Unified theory of magnetization dynamics with relativistic and nonrelativistic spin torques

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.

arXiv comment13 pages, 1 figure

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• Spin pumping at terahertz nutation resonances
• Influence of inter-sublattice coupling on the terahertz nutation spin dynamics in antiferromagnets
• Theory of magnetic inertial dynamics in two-sublattice ferromagnets
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• From the open Heisenberg model to the Landau-Lifshitz equation
• Terahertz spin dynamics driven by an optical spin-orbit torque
• Dynamics of the relativistic electron spin in an electromagnetic field
• Role of material-dependent properties in THz field-derivative-torque-induced nonlinear magnetization dynamics
• Theory of tensorial magnetic inertia in terahertz spin dynamics
• Spin-polarized current, spin-transfer torque and spin Hall effect in presence of an electromagnetic non-minimal coupling
• Spin torques and anomalous velocity in spin textures induced by fast electron injection from topological ferromagnets: The role of gauge fields
• The stochastic Landau--Lifshitz--Baryakhtar equation: Global solution and invariant measure
• Fast reversal of Néel vectors in antiferromagnets via domain-wall motion driven by vertically injected spin currents
• Field-derivative torque induced magnetization reversal in ferrimagnetic Gd${}_{3/2}$Yb${}_{1/2}$BiFe${}_5$O${}_{12}$