronic-structure algorithms and applied in the last twenty years by some of the leading materials modeling groups worldwide. Innovation and efficiency are still its main focus, with special attention paid to massively parallel architectures, and a great effort being devoted to user friendliness. QUANTUM ESPRESSO is evolving towards a distribution of independent and interoperable codes in the spirit of an open-source project, where researchers active in the field of electronic-structure calculations are encouraged to participate in the project by contributing their own codes or by implementing their own ideas into existing codes.
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Liechtenstein, A. I.; Anisimov, V. I.; Zaanen, J. Density-functional theory and strong interactions: Orbital ordering in Mott-Hubbard insulators. Phys. Rev. B: Condens. Matter Mater. Phys. 1995, 52, R5467– R5470, DOI: 10.1103/PhysRevB.52.R5467
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Density-functional theory and strong interactions: orbital ordering in Mott-Hubbard insulators
Liechtenstein, A. I.; Anisimov, V. I.; Zaanen, J.
Physical Review B: Condensed Matter (1995), 52 (8), R5467-R5470CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)
Evidence is presented that within the d.-functional theory orbital polarization has to be treated on an equal footing with spin polarization and charge d. for strongly interacting electron systems. Using a basis-set independent generalization of the LDA + U functional, we show that electronic orbital ordering is a necessary condition to obtain the correct crystal structure and parameters of the exchange interaction for the Mott-Hubbard insulator KCuF3.
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Lado, J. L.; Fernández-Rossier, J. On the origin of magnetic anisotropy in two dimensional CrI₃. 2D Mater. 2017, 4, 035002 DOI: 10.1088/2053-1583/aa75ed
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On the origin of magnetic anisotropy in two dimensional CrI♂
Lado, J. L.; Fernandez-Rossier, J.
2D Materials (2017), 4 (3), 035002/1-035002/9CODEN: DMATB7; ISSN:2053-1583. (IOP Publishing Ltd.)
The observation of ferromagnetic order in a monolayer of CrI♂ has been recently reported, with a Curie temp. of 45 K and off-plane easy axis. Here we study the origin of magnetic anisotropy, a necessary ingredient to have magnetic order in two dimensions, combining two levels of modeling, d. functional calcns. and spin model Hamiltonians. We find two different contributions to the magnetic anisotropy of the material, favoring off-plane magnetization and opening a gap in the spin wave spectrum. First, ferromagnetic super-exchange across the ≃90 degree Cr-I-Cr bonds, are anisotropic, due to the spin-orbit interaction of the ligand I atoms. Second, a much smaller contribution that comes from the single ion anisotropy of the S = 3/2 Cr atom. Our results permit to establish the XXZ Hamiltonian, with a very small single ion anisotropy, as the adequate spin model for this system. Using spin wave theory we est. the Curie temp. and we highlight the essential role played by the gap that magnetic anisotropy induces on the magnon spectrum.
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45
Zollner, K.; Faria Junior, P. E.; Fabian, J. Proximity exchange effects in MoSe₂ and WSe₂ heterostructures with CrI₃: Twist angle, layer, and gate dependence. Phys. Rev. B: Condens. Matter Mater. Phys. 2019, 100, 085128 DOI: 10.1103/PhysRevB.100.085128
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Proximity exchange effects in MoSe32and WSe2 heterostructures with CrI3: twist angle, layer, and gate dependence
Zollner, Klaus; Faria Junior, Paulo E.; Fabian, Jaroslav
Physical Review B (2019), 100 (8), 085128CODEN: PRBHB7; ISSN:2469-9969. (American Physical Society)
Proximity effects in two-dimensional (2D) van der Waals heterostructures offer controllable ways to tailor the electronic band structure of adjacent materials. Proximity exchange in particular is important for making materials magnetic without hosting magnetic ions. Such synthetic magnets could be used for studying magnetotransport in high-mobility 2D materials, or magneto-optics in highly absorptive nominally nonmagnetic semiconductors. Using first-principles calcns., we show that the proximity exchange in monolayer MoSe2 and WSe2 due to ferromagnetic monolayer CrI3 can be tuned (even qual.) by twisting and gating. Remarkably, the proximity exchange remains the same when using antiferromagnetic CrI3 bilayer, paving the way for optical and elec. detection of layered antiferromagnets. Interestingly, the proximity exchange is opposite to the exchange of the adjacent antiferromagnetic layer. Finally, we show that the proximity exchange is confined to the layer adjacent to CrI3, and that adding a sepg. hBN barrier drastically reduces the proximity effect. We complement our ab initio results with tight-binding modeling and solve the Bethe-Salpeter equation to provide exptl. verifiable optical signatures (in the exciton spectra) of the proximity exchange effects.
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Zhang, S. S.-L.; Vignale, G.; Zhang, S. Anisotropic magnetoresistance driven by surface spin-orbit scattering. Phys. Rev. B: Condens. Matter Mater. Phys. 2015, 92, 024412 DOI: 10.1103/PhysRevB.92.024412
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Anisotropic magnetoresistance driven by surface spin-orbit scattering
Zhang, Steven S.-L.; Vignale, Giovanni; Zhang, Shufeng
Physical Review B: Condensed Matter and Materials Physics (2015), 92 (2), 024412/1-024412/6CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
In a bilayer consisting of an insulator and a ferromagnetic metal (FM), interfacial spin-orbit scattering leads to spin mixing of the two conducting channels of the FM, which results in an unconventional anisotropic magnetoresistance (AMR). We theor. investigate the magnetotransport in such bilayer structures by solving the spinor Boltzmann transport equation with the generalized Fuchs-Sondheimer boundary condition that takes into account the effect of spin-orbit scattering at the interface. We find that the new AMR exhibits a peculiar angular dependence which can serve as a genuine exptl. signature. We also det. the dependence of the AMR on film thickness as well as resistivity spin asymmetry of the FM.
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47
Kresse, G.; Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B: Condens. Matter Mater. Phys. 1999, 59, 1758– 1775, DOI: 10.1103/PhysRevB.59.1758
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From ultrasoft pseudopotentials to the projector augmented-wave method
Kresse, G.; Joubert, D.
Physical Review B: Condensed Matter and Materials Physics (1999), 59 (3), 1758-1775CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)
The formal relationship between ultrasoft (US) Vanderbilt-type pseudopotentials and Blochl's projector augmented wave (PAW) method is derived. The total energy functional for US pseudopotentials can be obtained by linearization of two terms in a slightly modified PAW total energy functional. The Hamilton operator, the forces, and the stress tensor are derived for this modified PAW functional. A simple way to implement the PAW method in existing plane-wave codes supporting US pseudopotentials is pointed out. In addn., crit. tests are presented to compare the accuracy and efficiency of the PAW and the US pseudopotential method with relaxed-core all-electron methods. These tests include small mols. (H2, H2O, Li2, N2, F2, BF3, SiF4) and several bulk systems (diamond, Si, V, Li, Ca, CaF2, Fe, Co, Ni). Particular attention is paid to the bulk properties and magnetic energies of Fe, Co, and Ni.
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48
Schlipf, M.; Gygi, F. Optimization algorithm for the generation of ONCV pseudopotentials. Comput. Phys. Commun. 2015, 196, 36, DOI: 10.1016/j.cpc.2015.05.011
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Optimization algorithm for the generation of ONCV pseudopotentials
Schlipf, Martin; Gygi, Francois
Computer Physics Communications (2015), 196 (), 36-44CODEN: CPHCBZ; ISSN:0010-4655. (Elsevier B.V.)
We present an optimization algorithm to construct pseudopotentials and use it to generate a set of Optimized Norm-Conserving Vanderbilt (ONCV) pseudopotentials for elements up to Z = 83 (Bi) (excluding Lanthanides). We introduce a quality function that assesses the agreement of a pseudopotential calcn. with all-electron FLAPW results, and the necessary plane-wave energy cutoff. This quality function allows us to use a Nelder-Mead optimization algorithm on a training set of materials to optimize the input parameters of the pseudopotential construction for most of the periodic table. We control the accuracy of the resulting pseudopotentials on a test set of materials independent of the training set. We find that the automatically constructed pseudopotentials (http://www.quantum-simulation.org) provide a good agreement with the all-electron results obtained using the FLEUR code with a plane-wave energy cutoff of approx. 60 Ry.
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49
MacNeill, D.; Stiehl, G. M.; Guimaraes, M. H. D.; Buhrman, R. A.; Park, J.; Ralph, D. C. Control of spin-orbit torques through crystal symmetry in WTe₂/ferromagnet bilayers. Nat. Phys. 2017, 13, 300, DOI: 10.1038/nphys3933
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Control of spin-orbit torques through crystal symmetry in WTe2/ferromagnet bilayers
MacNeill, D.; Stiehl, G. M.; Guimaraes, M. H. D.; Buhrman, R. A.; Park, J.; Ralph, D. C.
Nature Physics (2017), 13 (3), 300-305CODEN: NPAHAX; ISSN:1745-2473. (Nature Publishing Group)
