Spin conductance, dynamic spin stiffness and spin diffusion in itinerant magnets

TL;DR

This paper explores the dynamic properties of spin transport in itinerant magnets, introducing the concept of dynamic spin stiffness and a new method to estimate spin diffusion in the Hubbard model.

Contribution

It introduces the dynamic spin stiffness D_s as an analog to charge stiffness and develops a new extrapolation scheme for spin diffusion in the Hubbard model.

Findings

Dynamic spin stiffness D_s differs from traditional spin stiffness rho_s.

Low-frequency spin conductance G_s(omega) characterizes different spin transport regimes.

A new extrapolation method for spin diffusion coefficient in the Hubbard model's paramagnetic phase.

Abstract

We discuss analogies between the charge- and spin response functions of itinerant magnets. We show that the spin-analog of the charge stiffness is not given by the usual spin stiffness rho_s, but by the dynamic spin stiffness D_s, which is obtained from the dynamic spin conductance G_s (omega) in the limit of vanishing frequency omega. The low-frequency behavior of G_s (omega) is used to define ideal spin conductors, normal spin conductors, and spin insulators. Assuming diffusive spin dynamics, we show that the spin diffusion coefficient is proportional to lim_{omega rightarrow 0} {Re} {G}_s (omega). We exploit this fact to develop a new extrapolation scheme for the spin diffusion coefficient in the paramagnetic phase of the Hubbard model.