Nonanalytic Magnetization Dependence of the Magnon Effective Mass in Itinerant Quantum Ferromagnets

TL;DR

This paper predicts a nonanalytic dependence of magnon effective mass on magnetization in itinerant quantum ferromagnets, influenced by weak-localization effects, with specific dispersion relations derived for different dimensions and disorder levels.

Contribution

It introduces a novel nonanalytic magnetization dependence of magnon dispersion in itinerant ferromagnets due to weak-localization physics effects.

Findings

Dispersion relation a  m^{1-} k^2 for disordered systems

Dispersion relation a  m^{1-} k^2 for clean systems

Proposes experiments to test the theoretical predictions

Abstract

The spin wave dispersion relation in both clean and disordered itinerant quantum ferromagnets is calculated. It is found that effects akin to weak-localization physics cause the frequency of the spin-waves to be a nonanalytic function of the magnetization m. For low frequencies \Omega, small wavevectors k, and small m, the dispersion relation is found to be of the form \Omega ~ m^{1-\alpha} k^2, with \alpha = (4-d)/2 (2<d<4) for disordered systems, and \alpha = (3-d) (1<d<3) for clean ones. In d=4 (disordered) and d=3 (clean), \Omega ~ m ln(1/m) k^2. Experiments to test these predictions are proposed.