---
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.'
author:
- 'Jiang Xiao and A. Zangwill'
- 'M. D. Stiles'
title: Spin Transfer Torque for Continuously Variable Magnetization
---

Introduction
============

The use of electric current to control magnetization in nanometer-sized structures is a major theme in the maturing field of spintronics. [@Fert:2003] An outstanding example is the theoretical prediction of current-induced magnetization precession and switching in single domain multilayers [@SB] and its subsequent experimental confirmation in spin-valve nanopillars. [@Kiselev:2003] The physics of this spin-transfer effect is that a single domain ferromagnet 