Spin Transfer Torque for Continuously Variable Magnetization

Published

February 21, 2006

Author(s)

J Xiao, A Zangwill, Mark D. Stiles

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.

Citation

Physical Review B (Condensed Matter and Materials Physics)

Volume

73

Issue

5

Pub Type

Journals

Keywords

adiabatic approximation, Domain wall, ferromagnet, magnetization dynamics, non-uniform magnetization, spin current, spin-flip scattering, spin-transfer torque

Citation

Xiao, J. , Zangwill, A. and Stiles, M. (2006), Spin Transfer Torque for Continuously Variable Magnetization, Physical Review B (Condensed Matter and Materials Physics) (Accessed March 2, 2025)