# Origin of adiabatic and non-adiabatic spin transfer torques in current-driven magnetic domain wall motion

## TL;DR

This paper develops a comprehensive quantum-classical theory for current-driven magnetic domain wall motion, elucidating the origins of adiabatic and non-adiabatic spin transfer torques through coupled equations of motion.

## Contribution

It introduces a coupled quantum-classical framework that captures the correlated dynamics of spins and magnetization, clarifying the distinct roles of adiabatic and non-adiabatic torques.

## Key findings

- Hierarchy of two time scales: Boltzmann relaxation and Gilbert damping.
- Non-adiabatic torque linked to Boltzmann relaxation time.
- Adiabatic torque associated with Gilbert damping time.

## Abstract

A consistent theory to describe the correlated dynamics of quantum mechanical itinerant spins and semiclassical local magnetization is given. We consider the itinerant spins as quantum mechanical operators, whereas local moments are considered within classical Lagrangian formalism. By appropriately treating fluctuation space spanned by basis functions, including a zero-mode wave function, we construct coupled equations of motion for the collective coordinate of the center-of-mass motion and the localized zero-mode coordinate perpendicular to the domain wall plane. By solving them, we demonstrate that the correlated dynamics is understood through a hierarchy of two time scales: Boltzmann relaxation time when a non-adiabatic part of the spin-transfer torque appears, and Gilbert damping time when adiabatic part comes up.