Spin-orbit torque in metallic heterostructures arises due to multiple microscopic mechanisms, which presents a challenge for theoretical understanding and interpretation of the experimental data. First-principles calculations provide valuable insight through controlled studies of the dependence of spin-orbit torques on the relevant parameters in realistic disordered heterostructures. Recent results from such calculations and progress in understanding the mechanisms of spin-orbit torque will be discussed. It was found that the damping-like torque in ferromagnet/heavy-metal bilayers tends to have a large interfacial contribution that is comparable to the conventional spin-Hall contribution. Calculations with varying degrees of interfacial intermixing show that it does not strongly affect the damping-like torque but can strongly enhance the field-like torque. Recent results for ferromagnet/normal-metal/ferromagnet trilayers and antiferromagnet/normal-metal bilayers will also be discussed.
The angular dependence of spin-orbit torque in disordered ferromagnet/heavy-metal bilayers is calculated using a first-principles nonequilibrium Green's function formalism with an explicit supercell disorder averaging. We consider Co/Pt, Co/Au, and Co/Pd bilayers with varying thicknesses and disorder strengths. In addition 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 experimental observations. The dampinglike torquance depends weakly on disorder strength, suggesting that it is dominated by the intrinsic mechanism. The fieldlike torquance declines with increasing disorder, consistent with the inverse spin-galvanic effect being dominant. It is found that 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. The calculated thickness dependence suggests that the dampinglike torque has a bulk-like contribution due to the spin-Hall effect and an interfacial contribution of a comparable magnitude.
Interfacial spin-flip scattering plays an important role in magnetoelectronic devices. Spin loss at metallic interfaces has usually been quantified by matching the magnetoresistance data for multilayers to the Valet-Fert model, while treating each interface as a fictitious bulk layer whose thickness is $\delta$ times the spin-diffusion length. However, the relation between the parameter $\delta$ and the scattering properties of the interface has been missing. We establish this relation using the properly generalized magnetoelectronic circuit theory, for both normal and ferromagnetic interfaces. It is found that the parameter $\delta$ extracted from the measurements on multilayers scales with the square root of the probability of spin-flip scattering. The spin-flip scattering probabilities are calculated for several specific interfaces using the Landauer-Büttiker method based on the first-principles electronic structure, and the results are compared with experimental data.
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