Recent discoveries regarding current-induced spin-orbit torques produced by heavy-metal/ferromagnet and topol.-insulator/ferromagnet bilayers provide the potential for dramatically improved efficiency in the manipulation of magnetic devices. However, in expts. performed to date, spin-orbit torques have an important limitation-the component of torque that can compensate magnetic damping is required by symmetry to lie within the device plane. This means that spin-orbit torques can drive the most current-efficient type of magnetic reversal (antidamping switching) only for magnetic devices with in-plane anisotropy, not the devices with perpendicular magnetic anisotropy that are needed for high-d. applications. Here we show exptl. that this state of affairs is not fundamental, but rather one can change the allowed symmetries of spin-orbit torques in spin-source/ferromagnet bilayer devices by using a spin-source material with low cryst. symmetry. We use WTe2, a transition-metal dichalcogenide whose surface crystal structure has only one mirror plane and no two-fold rotational invariance. Consistent with these symmetries, we generate an out-of-plane antidamping torque when current is applied along a low-symmetry axis of WTe2/Permalloy bilayers, but not when current is applied along a high-symmetry axis. Controlling spin-orbit torques by crystal symmetries in multilayer samples provides a new strategy for optimizing future magnetic technologies.
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50
Garello, K.; Miron, I. M.; Avci, C. O.; Freimuth, F.; Mokrousov, Y.; Blügel, S.; Auffret, S.; Boulle, O.; Gaudin, G.; Gambardella, P. Symmetry and magnitude of spin-orbit torques in ferromagnetic heterostructures. Nat. Nanotechnol. 2013, 8, 587, DOI: 10.1038/nnano.2013.145
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Symmetry and magnitude of spin-orbit torques in ferromagnetic heterostructures
Garello, Kevin; Miron, Ioan Mihai; Avci, Can Onur; Freimuth, Frank; Mokrousov, Yuriy; Bluegel, Stefan; Auffret, Stephane; Boulle, Olivier; Gaudin, Gilles; Gambardella, Pietro
Nature Nanotechnology (2013), 8 (8), 587-593CODEN: NNAABX; ISSN:1748-3387. (Nature Publishing Group)
Recent demonstrations of magnetization switching induced by in-plane current injection in heavy metal/ferromagnetic heterostructures have drawn increasing attention to spin torques based on orbital-to-spin momentum transfer. The symmetry, magnitude and origin of spin-orbit torques (SOTs), however, remain a matter of debate. Here the authors report on the three-dimensional vector measurement of SOTs in AlOx/Co/Pt and MgO/CoFeB/Ta trilayers using harmonic anal. of the anomalous and planar Hall effects. The authors provide a general scheme to measure the amplitude and direction of SOTs as a function of the magnetization direction. Based on space and time inversion symmetry arguments, heavy metal/ferromagnetic layers allow for two different SOTs having odd and even behavior with respect to magnetization reversal. Such torques include strongly anisotropic field-like and spin transfer-like components, which depend on the type of heavy metal layer and annealing treatment. These results call for SOT models that go beyond the spin Hall and Rashba effects studied thus far.
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51
Mahfouzi, F.; Nikolić, B. K.; Kioussis, N. Antidamping spin-orbit torque driven by spin-flip reflection mechanism on the surface of a topological insulator: A time-dependent nonequilibrium Green function approach. Phys. Rev. B: Condens. Matter Mater. Phys. 2016, 93, 115419, DOI: 10.1103/PhysRevB.93.115419
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Pesin, D. A.; MacDonald, A. H. Quantum kinetic theory of current-induced torques in Rashba ferromagnets. Phys. Rev. B: Condens. Matter Mater. Phys. 2012, 86, 014416 DOI: 10.1103/PhysRevB.86.014416
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Quantum kinetic theory of current-induced torques in Rashba ferromagnets
Pesin, D. A.; MacDonald, A. H.
Physical Review B: Condensed Matter and Materials Physics (2012), 86 (1), 014416/1-014416/5CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
Motivated by recent exptl. studies of thin-film devices contg. a single ferromagnetic layer, we develop a quantum kinetic theory of current-induced magnetic torques in Rashba-model ferromagnets. We find that the current-induced spin densities, responsible for the switching behavior, are due most essentially to spin-dependent quasiparticle lifetimes and derive analytic expressions for relevant limits of a simple model. Quant. model parameter ests. suggest that spin-orbit coupling in the adjacent metal normal magnetic layer must play an essential role in the strength of the switching effect.
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Kalitsov, A.; Nikolaev, S. A.; Velev, J.; Chshiev, M.; Mryasov, O. Intrinsic spin-orbit torque in a single-domain nanomagnet. Phys. Rev. B: Condens. Matter Mater. Phys. 2017, 96, 214430, DOI: 10.1103/PhysRevB.96.214430
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Zollner, K.; Petrović, M. D.; Dolui, K.; Plecháč, P.; Nikolić, B. K.; Fabian, J. Purely interfacial and highly tunable spin-orbit torque in graphene doubly proximitized by two-dimensional magnet Cr₂Ge₂Te₆ and monolayer WS₂. arXiv, 2019, 1910.08072, https://arxiv.org/abs/1910.08072.
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Zhang, W.-B.; Qu, Q.; Zhu, P.; Lam, C.-H. Robust intrinsic ferromagnetism and half semiconductivity in stable two-dimensional single-layer chromium trihalides. J. Mater. Chem. C 2015, 3, 12457– 12468, DOI: 10.1039/C5TC02840J
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Robust intrinsic ferromagnetism and half semiconductivity in stable two-dimensional single-layer chromium trihalides
Zhang, Wei-Bing; Qu, Qian; Zhu, Peng; Lam, Chi-Hang
Journal of Materials Chemistry C: Materials for Optical and Electronic Devices (2015), 3 (48), 12457-12468CODEN: JMCCCX; ISSN:2050-7534. (Royal Society of Chemistry)
Two-dimensional (2D) intrinsic ferromagnetic (FM) semiconductors are crucial to develop low-dimensional spintronic devices. Using d. functional theory, we show that single-layer chromium trihalides (SLCTs) (CrX3 (X = F, Cl, Br, I)) constitute a series of stable 2D intrinsic FM semiconductors. A free-standing SLCT can be easily exfoliated from the bulk crystal, due to a low cleavage energy and a high in-plane stiffness. Electronic structure calcns. using the HSE06 functional indicate that both bulk and single-layer CrX3 are half semiconductors with indirect gaps and their valence and conduction bands are fully spin-polarized in the same spin direction. The energy gaps and absorption edges of CrBr3 and CrI3 are found to be in the visible frequency range, which implies possible opto-electronic applications. Furthermore, SLCTs are found to possess a large magnetic moment of 3 μB per formula unit and a sizable magnetic anisotropy energy. The magnetic exchange consts. of SLCTs are then extd. using the Heisenberg spin Hamiltonian and the microscopic origins of the various exchange interactions are analyzed. A competition between a near 90° FM superexchange and a direct antiferromagnetic (AFM) exchange results in a FM nearest-neighbor exchange interaction. The next and third nearest-neighbor exchange interactions are found to be FM and AFM, resp., and this can be understood by the angle-dependent extended Cr-X-X-Cr superexchange interaction. Moreover, the Curie temps. of SLCTs are also predicted using Monte Carlo simulations and the values can be further increased by applying a biaxial tensile strain. The unique combination of robust intrinsic ferromagnetism, half semicond. and large magnetic anisotropy energies renders the SLCTs as promising candidates for next-generation semiconductor spintronic applications.
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56
Baumgartner, M.; Garello, K.; Mendil, J.; Avci, C. O.; Grimaldi, E.; Murer, C.; Feng, J.; Gabureac, M.; Stamm, C.; Acremann, Y.; Finizio, S.; Wintz, S.; Raabe, J.; Gambardella, P. Spatially and time-resolved magnetization dynamics driven by spin-orbit torques. Nat. Nanotechnol. 2017, 12, 980, DOI: 10.1038/nnano.2017.151
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Spatially and time-resolved magnetization dynamics driven by spin-orbit torques
Baumgartner, Manuel; Garello, Kevin; Mendil, Johannes; Avci, Can Onur; Grimaldi, Eva; Murer, Christoph; Feng, Junxiao; Gabureac, Mihai; Stamm, Christian; Acremann, Yves; Finizio, Simone; Wintz, Sebastian; Raabe, Jorg; Gambardella, Pietro
Nature Nanotechnology (2017), 12 (10), 980-986CODEN: NNAABX; ISSN:1748-3387. (Nature Research)
Current-induced spin-orbit torques are one of the most effective ways to manipulate the magnetization in spintronic devices, and hold promise for fast switching applications in nonvolatile memory and logic units. Here, the authors report the direct observation of spin-orbit-torque-driven magnetization dynamics in Pt/Co/AlOx dots during current pulse injection. Time-resolved x-ray images with 25 nm spatial and 100 ps temporal resoln. reveal that switching is achieved within the duration of a subnanosecond current pulse by the fast nucleation of an inverted domain at the edge of the dot and propagation of a tilted domain wall across the dot. The nucleation point is deterministic and alternates between the four dot quadrants depending on the sign of the magnetization, current and external field. The authors' measurements reveal how the magnetic symmetry is broken by the concerted action of the damping-like and field-like spin-orbit torques and the Dzyaloshinskii-Moriya interaction, and show that reproducible switching events can be obtained for over 1012 reversal cycles.
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Cited By

