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

TL;DR

This paper investigates how thermal equilibration in thin ferromagnetic films affects spin currents and voltage signals in spin-Seebeck experiments, emphasizing the role of surface modes and their impact on measurable voltages.

Contribution

It provides a detailed analysis of thermal equilibration processes and their influence on spin currents and voltages, highlighting the significance of surface modes in thin-film ferromagnets.

Findings

Thermal equilibration involves two surface modes with lengths depending on coupling.

Thermal gradients induce spin fluxes and magnetoelectrochemical potential gradients.

The resulting transverse voltage varies as sinh(x/λ), linking thermal and spin transport.

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 $\sinh{(x/\lambda)}$.