Theory of transverse spin dynamics in a polarized Fermi liquid and an itinerant ferromagnet

TL;DR

This paper derives generalized equations for transverse spin dynamics in polarized Fermi liquids and itinerant ferromagnets, revealing polarization-dependent spin wave behavior and damping at zero temperature.

Contribution

It provides a derivation of spin dynamics equations free from constant Fermi velocity assumptions, applicable to both paramagnetic Fermi liquids and itinerant ferromagnets.

Findings

Spin wave frequency is proportional to the square of the wave vector.

Damping of spin waves remains finite at zero temperature.

Polarization affects the diffusion coefficient differently in Fermi liquids and ferromagnets.

Abstract

The linear equations for transverse spin dynamics in a weakly polarized degenerate Fermi liquid with arbitrary relationship between temperature and polarization are derived from Landau-Silin phenomenological kinetic equation with general form of two-particle collision integral. Unlike the previous treatment where Fermi velocity and density of states have been taken as constants independent of polarization here we made derivation free from this assumption. The obtained equations are applicable for description of spin dynamics in paramagnetic Fermi liquid with finite polarization as well in an itinerant ferromagnet. In both cases transverse spin wave frequency is found to be proportional to the square of the wave vector with complex constant of proportionality (diffusion coefficient) such that the damping has a finite value at T=0. The polarization dependence of the diffusion coefficient is found to be different for a polarized Fermi liquid and for an itinerant ferromagnet. These conclusions are confirmed by derivation of transverse spin wave dispersion law in frame of field theoretical methods from the integral equation for the vortex function. It is shown that similar derivation taking into consideration the divergency of static transverse susceptibility also leads to the same attenuating spin wave spectrum.