This article is cited by 3 publications.

D. Soriano, M. I. Katsnelson, J. Fernández-Rossier. Magnetic Two-Dimensional Chromium Trihalides: A Theoretical Perspective. Nano Letters 2020, 20 (9) , 6225-6234. https://doi.org/10.1021/acs.nanolett.0c02381
Luman Zhang, Xinyu Huang, Hongwei Dai, Mingshan Wang, Hui Cheng, Lei Tong, Zheng Li, Xiaotao Han, Xia Wang, Lei Ye, Junbo Han. Proximity‐Coupling‐Induced Significant Enhancement of Coercive Field and Curie Temperature in 2D van der Waals Heterostructures. Advanced Materials 2020, 32 (38) , 2002032. https://doi.org/10.1002/adma.202002032
Chenghao Shen, Timothy Leeney, Alex Matos-Abiague, Benedikt Scharf, Jong E. Han, Igor Žutić. Resonant tunneling anisotropic magnetoresistance induced by magnetic proximity. Physical Review B 2020, 102 (4) https://doi.org/10.1103/PhysRevB.102.045312

Abstract
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Figure 1
Figure 1. Schematic view of the CrI₃/TaSe₂ vdW heterostructure consisting of an insulating antiferromagnetic bilayer of CrI₃ and a nonmagnetic metallic monolayer TMD TaSe₂. The unpolarized charge current is injected parallel to the interface by a small applied bias voltage V_b between the left and right macroscopic reservoirs. The current flows through the monolayer of TaSe₂ as well as through the first monolayer (see the Supporting Information) of CrI₃ due to evanescent wave functions injected into it by TaSe₂. The unit vectors of magnetizations on the two CrI₃ monolayers are denoted by m₁ and m₂. The heterostructure is assumed to be infinite in the xy-plane.
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Figure 2
Figure 2. Current-driven nonequilibrium spin density S_CD = (S_CD^x,S_CD^y,S_CD^z) in the linear-response regime within a bilayer-CrI₃/monolayer-TaSe₂ vdW heterostructure for (a) m₁∥x̂; (b) m₁∥ŷ; (c) m₁∥ẑ. Vertical dashed lines indicate the position of each atomic plane. The area of the common rectangular supercell of the vdW heterostructure in Figure 1 is denoted by , where a = 6.85 Å is the lattice constant of bulk CrI₃. Shaded green areas represent rescaled S_CD^y in the spatial region of the first monolayer of CrI₃, which is in direct contact with the monolayer of TaSe₂.
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Figure 3
Figure 3. First-principles-computed bands of the bilayer-CrI₃/monolayer-TaSe₂ vdW heterostructure with SOC turned on. We use Hubbard U = 2.0 eV and U = 0 eV for (a) and (c), respectively, in ncDFT + U calculations where the color corresponds to the equilibrium spin expectation value, (σ̂_z is the Pauli matrix) in the eigenstates |Ψ_k⟩ of ncDFT Hamiltonian (for the other two components, S_eq^x and S_eq^y, and their texture in k-space, see the Supporting Information). Panels (b) and (d) show the same band structures as (a) and (c), respectively, but with different colored symbols corresponding to projections onto different monolayers.
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Figure 4
Figure 4. Azimuthal (θ) and polar (φ) angle dependence of the magnitude of SOT component |T^o| (odd in m₁) for different orientations of the magnetization m₁ = (sin θ cosφ, sin θ sinφ, cos θ) on the first monolayer of CrI₃. The magnetization is rotated within the (a) xz-plane; (b) xy-plane; (c) yz-plane. Solid blue lines are fit to NEGF + ncDFT-computed SOT values (red dots) using eq 6 with fitting parameters from Table 1.
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Figure 5
Figure 5. Classical dynamics of magnetizations (a, b) m₁(t) on the first monolayer of CrI₃ and (c, d) m₂(t) on the second monolayer of CrI₃. The two magnetizations are exchange coupled [eq 7], while according to Figure 2 only m₁(t) experiences SOT from Figure 4. The dynamics is obtained by solving two coupled LLG equations [eq 8] for m₁(t) and m₂(t). The bias voltage V_b = 0.2 V is dc in (a) and (c), while in (b) and (d) we use a sequence of short rectangular voltage pulses of the same amplitude with pulse duration δt_ON = 1.0 ps followed by a pause of δt_OFF = 100 ps during which no voltage is applied. A movie animating m₁(t) in panel (b) as well as m₂(t) in panel (d) is provided in the Supporting Information.
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Figure 6
Figure 6. TMR vs angle θ between magnetizations m₁ and m₂ on two monolayers of CrI₃ in Figure 1 for vertical read current(17) flowing perpendicularly (i.e., along the z-axis in Figure 1) through the bilayer-CrI₃/monolayer-TaSe₂ vdW heterostructure. The heterostructure is sandwiched between two semi-infinite graphite leads with (red squares) and without (blue circles) the bilayer of hBN inserted between the leads and the vdW heterostructure, as illustrated in the inset.
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1. 1
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  The realization of long-range ferromagnetic order in two-dimensional van der Waals crystals, combined with their rich electronic and optical properties, could lead to new magnetic, magnetoelec. and magneto-optic applications. In two-dimensional systems, the long-range magnetic order is strongly suppressed by thermal fluctuations, according to the Mermin-Wagner theorem; however, these thermal fluctuations can be counteracted by magnetic anisotropy. Previous efforts, based on defect and compn. engineering, or the proximity effect, introduced magnetic responses only locally or extrinsically. Here we report intrinsic long-range ferromagnetic order in pristine Cr2Ge2Te6 at. layers, as revealed by scanning magneto-optic Kerr microscopy. In this magnetically soft, two-dimensional van der Waals ferromagnet, we achieve unprecedented control of the transition temp. (between ferromagnetic and paramagnetic states) using very small fields (smaller than 0.3 T). This result is in contrast to the insensitivity of the transition temp. to magnetic fields in the three-dimensional regime. We found that the small applied field leads to an effective anisotropy that is much greater than the near-zero magnetocryst. anisotropy, opening up a large spin-wave excitation gap. We explain the obsd. phenomenon using renormalized spin-wave theory and conclude that the unusual field dependence of the transition temp. is a hallmark of soft, two-dimensional ferromagnetic van der Waals crystals. Cr2Ge2Te6 is a nearly ideal two-dimensional Heisenberg ferromagnet and so will be useful for studying fundamental spin behaviors, opening the door to exploring new applications such as ultra-compact spintronics.
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2. 2
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  Since the discovery of graphene, the family of two-dimensional materials has grown, displaying a broad range of electronic properties. Recent addns. include semiconductors with spin-valley coupling, Ising superconductors that can be tuned into a quantum metal, possible Mott insulators with tunable charge-d. waves, and topol. semimetals with edge transport. However, no two-dimensional crystal with intrinsic magnetism has yet been discovered; such a crystal would be useful in many technologies from sensing to data storage. Theor., magnetic order is prohibited in the two-dimensional isotropic Heisenberg model at finite temps. by the Mermin-Wagner theorem. Magnetic anisotropy removes this restriction, however, and enables, for instance, the occurrence of two-dimensional Ising ferromagnetism. Here we use magneto-optical Kerr effect microscopy to demonstrate that monolayer chromium triiodide (CrI3) is an Ising ferromagnet with out-of-plane spin orientation. Its Curie temp. of 45 K is only slightly lower than that of the bulk crystal, 61 K, which is consistent with a weak interlayer coupling. Moreover, our studies suggest a layer-dependent magnetic phase, highlighting thickness-dependent phys. properties typical of van der Waals crystals. Remarkably, bilayer CrI3 displays suppressed magnetization with a metamagnetic effect, whereas in trilayer CrI3 the interlayer ferromagnetism obsd. in the bulk crystal is restored. This work creates opportunities for studying magnetism by harnessing the unusual features of atomically thin materials, such as elec. control for realizing magnetoelectronics, and van der Waals engineering to produce interface phenomena.
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  Gibertini, M.; Koperski, M.; Morpurgo, A. F.; Novoselov, K. S. Magnetic 2D materials and heterostructures. Nat. Nanotechnol. 2019, 14, 408– 419, DOI: 10.1038/s41565-019-0438-6
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  Magnetic 2D materials and heterostructures
  Gibertini, M.; Koperski, M.; Morpurgo, A. F.; Novoselov, K. S.
  Nature Nanotechnology (2019), 14 (5), 408-419CODEN: NNAABX; ISSN:1748-3387. (Nature Research)
  The family of two-dimensional (2D) materials grows day by day, hugely expanding the scope of possible phenomena to be explored in two dimensions, as well as the possible van der Waals (vdW) heterostructures that one can create. Such 2D materials currently cover a vast range of properties. Until recently, this family has been missing one crucial member: 2D magnets. The situation has changed over the past 2 years with the introduction of a variety of atomically thin magnetic crystals. Here we will discuss the difference between magnetic states in 2D materials and in bulk crystals and present an overview of the 2D magnets that have been explored recently. We will focus on the case of the two most studied systems-semiconducting CrI3 and metallic Fe3GeTe2-and illustrate the phys. phenomena that have been obsd. Special attention will be given to the range of new van der Waals heterostructures that became possible with the appearance of 2D magnets, offering new perspectives in this rapidly expanding field.
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  Burch, K. S.; Mandrus, D.; Park, J.-G. Magnetism in two-dimensional van der Waals materials. Nature 2018, 563, 47– 52, DOI: 10.1038/s41586-018-0631-z
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  Magnetism in two-dimensional van der Waals materials
  Burch, Kenneth S.; Mandrus, David; Park, Je-Geun
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  The discovery of materials has often introduced new phys. paradigms and enabled the development of novel devices. Two-dimensional magnetism, which is assocd. with strong intrinsic spin fluctuations, has long been the focus of fundamental questions in condensed matter physics regarding our understanding and control of new phases. Here we discuss magnetic van der Waals materials: two-dimensional at. crystals that contain magnetic elements and thus exhibit intrinsic magnetic properties. These cleavable materials provide the ideal platform for exploring magnetism in the two-dimensional limit, where new phys. phenomena are expected, and represent a substantial shift in our ability to control and investigate nanoscale phases. We present the theor. background and motivation for investigating this class of crystals, describe the material landscape and the current exptl. status of measurement techniques as well as devices, and discuss promising future directions for the study of magnetic van der Waals materials.
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  Cortie, D. L.; Causer, G. L.; Rule, K. C.; Fritzsche, H.; Kreuzpaintner, W.; Klose, F. Two-Dimensional Magnets: Forgotten History and Recent Progress towards Spintronic Applications. Adv. Funct. Mater. 2019, 0, 1901414, DOI: 10.1002/adfm.201901414
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  Li, H.; Ruan, S.; Zeng, Y.-J. Intrinsic Van Der Waals Magnetic Materials from Bulk to the 2D Limit: New Frontiers of Spintronics. Adv. Mater. 2019, 31, 1900065, DOI: 10.1002/adma.201900065
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  Alghamdi, M.; Lohmann, M.; Li, J.; Jothi, P. R.; Shao, Q.; Aldosary, M.; Su, T.; Fokwa, B. P. T.; Shi, J. Highly Efficient SpinOrbit Torque and Switching of Layered Ferromagnet Fe₃GeTe₂. Nano Lett. 2019, 19, 4400– 4405, DOI: 10.1021/acs.nanolett.9b01043
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  Highly Efficient Spin-Orbit Torque and Switching of Layered Ferromagnet Fe3GeTe2
  Alghamdi, Mohammed; Lohmann, Mark; Li, Junxue; Jothi, Palani R.; Shao, Qiming; Aldosary, Mohammed; Su, Tang; Fokwa, Boniface P. T.; Shi, Jing
  Nano Letters (2019), 19 (7), 4400-4405CODEN: NALEFD; ISSN:1530-6984. (American Chemical Society)
  Among van der Waals (vdW) layered ferromagnets, Fe3GeTe2 (FGT) is an excellent candidate material to form FGT/heavy metal heterostructures for studying the effect of spin-orbit torques (SOT). Its metallicity, strong perpendicular magnetic anisotropy built in the single at. layers, relatively high Curie temp. (Tc ∼ 225 K), and electrostatic gate tunability offer a tantalizing possibility of achieving the ultimate high SOT limit in monolayer all-vdW nanodevices. In this study, we fabricate heterostructures of FGT/Pt with 5 nm of Pt sputtered onto the atomically flat surface of ∼15-23 nm exfoliated FGT flakes. The spin current generated in Pt exerts a damping-like SOT on FGT magnetization. At ∼2.5 × 1011 A/m2 c.d., SOT causes the FGT magnetization to switch, which is detected by the anomalous Hall effect of FGT. To quantify the SOT effect, we measure the second harmonic Hall responses as the applied magnetic field rotates the FGT magnetization in the plane. Our anal. shows that the SOT efficiency is comparable with that of the best heterostructures contg. three-dimensional (3D) ferromagnetic metals and much larger than that of heterostructures contg. 3D ferrimagnetic insulators. Such large efficiency is attributed to the atomically flat FGT/Pt interface, which demonstrates the great potential of exploiting vdW heterostructures for highly efficient spintronic nanodevices.
