Current induced torques in the presence of spin-orbit coupling
Paul M. Haney, Mark D. Stiles
In systems with strong spin-orbit coupling, the relationship between spin-transfer torque and the divergence of the spin current is generalized to a relation between spin transfer torques, total angular momentum current, and mechanical torques. In ferromagnetic semiconductors, where the spin-orbit coupling is large, these considerations modify the behavior of the spin transfer torques. We illustrate the modifications with two examples. In the spin valve geometry, the spin transfer torque does not decay away from the interface, but approaches a constant value. For a single ferromagnetic-nonmagnetic interface, spin-orbit coupling gives rise to a microscopic electronic structure contribution to the mechanical torque.
and Stiles, M.
Current induced torques in the presence of spin-orbit coupling, Physical Review Letters, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=906100
(Accessed November 28, 2021)