Spin-orbit coupling mediated spin torque in a single ferromagnetic layer

Abstract

By considering a linear in momentum but otherwise arbitrary spin-orbit coupling (SOC), we derive a simple analytical expression for the current-driven spin torque in a single ferromagnetic layer. Explicit forms of the spin torque are given for structures with different SOC fields, in dependence of strain effects, growth direction, and/or symmetry under spatial inversion. The Landau-Lifshitz-Gilbert equation including the effects of the SOC mediated spin torque on the magnetization dynamics is briefly discussed.