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  Absence of ferromagnetism or antiferromagnetism in one- or two-dimensional isotropic Heisenberg models
  Mermin, N. David; Wagner, Hans
  Physical Review Letters (1966), 17 (22), 1133-6CODEN: PRLTAO; ISSN:0031-9007.
  It is rigorously proved that at any nonzero temp., a 1- and 2-dimensional isotropic spin-S Heisenberg model with finite-range exchange interaction can be neither ferromagnetic nor antiferromagnetic. The method of proof is capable of excluding a variety of types of ordering in 1 and 2 dimensions.
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11. 11
  Sivadas, N.; Okamoto, S.; Xu, X.; Fennie, C. J.; Xiao, D. Stacking-Dependent Magnetism in Bilayer CrI₃. Nano Lett. 2018, 18, 7658– 7664, DOI: 10.1021/acs.nanolett.8b03321
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  Stacking-Dependent Magnetism in Bilayer CrI3
  Sivadas, Nikhil; Okamoto, Satoshi; Xu, Xiaodong; Fennie, Craig. J.; Xiao, Di
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  We report the connection between the stacking order and magnetic properties of bilayer CrI3 using first-principles calcns. We show that the stacking order defines the magnetic ground state. By changing the interlayer stacking order, one can tune the interlayer exchange interaction between antiferromagnetic and ferromagnetic. To measure the predicted stacking-dependent magnetism, we propose using linear magnetoelec. effect. Our results not only gives a possible explanation for the obsd. antiferromagnetism in bilayer CrI3 but also have direct implications in heterostructures made of two-dimensional magnets.
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12. 12
  Jiang, P.; Wang, C.; Chen, D.; Zhong, Z.; Yuan, Z.; Lu, Z.-Y.; Ji, W. Stacking tunable interlayer magnetism in bilayer CrI₃. Phys. Rev. B: Condens. Matter Mater. Phys. 2019, 99, 144401, DOI: 10.1103/PhysRevB.99.144401
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  Stacking tunable interlayer magnetism in bilayer CrI3
  Jiang, Peiheng; Wang, Cong; Chen, Dachuan; Zhong, Zhicheng; Yuan, Zhe; Lu, Zhong-Yi; Ji, Wei
  Physical Review B (2019), 99 (14), 144401CODEN: PRBHB7; ISSN:2469-9969. (American Physical Society)
  Diverse interlayer tunability of phys. properties of two-dimensional layers mostly lies in the covalent-like quasibonding that is significant in electronic structures but rather weak for energetics. Such characteristics result in various stacking orders that are energetically comparable but may significantly differ in terms of electronic structures, e.g., magnetism. Inspired by several recent expts. showing interlayer antiferromagnetically coupled CrI3 bilayers, we carried out first-principles calcns. for CrI3 bilayers. We found that the antiferromagnetic coupling results from a different stacking order with the C2/m space group symmetry, rather than the graphene-like one with R3 as previously believed. Moreover, we demonstrated that the intra- and interlayer couplings in CrI3 bilayer are governed by two different mechanisms, namely ferromagnetic superexchange and direct-exchange interactions, which are largely decoupled because of their significant difference in strength at the strong- and weak-interaction limits. This allows the much weaker interlayer magnetic coupling to be more feasibly tuned by stacking orders solely. Given the fact that interlayer magnetic properties can be altered by changing crystal structure with different stacking orders, our work opens a paradigm for tuning interlayer magnetic properties with the freedom of stacking order in two-dimensional layered materials.
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13. 13
  Huang, B.; Clark, G.; Klein, D. R.; MacNeill, D.; Navarro-Moratalla, E.; Seyler, K. L.; Wilson, N.; McGuire, M. A.; Cobden, D. H.; Xiao, D.; Yao, W.; Jarillo-Herrero, P.; Xu, X. Electrical control of 2D magnetism in bilayer CrI₃. Nat. Nanotechnol. 2018, 13, 544– 548, DOI: 10.1038/s41565-018-0121-3
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  Electrical control of 2D magnetism in bilayer CrI3
  Huang, Bevin; Clark, Genevieve; Klein, Dahlia R.; MacNeill, David; Navarro-Moratalla, Efren; Seyler, Kyle L.; Wilson, Nathan; McGuire, Michael A.; Cobden, David H.; Xiao, Di; Yao, Wang; Jarillo-Herrero, Pablo; Xu, Xiaodong
  Nature Nanotechnology (2018), 13 (7), 544-548CODEN: NNAABX; ISSN:1748-3387. (Nature Research)
  Controlling magnetism via elec. fields addresses fundamental questions of magnetic phenomena and phase transitions1-3, and enables the development of elec. coupled spintronic devices, such as voltage-controlled magnetic memories with low operation energy4-6. Previous studies on dil. magnetic semiconductors such as (Ga,Mn)As and (In,Mn)Sb have demonstrated large modulations of the Curie temps. and coercive fields by altering the magnetic anisotropy and exchange interaction2,4,7-9. Owing to their unique magnetic properties10-14, the recently reported two-dimensional magnets provide a new system for studying these features15-19. For instance, a bilayer of chromium triiodide (CrI3) behaves as a layered antiferromagnet with a magnetic field-driven metamagnetic transition15,16. Here, we demonstrate electrostatic gate control of magnetism in CrI3 bilayers, probed by magneto-optical Kerr effect (MOKE) microscopy. At fixed magnetic fields near the metamagnetic transition, we realize voltage-controlled switching between antiferromagnetic and ferromagnetic states. At zero magnetic field, we demonstrate a time-reversal pair of layered antiferromagnetic states that exhibit spin-layer locking, leading to a linear dependence of their MOKE signals on gate voltage with opposite slopes. Our results allow for the exploration of new magnetoelec. phenomena and van der Waals spintronics based on 2D materials.
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14. 14
  Jiang, S.; Li, L.; Wang, Z.; Mak, K. F.; Shan, J. Controlling magnetism in 2D CrI₃ by electrostatic doping. Nat. Nanotechnol. 2018, 13, 549– 553, DOI: 10.1038/s41565-018-0135-x
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  Controlling magnetism in 2D CrI3 by electrostatic doping
  Jiang, Shengwei; Li, Lizhong; Wang, Zefang; Mak, Kin Fai; Shan, Jie
  Nature Nanotechnology (2018), 13 (7), 549-553CODEN: NNAABX; ISSN:1748-3387. (Nature Research)
  The at. thickness of two-dimensional materials provides a unique opportunity to control their elec.1 and optical2 properties as well as to drive the electronic phase transitions3 by electrostatic doping. The discovery of two-dimensional magnetic materials4-10 has opened up the prospect of the elec. control of magnetism and the realization of new functional devices11. A recent expt. based on the linear magneto-elec. effect has demonstrated control of the magnetic order in bilayer CrI3 by elec. fields12. However, this approach is limited to non-centrosym. materials11,13-16 magnetically biased near the antiferromagnet-ferromagnet transition. Here, we demonstrate control of the magnetic properties of both monolayer and bilayer CrI3 by electrostatic doping using CrI3-graphene vertical heterostructures. In monolayer CrI3, doping significantly modifies the satn. magnetization, coercive force and Curie temp., showing strengthened/weakened magnetic order with hole/electron doping. Remarkably, in bilayer CrI3, the electron doping above ∼2.5 × 1013 cm-2 induces a transition from an antiferromagnetic to a ferromagnetic ground state in the absence of a magnetic field. The result reveals a strongly doping-dependent interlayer exchange coupling, which enables robust switching of magnetization in bilayer CrI3 by small gate voltages.
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15. 15
  Jiang, S.; Shan, J.; Mak, K. F. Electric-field switching of two-dimensional van der Waals magnets. Nat. Mater. 2018, 17, 406– 410, DOI: 10.1038/s41563-018-0040-6
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  Electric-field switching of two-dimensional van der Waals magnets
  Jiang, Shengwei; Shan, Jie; Mak, Kin Fai
  Nature Materials (2018), 17 (5), 406-410CODEN: NMAACR; ISSN:1476-1122. (Nature Research)
  Controlling magnetism by purely elec. means is a key challenge to better information technol.1. A variety of material systems, including ferromagnetic (FM) metals2-4, FM semiconductors5, multiferroics6-8 and magnetoelec. (ME) materials9,10, have been explored for the elec.-field control of magnetism. The recent discovery of two-dimensional (2D) van der Waals magnets11,12 has opened a new door for the elec. control of magnetism at the nanometer scale through a van der Waals heterostructure device platform13. Here we demonstrate the control of magnetism in bilayer CrI3, an antiferromagnetic (AFM) semiconductor in its ground state12, by the application of small gate voltages in field-effect devices and the detection of magnetization using magnetic CD (MCD) microscopy. The applied elec. field creates an interlayer p.d., which results in a large linear ME effect, whose sign depends on the interlayer AFM order. We also achieve a complete and reversible elec. switching between the interlayer AFM and FM states in the vicinity of the interlayer spin-flip transition. The effect originates from the elec.-field dependence of the interlayer exchange bias.
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16. 16
  Locatelli, N.; Cros, V.; Grollier, J. Spin-torque building blocks. Nat. Mater. 2014, 13, 11– 20, DOI: 10.1038/nmat3823
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  Spin-torque building blocks
  Locatelli, N.; Cros, V.; Grollier, J.
  Nature Materials (2014), 13 (1), 11-20CODEN: NMAACR; ISSN:1476-1122. (Nature Publishing Group)
  The discovery of the spin-torque effect has made magnetic nanodevices realistic candidates for active elements of memory devices and applications. Magnetoresistive effects allow the read-out of increasingly small magnetic bits, and the spin torque provides an efficient tool to manipulate - precisely, rapidly and at low energy cost - the magnetic state, which is in turn the central information medium of spintronic devices. By keeping the same magnetic stack, but by tuning a device's shape and bias conditions, the spin torque can be engineered to build a variety of advanced magnetic nanodevices. Here we show that by assembling these nanodevices as building blocks with different functionalities, novel types of computing architecture can be envisaged. We focus in particular on recent concepts such as magnonics and spintronic neural networks.
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17. 17
  Zhou, J.; Qiao, J.; Duan, C.-G.; Bournel, A.; Wang, K. L.; Zhao, W. Large Tunneling Magnetoresistance in VSe₂/MoS₂ Magnetic Tunnel Junction. ACS Appl. Mater. Interfaces 2019, 11, 17647– 17653, DOI: 10.1021/acsami.9b02493
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  Large Tunneling Magnetoresistance in VSe2/MoS2 Magnetic Tunnel Junction
  Zhou, Jiaqi; Qiao, Junfeng; Duan, Chun-Gang; Bournel, Arnaud; Wang, Kang L.; Zhao, Weisheng
  ACS Applied Materials & Interfaces (2019), 11 (19), 17647-17653CODEN: AAMICK; ISSN:1944-8244. (American Chemical Society)
  Two-dimensional (2D) van der Waals (vdW) materials provide the possibility of realizing heterostructures with coveted properties. Here, we report a theor. investigation of the vdW magnetic tunnel junction (MTJ) based on VSe2/MoS2 heterojunction, where the VSe2 monolayer acts as a ferromagnet with room-temp. ferromagnetism. We propose the concept of spin-orbit torque (SOT) vdW MTJ with reliable reading and efficient writing operations. The nonequil. study reveals a large tunneling magnetoresistance of 846% at 300 K, identifying significantly its parallel and antiparallel states. Thanks to the strong spin Hall cond. of MoS2, SOT is promising for the magnetization switching of VSe2 free layer. Quantum-well states come into being and resonances appear in MTJ, suggesting that the voltage control can adjust transport properties effectively. The SOT vdW MTJ based on VSe2/MoS2 provides desirable performance and exptl. feasibility, offering new opportunities for 2D spintronics.
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18. 18
  Song, T.; Cai, X.; Tu, M. W.-Y.; Zhang, X.; Huang, B.; Wilson, N. P.; Seyler, K. L.; Zhu, L.; Taniguchi, T.; Watanabe, K.; McGuire, M. A.; Cobden, D. H.; Xiao, D.; Yao, W.; Xu, X. Giant tunneling magnetoresistance in spin-filter van der Waals heterostructures. Science 2018, 360, 1214– 1218, DOI: 10.1126/science.aar4851
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  Giant tunneling magnetoresistance in spin-filter van der Waals heterostructures
  Song, Tiancheng; Cai, Xinghan; Tu, Matisse Wei-Yuan; Zhang, Xiaoou; Huang, Bevin; Wilson, Nathan P.; Seyler, Kyle L.; Zhu, Lin; Taniguchi, Takashi; Watanabe, Kenji; McGuire, Michael A.; Cobden, David H.; Xiao, Di; Yao, Wang; Xu, Xiaodong
