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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.
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Flebus et al. (2016) studied this question.
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