Semiconductors are ubiquitous in device electronics, because their charge distributions can be conveniently manipulated with voltages to perform logic operations. Achieving a similar level of control over the spin degrees of freedom, either from electrons or nuclei, could provide intriguing prospects for both information processing and the study of fundamental solid-state physics issues. Here we report procedures that carry out the controlled transfer of spin angular momentum between electrons-confined to two dimensions and subjected to a perpendicular magnetic field-and the nuclei of the host semiconductor, using gate voltages only. We show that the spin transfer rate can be enhanced near a ferromagnetic ground state of the electron system, and that the induced nuclear spin polarization can be subsequently stored and 'read out'. These techniques can also be combined into a spectroscopic tool to detect the low-energy collective excitations in the electron system that promote the spin transfer. The existence of such excitations is contingent on appropriate electron-electron correlations, and these can be tuned by changing, for example, the electron density via a gate voltage.