  Science (Washington, DC, United States) (2018), 360 (6394), 1214-1218CODEN: SCIEAS; ISSN:0036-8075. (American Association for the Advancement of Science)
  Magnetic multilayer devices that exploit magnetoresistance are the backbone of magnetic sensing and data storage technologies. Here, the authors report multiple-spin-filter magnetic tunnel junctions (sf-MTJs) based on van der Waals (vdW) heterostructures in which atomically thin chromium triiodide (CrI3) acts as a spin-filter tunnel barrier sandwiched between graphene contacts. The authors demonstrate tunneling magnetoresistance that is drastically enhanced with increasing CrI3 layer thickness, reaching a record 19,000% for magnetic multilayer structures using four-layer sf-MTJs at low temps. Using magnetic CD measurements, the authors attribute these effects to the intrinsic layer-by-layer antiferromagnetic ordering of the atomically thin CrI3. The work reveals the possibility to push magnetic information storage to the atomically thin limit and highlights CrI3 as a superlative magnetic tunnel barrier for vdW heterostructure spintronic devices.
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19. 19
  Klein, D. R.; MacNeill, D.; Lado, J. L.; Soriano, D.; Navarro-Moratalla, E.; Watanabe, K.; Taniguchi, T.; Manni, S.; Canfield, P.; Fernández-Rossier, J.; Jarillo-Herrero, P. Probing magnetism in 2D van der Waals crystalline insulators via electron tunneling. Science 2018, 360, 1218– 1222, DOI: 10.1126/science.aar3617
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  19
  Probing magnetism in 2D van der Waals crystalline insulators via electron tunneling
  Klein, D. R.; MacNeill, D.; Lado, J. L.; Soriano, D.; Navarro-Moratalla, E.; Watanabe, K.; Taniguchi, T.; Manni, S.; Canfield, P.; Fernandez-Rossier, J.; Jarillo-Herrero, P.
  Science (Washington, DC, United States) (2018), 360 (6394), 1218-1222CODEN: SCIEAS; ISSN:0036-8075. (American Association for the Advancement of Science)
  Magnetic insulators are a key resource for next-generation spintronic and topol. devices. The family of layered metal halides promises varied magnetic states, including ultrathin insulating multiferroics, spin liqs., and ferromagnets, but device-oriented characterization methods are needed to unlock their potential. Here, the authors report tunneling through the layered magnetic insulator CrI3 as a function of temp. and applied magnetic field. The authors elec. detect the magnetic ground state and interlayer coupling and observe a field-induced metamagnetic transition. The metamagnetic transition results in magnetoresistances of 95, 300, and 550% for bilayer, trilayer, and tetralayer CrI3 barriers, resp. The authors further measure inelastic tunneling spectra for their junctions, unveiling a rich spectrum consistent with collective magnetic excitations (magnons) in CrI3.
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20. 20
  Wang, Z.; Gutiérrez-Lezama, I.; Ubrig, N.; Kroner, M.; Gibertini, M.; Taniguchi, T.; Watanabe, K.; Imamoglu, A.; Giannini, E.; Morpurgo, A. F. Very large tunneling magnetoresistance in layered magnetic semiconductor CrI₃. Nat. Commun. 2018, 9, 2516, DOI: 10.1038/s41467-018-04953-8
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  20
  Very large tunneling magnetoresistance in layered magnetic semiconductor CrI3
  Wang Zhe; Gutierrez-Lezama Ignacio; Ubrig Nicolas; Gibertini Marco; Giannini Enrico; Morpurgo Alberto F; Wang Zhe; Gutierrez-Lezama Ignacio; Ubrig Nicolas; Gibertini Marco; Morpurgo Alberto F; Kroner Martin; Imamoglu Atac; Taniguchi Takashi; Watanabe Kenji
  Nature communications (2018), 9 (1), 2516 ISSN:.
  Magnetic layered van der Waals crystals are an emerging class of materials giving access to new physical phenomena, as illustrated by the recent observation of 2D ferromagnetism in Cr2Ge2Te6 and CrI3. Of particular interest in semiconductors is the interplay between magnetism and transport, which has remained unexplored. Here we report magneto-transport measurements on exfoliated CrI3 crystals. We find that tunneling conduction in the direction perpendicular to the crystalline planes exhibits a magnetoresistance as large as 10,000%. The evolution of the magnetoresistance with magnetic field and temperature reveals that the phenomenon originates from multiple transitions to different magnetic states, whose possible microscopic nature is discussed on the basis of all existing experimental observations. This observed dependence of the conductance of a tunnel barrier on its magnetic state is a phenomenon that demonstrates the presence of a strong coupling between transport and magnetism in magnetic van der Waals semiconductors.
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21. 21
  Song, T.; Tu, M. W.-Y.; Carnahan, C.; Cai, X.; Taniguchi, T.; Watanabe, K.; McGuire, M. A.; Cobden, D. H.; Xiao, D.; Yao, W.; Xu, X. Voltage Control of a van der Waals Spin-Filter Magnetic Tunnel Junction. Nano Lett. 2019, 19, 915– 920, DOI: 10.1021/acs.nanolett.8b04160
  [ACS Full Text ], [CAS], Google Scholar
  21
  Voltage Control of a van der Waals Spin-Filter Magnetic Tunnel Junction
  Song Tiancheng; Cai Xinghan; Cobden David H; Xu Xiaodong; Tu Matisse Wei-Yuan; Yao Wang; Carnahan Caitlin; Xiao Di; Taniguchi Takashi; Watanabe Kenji; McGuire Michael A; Xu Xiaodong
  Nano letters (2019), 19 (2), 915-920 ISSN:.
  Atomically thin chromium triiodide (CrI3) has recently been identified as a layered antiferromagnetic insulator, in which adjacent ferromagnetic monolayers are antiferromagnetically coupled. This unusual magnetic structure naturally comprises a series of antialigned spin filters, which can be utilized to make spin-filter magnetic tunnel junctions with very large tunneling magnetoresistance (TMR). Here we report voltage control of TMR formed by four-layer CrI3 sandwiched by monolayer graphene contacts in a dual-gated structure. By varying the gate voltages at fixed magnetic field, the device can be switched reversibly between bistable magnetic states with the same net magnetization but drastically different resistance (by a factor of 10 or more). In addition, without switching the state, the TMR can be continuously modulated between 17,000% and 57,000%, due to the combination of spin-dependent tunnel barrier with changing carrier distributions in the graphene contacts. Our work demonstrates new kinds of magnetically moderated transistor action and opens up possibilities for voltage-controlled van der Waals spintronic devices.
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22. 22
  Manchon, A.; Železný, J.; Miron, I. M.; Jungwirth, T.; Sinova, J.; Thiaville, A.; Garello, K.; Gambardella, P. Current-induced spin-orbit torques in ferromagnetic and antiferromagnetic systems. Rev. Mod. Phys. 2019, 91, 035004 DOI: 10.1103/RevModPhys.91.035004
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  22
  Current-induced spin-orbit torques in ferromagnetic and antiferromagnetic systems
  Manchon, A.; Zelezny, J.; Miron, I. M.; Jungwirth, T.; Sinova, J.; Thiaville, A.; Garello, K.; Gambardella, P.
  Reviews of Modern Physics (2019), 91 (3), 035004CODEN: RMPHAT; ISSN:1539-0756. (American Physical Society)
  Spin-orbit coupling in inversion-asym. magnetic crystals and structures has emerged as a powerful tool to generate complex magnetic textures, interconvert charge and spin under applied current, and control magnetization dynamics. Current-induced spin-orbit torques mediate the transfer of angular momentum from the lattice to the spin system, leading to sustained magnetic oscillations or switching of ferromagnetic as well as antiferromagnetic structures. The manipulation of magnetic order, domain walls, and skyrmions by spin-orbit torques provides evidence of the microscopic interactions between charge and spin in a variety of materials and opens novel strategies to design spintronic devices with potentially high impact in data storage, nonvolatile logic, and magnonic applications. This paper reviews recent progress in the field of spin orbitronics, focusing on theor. models, material properties, and exptl. results obtained on bulk noncentrosym. conductors and multilayer heterostructures, including metals, semiconductors, and topol. insulator systems. Relevant aspects for improving the understanding and optimizing the efficiency of nonequil. spin-orbit phenomena in future nanoscale devices are also discussed.
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23. 23
  Ramaswamy, R.; Lee, J. M.; Cai, K.; Yang, H. Recent advances in spin-orbit torques: Moving towards device applications. Appl. Phys. Rev. 2018, 5, 031107 DOI: 10.1063/1.5041793
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  Recent advances in spin-orbit torques: Moving towards device applications
  Ramaswamy, Rajagopalan; Lee, Jong Min; Cai, Kaiming; Yang, Hyunsoo
  Applied Physics Reviews (2018), 5 (3), 031107/1-031107/19CODEN: APRPG5; ISSN:1931-9401. (American Institute of Physics)
  The ability of spintronic devices to utilize an elec. current for manipulating the magnetization has resulted in large-scale developments, such as magnetic random access memories and boosted the spintronic research area. In this regard, over the last decade, magnetization manipulation using spin-orbit torque has been devoted a lot of research attention as it shows a great promise for future ultrafast and power efficient magnetic memories. In this review, we summarize the latest advancements in spin-orbit torque research and highlight some of the tech. challenges for practical spin-orbit torque devices. We will first introduce the basic concepts and highlight the latest material choices for spin-orbit torque devices. Then, we will summarize the important advancements in the study of magnetization switching dynamics using spin-orbit torque, which are important from scientific as well as technol. aspects. The final major section focuses on the concept of external assist field-free spin-orbit torque switching which is a requirement for practical spin-orbit torque devices. (c) 2018 American Institute of Physics.
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24. 24
  Nikolić, B. K.; Dolui, K.; Petrovi, M.; Plecháč, P.; Markussen, T.; Stokbro, K. In Handbook of Materials Modeling; Andreoni, W., Ed.; Springer: Cham, 2018; pp 1– 35.
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25. 25
  Belashchenko, K. D.; Kovalev, A. A.; van Schilfgaarde, M. First-principles calculation of spin-orbit torque in a Co/Pt bilayer. Phys. Rev. Materials 2019, 3, 011401 DOI: 10.1103/PhysRevMaterials.3.011401
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  First-principles calculation of spin-orbit torque in a Co/Pt bilayer
  Belashchenko, K. D.; Kovalev, Alexey A.; van Schilfgaarde, M.
  Physical Review Materials (2019), 3 (1), 011401CODEN: PRMHBS; ISSN:2475-9953. (American Physical Society)
  The angular dependence of spin-orbit torque in a disordered Co/Pt bilayer is calcd. using a first-principles nonequil. Green's function formalism with an explicit supercell averaging over Anderson disorder. In addn. to the usual dampinglike and fieldlike terms, the odd torque contains a sizable planar Hall-like term (m·E)m×(z×m) whose contribution to current-induced damping is consistent with exptl. observations. The dampinglike and planar Hall-like torquances depend weakly on disorder strength, while the fieldlike torquance declines with increasing disorder. The torques that contribute to damping are almost entirely due to spin-orbit coupling on the Pt atoms, but the fieldlike torque does not require it.
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26. 26
  Belashchenko, K. D.; Kovalev, A. A.; van Schilfgaarde, M. Interfacial contributions to spin-orbit torque and magnetoresistance in ferromagnet/heavy-metal bilayers. Phys. Rev. B: Condens. Matter Mater. Phys. 2020, 101, 020407R, DOI: 10.1103/PhysRevB.101.020407
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27. 27
  Stefanucci, G.; van Leeuwen, R. Nonequilibrium Many-Body Theory of Quantum Systems: A Modern Introduction; Cambridge University Press: Cambridge, 2013.
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28. 28
  Capelle, K.; Vignale, G.; Györffy, B. L. Spin Currents and Spin Dynamics in Time-Dependent Density-Functional Theory. Phys. Rev. Lett. 2001, 87, 206403, DOI: 10.1103/PhysRevLett.87.206403
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  Spin Currents and Spin Dynamics in Time-Dependent Density-Functional Theory
  Capelle, K.; Vignale, G.; Gyorffy, B. L.
  Physical Review Letters (2001), 87 (20), 206403/1-206403/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
  We derive and analyze the equation of motion for the spin degrees of freedom within time-dependent spin-d.-functional theory (TD-SDFT). The results are (i) a prescription for obtaining many-body corrections to the single-particle spin currents from the Kohn-Sham equation of TD-SDFT, (ii) the existence of an exchange-correlation (xc) torque within TD-SDFT, (iii) a prescription for calcg., from TD-SDFT, the torque exerted by spin currents on the spin magnetization, (iv) a novel exact constraint on approx. xc functionals, and (v) the discovery of serious deficiencies of popular approxns. to TD-SDFT when applied to spin dynamics.
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29. 29
