Thermal Equilibration and Thermally-Induced Spin Currents in a Thin-Film Ferromagnet on a Substrate

Abstract

Recent spin-Seebeck experiments on thin ferromagnetic films apply a temperature difference $\Delta T_x$ along the length $x$ and measure a (transverse) voltage difference $\Delta V_y$ along the width $y$. The connection between these effects is complex, involving: (1) thermal equilibration between sample and substrate; (2) spin currents along the height (or thickness) $z$; and (3) the measured voltage difference. The present work studies in detail the first of these steps, and outlines the other two steps. Thermal equilibration processes between the magnons and phonons in the sample, as well as between the sample and the substrate leads to two surface modes, with surface lengths $\lambda$, to provide for thermal equilibration. Increasing the coupling between the two modes increases the longer mode length and decreases the shorter mode length. The applied thermal gradient along $x$ leads to a thermal gradient along $z$ that varies as $\sinh (x/\lambda )$, which can in turn produce fluxes of the carriers of up- and down- spins along $z$, and gradients of their associated \textit{magnetoelectrochemical potentials} ${\bar{\mu }}_{\uparrow ,\downarrow }$, which vary as $\sinh (x/\lambda )$. By the inverse spin Hall effect, this spin current along $z$ can produce a transverse (along $y$) voltage difference $\Delta V_y$, which also varies as $\sinh (x/\lambda )$.

14 pages, 7 figures, 1 table

References in corpus (8)

• Spin Seebeck insulator
• Observation of the Spin-Seebeck Effect in a Ferromagnetic Semiconductor
• Theory of magnon-driven spin Seebeck effect
• Phonon driven spin distribution due to the spin-Seebeck effect
• Gigantic enhancement of spin Seebeck effect by phonon drag
• Spin Pumping of Current in Non-Uniform Conducting Magnets
• Theory of spin Hall effect
• Current Flow in Uniform Ferromagnets: Bulk and Surface Heating Rates

Cited by in corpus (3)

• Generalized two-temperature model for coupled phonon-magnon diffusion
• On the longitudinal spin current induced by a temperature gradient in a ferromagnetic insulator
• Magnon-driven longitudinal spin Seebeck effect in F|N and N|F|N structures: role of asymmetric in-plane magnetic anisotropy