Unified theory of magnetization dynamics with relativistic and nonrelativistic spin torques

TL;DR

This paper rigorously derives a unified, fundamental theory of magnetization dynamics incorporating both relativistic and nonrelativistic spin torques from first principles, clarifying their mathematical forms and origins.

Contribution

It provides a first-principles derivation of various spin-torque terms, including new relativistic torques, and clarifies their mathematical differences in spin dynamics equations.

Findings

Derived nonrelativistic and relativistic spin-transfer torques from fundamental theory.

Identified a previously unnoticed relativistic spin-torque term.

Showed different mathematical forms of spin-torques in Landau-Lifshitz and Gilbert equations.

Abstract

Spin torques play a crucial role in operative properties of modern spintronic devices. To study current-driven magnetization dynamics, spin-torque terms providing the action of spin-polarized currents have previously often been added in a phenomenological way to the Landau-Lifshitz-Gilbert equation describing the local spin dynamics, yet without derivation from fundamental principles. Here, starting from the Dirac-Kohn-Sham theory and incorporating nonlocal spin transport we rigorously derive the various spin-torque terms that appear in current-driven magnetization dynamics. In particular we obtain an extended magnetization dynamics equation that precisely contains the nonrelativistic adiabatic and relativistic nonadiabatic spin-transfer torques (STTs) of the Berger and Zhang-Li forms as well as relativistic spin-orbit torques (SOTs). We derive in addition a previously unnoticed relativistic spin-torque term and moreover show that the various obtained spin-torque terms do not appear in the same mathematical form in both the Landau-Lifshitz and Landau-Lifshitz-Gilbert equations of spin dynamics.