  Eich, F. G.; Gross, E. K. U. Transverse Spin-Gradient Functional for Noncollinear Spin-Density-Functional Theory. Phys. Rev. Lett. 2013, 111, 156401, DOI: 10.1103/PhysRevLett.111.156401
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  29
  Transverse spin-gradient functional for noncollinear spin-density-functional theory
  Eich, F. G.; Gross, E. K. U.
  Physical Review Letters (2013), 111 (15), 156401/1-156401/5CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
  We present a novel functional for spin-d.-functional theory aiming at the description of noncollinear magnetic structures. The construction of the functional employs the spin-spiral-wave state of the uniform electron gas as ref. system. We show that the functional depends on transverse gradients of the spin magnetization; i.e., in contrast with the widely used local spin d. approxn., the functional is sensitive to local changes of the direction of the spin magnetization. As a consequence the exchange-correlation magnetic field is not parallel to the spin magnetization and a local spin torque is present in the ground state of the Kohn-Sham system. As a proof of principle, we apply the functional to a Chromium monolayer in the noncollinear 120°-Neel state.
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30. 30
  Ellis, M. O. A.; Stamenova, M.; Sanvito, S. Multiscale modeling of current-induced switching in magnetic tunnel junctions using ab initio spin-transfer torques. Phys. Rev. B: Condens. Matter Mater. Phys. 2017, 96, 224410, DOI: 10.1103/PhysRevB.96.224410
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31. 31
  Freimuth, F.; Blügel, S.; Mokrousov, Y. Spin-orbit torques in Co/Pt(111) and Mn/W(001) magnetic bilayers from first principles. Phys. Rev. B: Condens. Matter Mater. Phys. 2014, 90, 174423, DOI: 10.1103/PhysRevB.90.174423
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  31
  Spin-orbit torques in Co/Pt(111) and Mn/W(001) magnetic bilayers from first principles
  Freimuth, Frank; Bluegel, Stefan; Mokrousov, Yuriy
  Physical Review B: Condensed Matter and Materials Physics (2014), 90 (17), 174423/1-174423/10, 10 pp.CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
  An applied elec. current through a space-inversion asym. magnet induces spin-orbit torques (SOTs) on the magnetic moments, which holds much promise for future memory devices. We discuss general Green's function expressions suitable to compute the linear-response SOT in disordered ferromagnets. The SOT can be decompd. into an even and an odd component with respect to magnetization reversal, where in the limit of vanishing disorder the even SOT is given by the const. Berry curvature of the occupied states, while the odd part exhibits a divergence with respect to disorder strength. Within this formalism, we perform first-principles d.-functional theory calcns. of the SOT in Co/Pt(111) and Mn/W(001) magnetic bilayers. We find the even and odd torque components to be of comparable magnitude. Moreover, the odd torque depends strongly on an addnl. capping layer, while the even torque is less sensitive. We show that the even torque is nearly entirely mediated by spin currents in contrast to the odd torque, which can contain an important contribution not due to spin transfer. Our results are in agreement with expts., showing that our linear-response theory is well-suited for the description of SOTs in complex ferromagnets.
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32. 32
  Mahfouzi, F.; Kioussis, N. First-principles study of the angular dependence of the spin-orbit torque in Pt/Co and Pd/Co bilayers. Phys. Rev. B: Condens. Matter Mater. Phys. 2018, 97, 224426, DOI: 10.1103/PhysRevB.97.224426
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33. 33
  Edelstein, V. M. Spin polarization of conduction electrons induced by electric current in two-dimensional asymmetric electron systems. Solid State Commun. 1990, 73, 233, DOI: 10.1016/0038-1098(90)90963-C
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34. 34
  Aronov, A. G.; Lyanda-Geller, Y. B. Nuclear electric resonance and orientation of carrier spins by an electric field. JETP Letters 1989, 50, 431
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35. 35
  Chang, P.-H.; Markussen, T.; Smidstrup, S.; Stokbro, K.; Nikolić, B. K. Nonequilibrium spin texture within a thin layer below the surface of current-carrying topological insulator Bi₂Se₃: A first-principles quantum transport study. Phys. Rev. B: Condens. Matter Mater. Phys. 2015, 92, 201406R, DOI: 10.1103/PhysRevB.92.201406
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  Nonequilibrium spin texture within a thin layer below the surface of current-carrying topological insulator Bi2Se3: a first-principles quantum transport study
  Chang, Po-Hao; Markussen, Troels; Smidstrup, Soeren; Stokbro, Kurt; Nikolic, Branislav K.
  Physical Review B: Condensed Matter and Materials Physics (2015), 92 (20), 201406/1-201406/5CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
  We predict that unpolarized charge current injected into a ballistic thin film of prototypical topol. insulator (TI) Bi2Se3 will generate a noncollinear spin texture S(r) on its surface. Furthermore, the nonequil. spin texture will extend into an ≃2-nm-thick layer below the TI surfaces due to penetration of evanescent wave functions from the metallic surfaces into the bulk of TI. Averaging S(r)over a few angstroms along the longitudinal direction defined by the current flow reveals a large component pointing in the transverse direction. In addn., we find an order of magnitude smaller out-of-plane component when the direction of injected current with respect to Bi and Se atoms probes the largest hexagonal warping of the Dirac-cone dispersion on the TI surface. Our anal. is based on an extension of the nonequil. Green's functions combined with d. functional theory (NEGF+DFT) to situations involving noncollinear spins and spin-orbit coupling. We also demonstrate how DFT calcns. with a properly optimized local orbital basis set can precisely match putatively more accurate calcns. with a plane-wave basis set for the supercell of Bi2Se3.
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36. 36
  Marmolejo-Tejada, J. M.; Chang, P.-H.; Lazić, P.; Smidstrup, S.; Stradi, D.; Stokbro, K.; Nikolić, B. K. Proximity band structure and spin textures on both sides of topological-insulator/ferromagnetic-metal Interface and their charge transport probes. Nano Lett. 2017, 17, 5626, DOI: 10.1021/acs.nanolett.7b02511
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  36
  Proximity band structure and spin textures on both sides of topological-insulator/ferromagnetic-metal interface and their charge transport probes
  Marmolejo-Tejada, Juan Manuel; Dolui, Kapildeb; Lazic, Predrag; Chang, Po-Hao; Smidstrup, Soeren; Stradi, Daniele; Stokbro, Kurt; Nikolic, Branislav K.
  Nano Letters (2017), 17 (9), 5626-5633CODEN: NALEFD; ISSN:1530-6984. (American Chemical Society)
  The control of recently obsd. spintronic effects in topol.-insulator/ferromagnetic-metal (TI/FM) heterostructures is thwarted by the lack of understanding of band structure and spin textures around their interfaces. Here we combine d. functional theory with Green's function techniques to obtain the spectral function at any plane passing through atoms of Bi2Se3 and Co or Cu layers comprising the interface. Instead of naively assumed Dirac cone gapped by the proximity exchange field spectral function, we find that the Rashba ferromagnetic model describes the spectral function on the surface of Bi2Se3 in contact with Co near the Fermi level E0F, where circular and snowflake-like const. energy contours coexist around which spin locks to momentum. The remnant of the Dirac cone is hybridized with evanescent wave functions from metallic layers and pushed, due to charge transfer from Co or Cu layers, a few tenths of an electron-volt below E0F for both Bi2Se3/Co and Bi2Se3/Cu interfaces while hosting distorted helical spin texture wounding around a single circle. These features explain recent observation of sensitivity of spin-to-charge conversion signal at TI/Cu interface to tuning of E0F. Crucially for spin-orbit torque in TI/FM heterostructures, few monolayers of Co adjacent to Bi2Se3 host spectral functions very different from the bulk metal, as well as in-plane spin textures (despite Co magnetization being out-of-plane) due to proximity spin-orbit coupling in Co induced by Bi2Se3. We predict that out-of-plane tunneling anisotropic magnetoresistance in Cu/Bi2Se3/Co vertical heterostructure can serve as a sensitive probe of the type of spin texture residing at E0F.
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37. 37
  Zhu, Z. Y.; Cheng, Y. C.; Schwingenschlögl, U. Giant spin-orbit-induced spin splitting in two-dimensional transition-metal dichalcogenide semiconductors. Phys. Rev. B: Condens. Matter Mater. Phys. 2011, 84, 153402, DOI: 10.1103/PhysRevB.84.153402
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  Giant spin-orbit-induced spin splitting in two-dimensional transition-metal dichalcogenide semiconductors
  Zhu, Z. Y.; Cheng, Y. C.; Schwingenschlogl, U.
  Physical Review B: Condensed Matter and Materials Physics (2011), 84 (15), 153402/1-153402/5CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
  Fully relativistic first-principles calcns. based on d. functional theory are performed to study the spin-orbit-induced spin splitting in monolayer systems of the transition-metal dichalcogenides MoS2, MoSe2, WS2, and WSe2. All these systems are identified as direct-band-gap semiconductors. Giant spin splittings of 148-456 meV result from missing inversion symmetry. Full out-of-plane spin polarization is due to the two-dimensional nature of the electron motion and the potential gradient asymmetry. By suppression of the Dyakonov-Perel spin relaxation, spin lifetimes are expected to be very long. Because of the giant spin splittings, the studied materials have great potential in spintronics applications.
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38. 38
  Ge, Y.; Liu, A. Y. Effect of dimensionality and spin-orbit coupling on charge-density-wave transition in 2H-TaSe₂. Phys. Rev. B: Condens. Matter Mater. Phys. 2012, 86, 104101, DOI: 10.1103/PhysRevB.86.104101
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  Effect of dimensionality and spin-orbit coupling on charge-density-wave transition in 2H-TaSe2
  Ge, Yizhi; Liu, Amy Y.
  Physical Review B: Condensed Matter and Materials Physics (2012), 86 (10), 104101/1-104101/7CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
  A first-principles investigation of the charge-d.-wave (CDW) instability in bulk and single-layer 2H-TaSe2 is presented, focusing on the origin of the CDW instability, the role of the interlayer interactions, and the effect of spin-orbit coupling. While interlayer interactions and spin-orbit coupling have a nontrivial effect on the electronic structure and Fermi surface, the CDW instability is predicted to remain robust, with little or no change in the ordering wave vector. This is in contrast to the closely related 2H-NbSe2 material, where the CDW wave vector depends on dimensionality. The results are analyzed in terms of the interplay between the momentum dependence of the electron-phonon coupling and that of the electronic response function.
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39. 39
  Petrović, M. D.; Popescu, B. S.; Bajpai, U.; Plecháč, P.; Nikolić, B. K. Spin and Charge Pumping by a Steady or Pulse-Current-Driven Magnetic Domain Wall: A Self- Consistent Multiscale Time-Dependent Quantum-Classical Hybrid Approach. Phys. Rev. Appl. 2018, 10, 054038 DOI: 10.1103/PhysRevApplied.10.054038
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  39
  Spin and Charge Pumping by a Steady or Pulse-Current-Driven Magnetic Domain Wall: A Self-Consistent Multiscale Time-Dependent Quantum-Classical Hybrid Approach
  Petrovic, Marko D.; Popescu, Bogdan S.; Bajpai, Utkarsh; Plechac, Petr; Nikolic, Branislav K.
  Physical Review Applied (2018), 10 (5), 054038CODEN: PRAHB2; ISSN:2331-7019. (American Physical Society)
  We introduce a multiscale framework that combines a time-dependent nonequil. Green-function (TDNEGF) algorithm, scaling linearly in the no. of time steps and describing quantum-mech. the conduction electrons in the presence of time-dependent fields of arbitrary strength or frequency, with classical time evolution of localized magnetic moments described by the Landau-Lifshitz-Gilbert (LLG) equation. The TDNEGF+LLG framework can be applied to a variety of problems where current-driven spin torque induces the dynamics of magnetic moments as the key resource for next-generation spintronics. Previous approaches to such nonequil. many-body systems (like the steady-state-NEGF+LLG framework) neglect noncommutativity of a quantum Hamiltonian of conduction electrons at different times and, therefore, the impact of time-dependent magnetic moments on electrons leading to the pumping of spin and charge currents. The pumped currents can, in turn, self-consistently affect the dynamics of magnetic moments themselves. Using the magnetic domain wall (DW) as an example, we predict that its motion will pump time-dependent spin and charge currents (on top of the unpolarized dc charge current injected through normal-metal leads to drive the DW motion), where the latter can be viewed as a realization of quantum charge pumping due to the time dependence of the Hamiltonian and the left-right symmetry breaking of the two-terminal device structure. The conversion of ac components of spin current, whose amplitude increases (decreases) as the DW approaches (recedes from) the normal-metal lead, into ac voltage via the inverse spin Hall effect offers a tool to precisely track the DW position along magnetic nanowire. We also quantify the DW transient inertial displacement due to its acceleration and deceleration by pulse current and the entailed spin and charge pumping. Finally, TDNEGF+LLG as a nonperturbative (i.e., numerically exact) framework allows us to establish the limits of validity of the so-called spin-motive force (SMF) theory for pumped charge current by time-dependent magnetic textures-the perturbative anal. formula of SMF theory becomes inapplicable for large frequencies (but unrealistic in a magnetic system) and, more importantly, for increasing noncollinearity when the angles between neighboring magnetic moments exceed approx. 10o.
