Spin Pumping of Current in Non-Uniform Conducting Magnets
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We show that magnetic disequilibrium within a magnetic domain (e.g., by a magnetic field driving a domain wall) implies spin pumping of current within that domain. This has experimental implications for samples both with conducting leads and that are electrically isolated. For a two-band magnet these results are obtained first by simple arguments, and then by using irreversible thermodynamics to derive the full dynamical equations, with up and down spins each providing conduction and magnetism. It is known that in regions where the equilibrium magnetization is non-uniform, voltage gradients can drive both adiabatic and nonadiabatic bulk spin torques. Onsager relations then ensure that magnetic torques likewise drive related amounts of adiabatic and nonadiabatic currents what we call bulk spin pumping. As for recent spin-Berry phase work, we find that within a domain wall, the ratio of the effective electromotive force to the magnetic field is approximately given by P(2/e), where is the spin polarization. The adiabatic spin torque and spin-pumping terms are shown to be dissipative. We also discuss the issue of Landau-Lifshitz damping vs Gilbert damping; both irreversible thermodynamics and Langevin theory with near-equilibrium thermodynamic fluctuations lead to Landau-Lifshitz damping.
