Spin Transfer Torque for Continuously Variable Magnetization

TL;DR

This paper presents quantum and semi-classical calculations of spin current and torque in systems with continuously varying magnetization, challenging recent claims of non-adiabatic contributions due to spin flip scattering.

Contribution

It provides analytic and numerical results for spin transfer torque in systems with continuous magnetization variation, questioning the existence of certain non-adiabatic effects.

Findings

Adiabatic limit: conduction electrons follow combined exchange and velocity-dependent fields.

Non-adiabatic effects diminish exponentially with increasing domain wall width.

Results cast doubt on proposed non-adiabatic spin-transfer torque contributions.

Abstract

We report quantum and semi-classical calculations of spin current and spin-transfer torque in a free-electron Stoner model for systems where the magnetization varies continuously in one dimension.Analytic results are obtained for an infinite spin spiral and numerical results are obtained for realistic domain wall profiles. The adiabatic limit describes conduction electron spins that follow the sum of the exchange field and an effective, velocity-dependent field produced by the gradient of the magnetization in the wall. Non-adiabatic effects arise for short domain walls but their magnitude decreases exponentially as the wall width increases. Our results cast doubt on the existence of a recently proposed non-adiabatic contribution to the spin-transfer torque due to spin flip scattering.