Spin Pumping of Current in Non-Uniform Conducting Magnets

TL;DR

This paper demonstrates that spin transfer torque within non-uniform conducting magnets induces spin pumping of current, with implications for experimental setups, by deriving dynamical equations for two models and analyzing their effects.

Contribution

The study introduces a thermodynamic framework showing that magnetic torques can drive bulk spin pumping in non-uniform conductors, distinguishing between two models of conducting magnets.

Findings

Voltage gradients can drive spin torques in non-uniform regions.

Magnetic torques induce bulk spin pumping via Onsager relations.

The ratio of emf to magnetic field near a domain wall is approximately P(2μ_B/e).

Abstract

Using irreversible thermodynamics we show that current-induced spin transfer torque within a magnetic domain implies spin pumping of current within that domain. This has experimental implications for samples both with conducting leads and that are electrically isolated. These results are obtained by deriving the dynamical equations for two models of non-uniform conducting magnets: (1) a generic conducting magnet, with net conduction electron density n and net magnetization $\vec{M}$; and (2) a two-band magnet, with up and down spins each providing conduction and magnetism. For both models, in regions where the equilibrium magnetization is non-uniform, voltage gradients can drive adiabatic and non-adiabatic bulk spin torques. Onsager relations then ensure that magnetic torques likewise drive adiabatic and non-adiabatic currents -- what we call bulk spin pumping. For a given amount of adiabatic and non-adiabatic spin torque, the two models yield similar but distinct results for the bulk spin pumping, thus distinguishing the two models. As in the recent spin-Berry phase study by Barnes and Maekawa, we find that within a domain wall the ratio of the effective emf to the magnetic field is approximately given by $P(2\mu_{B}/e)$, where P is the spin polarization. The adiabatic spin torque and spin pumping terms are shown to be dissipative in nature.