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  Grimme, S. Semiempirical GGA-type density functional constructed with a long-range dispersion correction. J. Comput. Chem. 2006, 27, 1787– 1799, DOI: 10.1002/jcc.20495
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  Semiempirical GGA-type density functional constructed with a long-range dispersion correction
  Grimme, Stefan
  Journal of Computational Chemistry (2006), 27 (15), 1787-1799CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
  A new d. functional (DF) of the generalized gradient approxn. (GGA) type for general chem. applications termed B97-D is proposed. It is based on Becke's power-series ansatz from 1997 and is explicitly parameterized by including damped atom-pairwise dispersion corrections of the form C6·R-6. A general computational scheme for the parameters used in this correction has been established and parameters for elements up to xenon and a scaling factor for the dispersion part for several common d. functionals (BLYP, PBE, TPSS, B3LYP) are reported. The new functional is tested in comparison with other GGAs and the B3LYP hybrid functional on std. thermochem. benchmark sets, for 40 noncovalently bound complexes, including large stacked arom. mols. and group II element clusters, and for the computation of mol. geometries. Further cross-validation tests were performed for organometallic reactions and other difficult problems for std. functionals. In summary, it is found that B97-D belongs to one of the most accurate general purpose GGAs, reaching, for example for the G97/2 set of heat of formations, a mean abs. deviation of only 3.8 kcal mol-1. The performance for noncovalently bound systems including many pure van der Waals complexes is exceptionally good, reaching on the av. CCSD(T) accuracy. The basic strategy in the development to restrict the d. functional description to shorter electron correlation lengths scales and to describe situations with medium to large interat. distances by damped C6·R-6 terms seems to be very successful, as demonstrated for some notoriously difficult reactions. As an example, for the isomerization of larger branched to linear alkanes, B97-D is the only DF available that yields the right sign for the energy difference. From a practical point of view, the new functional seems to be quite robust and it is thus suggested as an efficient and accurate quantum chem. method for large systems where dispersion forces are of general importance.
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42. 42
  Giannozzi, P. QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials. J. Phys.: Condens. Matter 2009, 21, 395502, DOI: 10.1088/0953-8984/21/39/395502
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  QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials
  Giannozzi Paolo; Baroni Stefano; Bonini Nicola; Calandra Matteo; Car Roberto; Cavazzoni Carlo; Ceresoli Davide; Chiarotti Guido L; Cococcioni Matteo; Dabo Ismaila; Dal Corso Andrea; de Gironcoli Stefano; Fabris Stefano; Fratesi Guido; Gebauer Ralph; Gerstmann Uwe; Gougoussis Christos; Kokalj Anton; Lazzeri Michele; Martin-Samos Layla; Marzari Nicola; Mauri Francesco; Mazzarello Riccardo; Paolini Stefano; Pasquarello Alfredo; Paulatto Lorenzo; Sbraccia Carlo; Scandolo Sandro; Sclauzero Gabriele; Seitsonen Ari P; Smogunov Alexander; Umari Paolo; Wentzcovitch Renata M
  Journal of physics. Condensed matter : an Institute of Physics journal (2009), 21 (39), 395502 ISSN:.
  QUANTUM ESPRESSO is an integrated suite of computer codes for electronic-structure calculations and materials modeling, based on density-functional theory, plane waves, and pseudopotentials (norm-conserving, ultrasoft, and projector-augmented wave). The acronym ESPRESSO stands for opEn Source Package for Research in Electronic Structure, Simulation, and Optimization. It is freely available to researchers around the world under the terms of the GNU General Public License. QUANTUM ESPRESSO builds upon newly-restructured electronic-structure codes that have been developed and tested by some of the original authors of novel electronic-structure algorithms and applied in the last twenty years by some of the leading materials modeling groups worldwide. Innovation and efficiency are still its main focus, with special attention paid to massively parallel architectures, and a great effort being devoted to user friendliness. QUANTUM ESPRESSO is evolving towards a distribution of independent and interoperable codes in the spirit of an open-source project, where researchers active in the field of electronic-structure calculations are encouraged to participate in the project by contributing their own codes or by implementing their own ideas into existing codes.
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43. 43
  Liechtenstein, A. I.; Anisimov, V. I.; Zaanen, J. Density-functional theory and strong interactions: Orbital ordering in Mott-Hubbard insulators. Phys. Rev. B: Condens. Matter Mater. Phys. 1995, 52, R5467– R5470, DOI: 10.1103/PhysRevB.52.R5467
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  Density-functional theory and strong interactions: orbital ordering in Mott-Hubbard insulators
  Liechtenstein, A. I.; Anisimov, V. I.; Zaanen, J.
  Physical Review B: Condensed Matter (1995), 52 (8), R5467-R5470CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)
  Evidence is presented that within the d.-functional theory orbital polarization has to be treated on an equal footing with spin polarization and charge d. for strongly interacting electron systems. Using a basis-set independent generalization of the LDA + U functional, we show that electronic orbital ordering is a necessary condition to obtain the correct crystal structure and parameters of the exchange interaction for the Mott-Hubbard insulator KCuF3.
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44. 44
  Lado, J. L.; Fernández-Rossier, J. On the origin of magnetic anisotropy in two dimensional CrI₃. 2D Mater. 2017, 4, 035002 DOI: 10.1088/2053-1583/aa75ed
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  On the origin of magnetic anisotropy in two dimensional CrI♂
  Lado, J. L.; Fernandez-Rossier, J.
  2D Materials (2017), 4 (3), 035002/1-035002/9CODEN: DMATB7; ISSN:2053-1583. (IOP Publishing Ltd.)
  The observation of ferromagnetic order in a monolayer of CrI♂ has been recently reported, with a Curie temp. of 45 K and off-plane easy axis. Here we study the origin of magnetic anisotropy, a necessary ingredient to have magnetic order in two dimensions, combining two levels of modeling, d. functional calcns. and spin model Hamiltonians. We find two different contributions to the magnetic anisotropy of the material, favoring off-plane magnetization and opening a gap in the spin wave spectrum. First, ferromagnetic super-exchange across the ≃90 degree Cr-I-Cr bonds, are anisotropic, due to the spin-orbit interaction of the ligand I atoms. Second, a much smaller contribution that comes from the single ion anisotropy of the S = 3/2 Cr atom. Our results permit to establish the XXZ Hamiltonian, with a very small single ion anisotropy, as the adequate spin model for this system. Using spin wave theory we est. the Curie temp. and we highlight the essential role played by the gap that magnetic anisotropy induces on the magnon spectrum.
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45. 45
  Zollner, K.; Faria Junior, P. E.; Fabian, J. Proximity exchange effects in MoSe₂ and WSe₂ heterostructures with CrI₃: Twist angle, layer, and gate dependence. Phys. Rev. B: Condens. Matter Mater. Phys. 2019, 100, 085128 DOI: 10.1103/PhysRevB.100.085128
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  Proximity exchange effects in MoSe32and WSe2 heterostructures with CrI3: twist angle, layer, and gate dependence
  Zollner, Klaus; Faria Junior, Paulo E.; Fabian, Jaroslav
  Physical Review B (2019), 100 (8), 085128CODEN: PRBHB7; ISSN:2469-9969. (American Physical Society)
  Proximity effects in two-dimensional (2D) van der Waals heterostructures offer controllable ways to tailor the electronic band structure of adjacent materials. Proximity exchange in particular is important for making materials magnetic without hosting magnetic ions. Such synthetic magnets could be used for studying magnetotransport in high-mobility 2D materials, or magneto-optics in highly absorptive nominally nonmagnetic semiconductors. Using first-principles calcns., we show that the proximity exchange in monolayer MoSe2 and WSe2 due to ferromagnetic monolayer CrI3 can be tuned (even qual.) by twisting and gating. Remarkably, the proximity exchange remains the same when using antiferromagnetic CrI3 bilayer, paving the way for optical and elec. detection of layered antiferromagnets. Interestingly, the proximity exchange is opposite to the exchange of the adjacent antiferromagnetic layer. Finally, we show that the proximity exchange is confined to the layer adjacent to CrI3, and that adding a sepg. hBN barrier drastically reduces the proximity effect. We complement our ab initio results with tight-binding modeling and solve the Bethe-Salpeter equation to provide exptl. verifiable optical signatures (in the exciton spectra) of the proximity exchange effects.
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46. 46
  Zhang, S. S.-L.; Vignale, G.; Zhang, S. Anisotropic magnetoresistance driven by surface spin-orbit scattering. Phys. Rev. B: Condens. Matter Mater. Phys. 2015, 92, 024412 DOI: 10.1103/PhysRevB.92.024412
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  Anisotropic magnetoresistance driven by surface spin-orbit scattering
  Zhang, Steven S.-L.; Vignale, Giovanni; Zhang, Shufeng
  Physical Review B: Condensed Matter and Materials Physics (2015), 92 (2), 024412/1-024412/6CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
  In a bilayer consisting of an insulator and a ferromagnetic metal (FM), interfacial spin-orbit scattering leads to spin mixing of the two conducting channels of the FM, which results in an unconventional anisotropic magnetoresistance (AMR). We theor. investigate the magnetotransport in such bilayer structures by solving the spinor Boltzmann transport equation with the generalized Fuchs-Sondheimer boundary condition that takes into account the effect of spin-orbit scattering at the interface. We find that the new AMR exhibits a peculiar angular dependence which can serve as a genuine exptl. signature. We also det. the dependence of the AMR on film thickness as well as resistivity spin asymmetry of the FM.
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  Kresse, G.; Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B: Condens. Matter Mater. Phys. 1999, 59, 1758– 1775, DOI: 10.1103/PhysRevB.59.1758
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  From ultrasoft pseudopotentials to the projector augmented-wave method
  Kresse, G.; Joubert, D.
  Physical Review B: Condensed Matter and Materials Physics (1999), 59 (3), 1758-1775CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)
  The formal relationship between ultrasoft (US) Vanderbilt-type pseudopotentials and Blochl's projector augmented wave (PAW) method is derived. The total energy functional for US pseudopotentials can be obtained by linearization of two terms in a slightly modified PAW total energy functional. The Hamilton operator, the forces, and the stress tensor are derived for this modified PAW functional. A simple way to implement the PAW method in existing plane-wave codes supporting US pseudopotentials is pointed out. In addn., crit. tests are presented to compare the accuracy and efficiency of the PAW and the US pseudopotential method with relaxed-core all-electron methods. These tests include small mols. (H2, H2O, Li2, N2, F2, BF3, SiF4) and several bulk systems (diamond, Si, V, Li, Ca, CaF2, Fe, Co, Ni). Particular attention is paid to the bulk properties and magnetic energies of Fe, Co, and Ni.
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48. 48
  Schlipf, M.; Gygi, F. Optimization algorithm for the generation of ONCV pseudopotentials. Comput. Phys. Commun. 2015, 196, 36, DOI: 10.1016/j.cpc.2015.05.011
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  Optimization algorithm for the generation of ONCV pseudopotentials
