The angular dependence of spin-orbit torque in monolayer Fe3GeTe2Fe_3GeTe_2

In ferromagnetic systems lacking inversion symmetry, an applied electric field can control the ferromagnetic order parameters through the spin-orbit torque. The prototypical example is a bilayer heterostructure composed of a ferromagnet and a heavy metal that acts as a spin current source. In addition to such bilayers, spin-orbit coupling can mediate spin-orbit torques in ferromagnets that lack bulk inversion symmetry. A recently discovered example is the two-dimensional monolayer ferromagnet $Fe_3GeTe_2$. In this work, we use first-principles calculations to study the spin-orbit torque and ensuing magnetic dynamics in this material. By expanding the torque versus magnetization direction as a series of vector spherical harmonics, we find that higher order terms (up to $\ell=4$) are significant and play important roles in the magnetic dynamics. They give rise to deterministic, magnetic field-free electrical switching of perpendicular magnetization.Comment: 8 pages (3 pages appendix), 7 figure

Breakdown of the Drift-Diffusion Model for Transverse Spin Transport in a Disordered Pt Film

Spin-accumulation and spin-current profiles are calculated for a disordered Pt film subjected to an in-plane electric current within the nonequilibrium Green\u27s function approach. In the bulklike region of the sample, this approach captures the intrinsic spin Hall effect found in other calculations. Near the surfaces, the results reveal qualitative differences with the results of the widely used spin-diffusion model, even when the boundary conditions are modified to try to account for them. One difference is that the effective spin-diffusion length for transverse spin transport is significantly different from its longitudinal counterpart and is instead similar to the mean-free path. This feature may be generic for spin currents generated via the intrinsic spin Hall mechanism because of the differences in transport mechanisms compared to longitudinal spin transport. Orbital accumulation in the Pt film is only significant in the immediate vicinity of the surfaces and has a small component penetrating into the bulk only in the presence of spin-orbit coupling, as a secondary effect induced by the spin accumulation

Implementation of a non-equilibrium Green's function method to calculate spin transfer torque

We present an implementation of the steady state Keldysh approach in a Green's function multiple scattering scheme to calculate the non-equilibrium spin density. This density is used to obtain the spin transfer torque in junctions showing the magnetoresistance effect. We use our implementation to study the spin transfer torque in metallic Co/Cu/Co junctions.Comment: 4 pages, 4 figure