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Spin-orbit torques in ferromagnet/nonmagnet/ferromagnet trilayers are studied using a combination of symmetry analysis, circuit theory, semiclassical simulations, and first-principles calculations using the nonequilibrium Green's function method with supercell disorder averaging. We focus on unconventional processes involving the interplay between the two ferromagnetic layers, which are classified into direct and indirect mechanisms. The direct mechanism involves spin current generation by one ferromagnetic layer and its subsequent absorption by the other. In the indirect mechanism, the in-plane spin-polarized current from one ferromagnetic layer “leaks” into the other layer, where it is converted into an out-of-plane spin current and reabsorbed by the original layer. The direct mechanism results in a predominantly dampinglike torque, which damps the magnetization towards a certain direction 𝐬_𝑑. The indirect mechanism results in a predominantly fieldlike torque with respect to a generally different direction 𝐬_𝑓. Similarly to the current-in-plane giant magnetoresistance, the indirect mechanism is only active if the thickness of the nonmagnetic spacer is smaller than or comparable to the mean free path. Numerical calculations for a semiclassical model based on the Boltzmann equation confirm the presence of both direct and indirect mechanisms of spin current generation. First-principles calculations reveal sizable unconventional spin-orbit torques in Co/Cu/Co, Py/Cu/Py, and Co/Pt/Co trilayers and provide strong evidence of indirect spin current generation. 

Spin-accumulation and spin-current profiles are calculated for a disordered Pt film subjected to an in-plane electric current within the nonequilibrium Green's 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. 

Gate-tunable spin-dependent properties could be induced in graphene at room temperature through the magnetic proximity effect by placing it in contact with a metallic ferromagnet. Because strong chemical bonding with the metallic substrate makes gating ineffective, an intervening passivation layer is needed. Previously considered passivation layers result in a large shift of the Dirac point away from the Fermi level, so that unrealistically large gate fields are required to tune the spin polarization in graphene (Gr). We show that a monolayer of Au or Pt used as the passivation layer between Co and graphene brings the Dirac point closer to the Fermi level. In the Co/Pt/Gr system the proximity-induced spin polarization in graphene and its gate control are strongly enhanced by the presence of a surface band near the Fermi level. Furthermore, the shift of the Dirac point could be eliminated entirely by selecting submonolayer coverage in the passivation layer. Our findings open a path towards experimental realization of an optimized two-dimensional system with gate-tunable spin-dependent properties.