  Schlipf, Martin; Gygi, Francois
  Computer Physics Communications (2015), 196 (), 36-44CODEN: CPHCBZ; ISSN:0010-4655. (Elsevier B.V.)
  We present an optimization algorithm to construct pseudopotentials and use it to generate a set of Optimized Norm-Conserving Vanderbilt (ONCV) pseudopotentials for elements up to Z = 83 (Bi) (excluding Lanthanides). We introduce a quality function that assesses the agreement of a pseudopotential calcn. with all-electron FLAPW results, and the necessary plane-wave energy cutoff. This quality function allows us to use a Nelder-Mead optimization algorithm on a training set of materials to optimize the input parameters of the pseudopotential construction for most of the periodic table. We control the accuracy of the resulting pseudopotentials on a test set of materials independent of the training set. We find that the automatically constructed pseudopotentials (http://www.quantum-simulation.org) provide a good agreement with the all-electron results obtained using the FLEUR code with a plane-wave energy cutoff of approx. 60 Ry.
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49. 49
  MacNeill, D.; Stiehl, G. M.; Guimaraes, M. H. D.; Buhrman, R. A.; Park, J.; Ralph, D. C. Control of spin-orbit torques through crystal symmetry in WTe₂/ferromagnet bilayers. Nat. Phys. 2017, 13, 300, DOI: 10.1038/nphys3933
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  Control of spin-orbit torques through crystal symmetry in WTe2/ferromagnet bilayers
  MacNeill, D.; Stiehl, G. M.; Guimaraes, M. H. D.; Buhrman, R. A.; Park, J.; Ralph, D. C.
  Nature Physics (2017), 13 (3), 300-305CODEN: NPAHAX; ISSN:1745-2473. (Nature Publishing Group)
  Recent discoveries regarding current-induced spin-orbit torques produced by heavy-metal/ferromagnet and topol.-insulator/ferromagnet bilayers provide the potential for dramatically improved efficiency in the manipulation of magnetic devices. However, in expts. performed to date, spin-orbit torques have an important limitation-the component of torque that can compensate magnetic damping is required by symmetry to lie within the device plane. This means that spin-orbit torques can drive the most current-efficient type of magnetic reversal (antidamping switching) only for magnetic devices with in-plane anisotropy, not the devices with perpendicular magnetic anisotropy that are needed for high-d. applications. Here we show exptl. that this state of affairs is not fundamental, but rather one can change the allowed symmetries of spin-orbit torques in spin-source/ferromagnet bilayer devices by using a spin-source material with low cryst. symmetry. We use WTe2, a transition-metal dichalcogenide whose surface crystal structure has only one mirror plane and no two-fold rotational invariance. Consistent with these symmetries, we generate an out-of-plane antidamping torque when current is applied along a low-symmetry axis of WTe2/Permalloy bilayers, but not when current is applied along a high-symmetry axis. Controlling spin-orbit torques by crystal symmetries in multilayer samples provides a new strategy for optimizing future magnetic technologies.
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50. 50
  Garello, K.; Miron, I. M.; Avci, C. O.; Freimuth, F.; Mokrousov, Y.; Blügel, S.; Auffret, S.; Boulle, O.; Gaudin, G.; Gambardella, P. Symmetry and magnitude of spin-orbit torques in ferromagnetic heterostructures. Nat. Nanotechnol. 2013, 8, 587, DOI: 10.1038/nnano.2013.145
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  Symmetry and magnitude of spin-orbit torques in ferromagnetic heterostructures
  Garello, Kevin; Miron, Ioan Mihai; Avci, Can Onur; Freimuth, Frank; Mokrousov, Yuriy; Bluegel, Stefan; Auffret, Stephane; Boulle, Olivier; Gaudin, Gilles; Gambardella, Pietro
  Nature Nanotechnology (2013), 8 (8), 587-593CODEN: NNAABX; ISSN:1748-3387. (Nature Publishing Group)
  Recent demonstrations of magnetization switching induced by in-plane current injection in heavy metal/ferromagnetic heterostructures have drawn increasing attention to spin torques based on orbital-to-spin momentum transfer. The symmetry, magnitude and origin of spin-orbit torques (SOTs), however, remain a matter of debate. Here the authors report on the three-dimensional vector measurement of SOTs in AlOx/Co/Pt and MgO/CoFeB/Ta trilayers using harmonic anal. of the anomalous and planar Hall effects. The authors provide a general scheme to measure the amplitude and direction of SOTs as a function of the magnetization direction. Based on space and time inversion symmetry arguments, heavy metal/ferromagnetic layers allow for two different SOTs having odd and even behavior with respect to magnetization reversal. Such torques include strongly anisotropic field-like and spin transfer-like components, which depend on the type of heavy metal layer and annealing treatment. These results call for SOT models that go beyond the spin Hall and Rashba effects studied thus far.
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51. 51
  Mahfouzi, F.; Nikolić, B. K.; Kioussis, N. Antidamping spin-orbit torque driven by spin-flip reflection mechanism on the surface of a topological insulator: A time-dependent nonequilibrium Green function approach. Phys. Rev. B: Condens. Matter Mater. Phys. 2016, 93, 115419, DOI: 10.1103/PhysRevB.93.115419
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  Pesin, D. A.; MacDonald, A. H. Quantum kinetic theory of current-induced torques in Rashba ferromagnets. Phys. Rev. B: Condens. Matter Mater. Phys. 2012, 86, 014416 DOI: 10.1103/PhysRevB.86.014416
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  Quantum kinetic theory of current-induced torques in Rashba ferromagnets
  Pesin, D. A.; MacDonald, A. H.
  Physical Review B: Condensed Matter and Materials Physics (2012), 86 (1), 014416/1-014416/5CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
  Motivated by recent exptl. studies of thin-film devices contg. a single ferromagnetic layer, we develop a quantum kinetic theory of current-induced magnetic torques in Rashba-model ferromagnets. We find that the current-induced spin densities, responsible for the switching behavior, are due most essentially to spin-dependent quasiparticle lifetimes and derive analytic expressions for relevant limits of a simple model. Quant. model parameter ests. suggest that spin-orbit coupling in the adjacent metal normal magnetic layer must play an essential role in the strength of the switching effect.
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53. 53
  Kalitsov, A.; Nikolaev, S. A.; Velev, J.; Chshiev, M.; Mryasov, O. Intrinsic spin-orbit torque in a single-domain nanomagnet. Phys. Rev. B: Condens. Matter Mater. Phys. 2017, 96, 214430, DOI: 10.1103/PhysRevB.96.214430
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54. 54
  Zollner, K.; Petrović, M. D.; Dolui, K.; Plecháč, P.; Nikolić, B. K.; Fabian, J. Purely interfacial and highly tunable spin-orbit torque in graphene doubly proximitized by two-dimensional magnet Cr₂Ge₂Te₆ and monolayer WS₂. arXiv, 2019, 1910.08072, https://arxiv.org/abs/1910.08072.
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55. 55
  Zhang, W.-B.; Qu, Q.; Zhu, P.; Lam, C.-H. Robust intrinsic ferromagnetism and half semiconductivity in stable two-dimensional single-layer chromium trihalides. J. Mater. Chem. C 2015, 3, 12457– 12468, DOI: 10.1039/C5TC02840J
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  Robust intrinsic ferromagnetism and half semiconductivity in stable two-dimensional single-layer chromium trihalides
  Zhang, Wei-Bing; Qu, Qian; Zhu, Peng; Lam, Chi-Hang
  Journal of Materials Chemistry C: Materials for Optical and Electronic Devices (2015), 3 (48), 12457-12468CODEN: JMCCCX; ISSN:2050-7534. (Royal Society of Chemistry)
  Two-dimensional (2D) intrinsic ferromagnetic (FM) semiconductors are crucial to develop low-dimensional spintronic devices. Using d. functional theory, we show that single-layer chromium trihalides (SLCTs) (CrX3 (X = F, Cl, Br, I)) constitute a series of stable 2D intrinsic FM semiconductors. A free-standing SLCT can be easily exfoliated from the bulk crystal, due to a low cleavage energy and a high in-plane stiffness. Electronic structure calcns. using the HSE06 functional indicate that both bulk and single-layer CrX3 are half semiconductors with indirect gaps and their valence and conduction bands are fully spin-polarized in the same spin direction. The energy gaps and absorption edges of CrBr3 and CrI3 are found to be in the visible frequency range, which implies possible opto-electronic applications. Furthermore, SLCTs are found to possess a large magnetic moment of 3 μB per formula unit and a sizable magnetic anisotropy energy. The magnetic exchange consts. of SLCTs are then extd. using the Heisenberg spin Hamiltonian and the microscopic origins of the various exchange interactions are analyzed. A competition between a near 90° FM superexchange and a direct antiferromagnetic (AFM) exchange results in a FM nearest-neighbor exchange interaction. The next and third nearest-neighbor exchange interactions are found to be FM and AFM, resp., and this can be understood by the angle-dependent extended Cr-X-X-Cr superexchange interaction. Moreover, the Curie temps. of SLCTs are also predicted using Monte Carlo simulations and the values can be further increased by applying a biaxial tensile strain. The unique combination of robust intrinsic ferromagnetism, half semicond. and large magnetic anisotropy energies renders the SLCTs as promising candidates for next-generation semiconductor spintronic applications.
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56. 56
  Baumgartner, M.; Garello, K.; Mendil, J.; Avci, C. O.; Grimaldi, E.; Murer, C.; Feng, J.; Gabureac, M.; Stamm, C.; Acremann, Y.; Finizio, S.; Wintz, S.; Raabe, J.; Gambardella, P. Spatially and time-resolved magnetization dynamics driven by spin-orbit torques. Nat. Nanotechnol. 2017, 12, 980, DOI: 10.1038/nnano.2017.151
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  Spatially and time-resolved magnetization dynamics driven by spin-orbit torques
  Baumgartner, Manuel; Garello, Kevin; Mendil, Johannes; Avci, Can Onur; Grimaldi, Eva; Murer, Christoph; Feng, Junxiao; Gabureac, Mihai; Stamm, Christian; Acremann, Yves; Finizio, Simone; Wintz, Sebastian; Raabe, Jorg; Gambardella, Pietro
  Nature Nanotechnology (2017), 12 (10), 980-986CODEN: NNAABX; ISSN:1748-3387. (Nature Research)
  Current-induced spin-orbit torques are one of the most effective ways to manipulate the magnetization in spintronic devices, and hold promise for fast switching applications in nonvolatile memory and logic units. Here, the authors report the direct observation of spin-orbit-torque-driven magnetization dynamics in Pt/Co/AlOx dots during current pulse injection. Time-resolved x-ray images with 25 nm spatial and 100 ps temporal resoln. reveal that switching is achieved within the duration of a subnanosecond current pulse by the fast nucleation of an inverted domain at the edge of the dot and propagation of a tilted domain wall across the dot. The nucleation point is deterministic and alternates between the four dot quadrants depending on the sign of the magnetization, current and external field. The authors' measurements reveal how the magnetic symmetry is broken by the concerted action of the damping-like and field-like spin-orbit torques and the Dzyaloshinskii-Moriya interaction, and show that reproducible switching events can be obtained for over 1012 reversal cycles.
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The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.nanolett.9b04556.
- Movie, accompanying Figure 5a,b, animates the time evolution of magnetizations, m₁(t) and m₂(t) in Figure 1, driven by a sequence of rectangular voltage pulses (MP4)
- Additional details for Figure 2, such as the spatial profile of local current density on different monolayers of the bilayer-CrI₃/monolayer-TaSe₂ vdW heterostructure, as well as for Figure 3, such as spin textures in the bilayer-CrI₃/monolayer-TaSe₂ vdW heterostructure vs spin textures in an isolated monolayer-TaSe₂ (PDF)
- pdf
  nl9b04556_si_002.pdf (5.98 MB)
- mp4 video
  nl9b04556_si_001.mp4 (3.0 MB)
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Proximity Spin–Orbit Torque on a Two-Dimensional Magnet within van der Waals Heterostructure: Current-Driven Antiferromagnet-to-Ferromagnet Reversible Nonequilibrium Phase Transition in Bilayer CrI3

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Abstract

Introduction

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6

Methodology

Nonequilibrium Spin Density

Angular Dependence of SOT

SOT-Driven Classical Dynamics of Magnetization

TMR as a Probe of AFM–FM Transition

Supporting Information

pdf

mp4 video

Terms & Conditions

Acknowledgments

References

Cited By

Abstract

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6

References

Supporting Information

Supporting Information

pdf

mp4 video

Terms & Conditions

STEP 1:

STEP 2:

OOPS

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Proximity Spin–Orbit Torque on a Two-Dimensional Magnet within van der Waals Heterostructure: Current-Driven Antiferromagnet-to-Ferromagnet Reversible Nonequilibrium Phase Transition in Bilayer CrI₃