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Spin torques play a crucial role in operative properties of modern spintronicdevices. To study current-driven magnetization dynamics, spin-torque termsproviding the action of spin-polarized currents have previously often beenadded in a phenomenological way to the Landau-Lifshitz-Gilbert equationdescribing the local spin dynamics, yet without derivation from fundamentalprinciples. Here, starting from the Dirac-Kohn-Sham theory and incorporatingnonlocal spin transport we rigorously derive the various spin-torque terms thatappear in current-driven magnetization dynamics. In particular we obtain anextended magnetization dynamics equation that precisely contains thenonrelativistic adiabatic and relativistic nonadiabatic spin-transfer torques(STTs) of the Berger and Zhang-Li forms as well as relativistic spin-orbittorques (SOTs). We derive in addition a previously unnoticed relativisticspin-torque term and moreover show that the various obtained spin-torque termsdo not appear in the same mathematical form in both the Landau-Lifshitz andLandau-Lifshitz-Gilbert equations of spin dynamics.

Unified theory of magnetization dynamics with relativistic and nonrelativistic spin torques