Landau-Lifshitz theory of the magnon-drag thermopower

¹ Institute for Theoretical Physics and Center for Extreme Matter and Emergent Phenomena, Utrecht University Leuvenlaan 4, 3584 CE Utrecht, The Netherlands
² Department of Physics and Astronomy, University of California - Los Angeles, CA 90095, USA
³ Department of Applied Physics, Eindhoven University of Technology - PO Box 513, 5600 MB, Eindhoven, The Netherlands

Received: 8 August 2016
Accepted: 23 September 2016

Abstract

Metallic ferromagnets subjected to a temperature gradient exhibit a magnonic drag of the electric current. We address this problem by solving a stochastic Landau-Lifshitz equation to calculate the magnon-drag thermopower. The long-wavelength magnetic dynamics result in two contributions to the electromotive force acting on electrons: 1) An adiabatic Berry-phase force related to the solid angle subtended by the magnetic precession and 2) a dissipative correction thereof, which is rooted microscopically in the spin-dephasing scattering. The first contribution results in a net force pushing the electrons towards the hot side, while the second contribution drags electrons towards the cold side, i.e., in the direction of the magnonic drift. The ratio between the two forces is proportional to the ratio between the Gilbert damping coefficient α and the coefficient β parametrizing the dissipative contribution to the electromotive force.