Landau-Lifshitz theory of the longitudinal spin Seebeck effect

TL;DR

This paper develops a theoretical framework based on the Landau-Lifshitz-Gilbert model to understand how thermal gradients induce spin currents across ferromagnet-paramagnet interfaces, highlighting the role of magnons and length scales.

Contribution

It introduces a comprehensive Landau-Lifshitz-based theory for the longitudinal spin Seebeck effect, incorporating both classical and quantum magnetic fluctuations.

Findings

Identification of key length scales affecting spin current dependence on film thickness

Demonstration of the role of magnons in establishing nonequilibrium steady states

Clarification of the quantum crossover in high-frequency magnetic fluctuations

Abstract

Thermal-bias-induced spin angular momentum transfer between a paramagnetic metal and ferromagnetic insulator is studied theoretically based on the stochastic Landau-Lifshitz-Gilbert (LLG) phenomenology. Magnons in the ferromagnet establish a nonequilibrium steady state by equilibrating with phonons via bulk Gilbert damping and electrons in the paramagnet via spin pumping, according to the fluctuation-dissipation theorem. Subthermal magnons and the associated spin currents are treated classically, while the appropriate quantum crossover is imposed on high-frequency magnetic fluctuations. We identify several length scales in the ferromagnet, which govern qualitative changes in the dependence of the thermally-induced spin current on the magnetic film thickness.