Fermi Liquid Theory for Spin Current Dynamics of a Ferromagnet

Abstract

Theoretical understanding of spin dynamics in ferromagnets is a crucial question in spintronics. A recent work considered the dynamical equations for ferromagnets using Onsager’s irreversible thermodynamics with fundamental variables magnetization \(\vec {M}\) and spin current \(\vec {J}_{i}\). The resulting equations have the same structure as Leggett’s Fermi liquid theory for the nuclear paramagnet \(^{3}\)He. Specifically, \(\partial _{t}\vec {J}_{i}\) contains a term varying as \(\partial _{i}\vec {M}\) that we interpret as associated with a vector spin pressure and a term giving a mean-field along \(\vec {M}\), about which \(\vec {J}_{i}\) precesses. (There is also a decay term in \(\partial _{t}\vec {M}\) not normally present in the Leggett equations, which are intended for shorter-time spin-echo experiments.) The present work applies Fermi liquid theory to \(\vec {J}_{i}\) of ferromagnets. The resulting dynamical equation for \(\vec {J}_i\) confirms the form of \(\vec {J}_i\) found earlier using irreversible thermodynamics, but now the previously unknown exchange constant is given in terms of the quasiparticle interaction parameters of Fermi liquid theory. Our results indicate that study of spin currents in ferromagnets can yield information about the Fermi liquid coefficients.