Spin-Current Relaxation Time in Spin-Polarized Heisenberg Paramagnets

TL;DR

This paper investigates the relaxation dynamics of spin correlations in highly polarized Heisenberg paramagnets using classical simulations, revealing a hierarchy of frequency scales and proposing a modified correlation function model.

Contribution

It introduces a classical simulation approach for large-spin systems to analyze spin correlation functions and proposes a new form for the correlation function at high polarization.

Findings

Identification of a hierarchy of frequency scales at high polarization

Observation of a wavelength-dependent spin-wave frequency proportional to q^2

Modification of spin diffusion coefficients based on the new correlation function form

Abstract

We study the spatial Fourier transform of the spin correlation function G_q(t) in paramagnetic quantum crystals by direct simulation of a 1d lattice of atoms interacting via a nearest-neighbor Heisenberg exchange Hamiltonian. Since it is not practical to diagonalize the s=1/2 exchange Hamiltonian for a lattice which is of sufficient size to study long-wavelength (hydrodynamic) fluctuations, we instead study the s -> infinity limit and treat each spin as a vector with a classical equation of motion. The simulations give a detailed picture of the correlation function G_q(t) and its time derivatives. At high polarization, there seems to be a hierarchy of frequency scales: the local exchange frequency, a wavelength-independent relaxation rate 1/tau that vanishes at large polarization P ->1, and a wavelength-dependent spin-wave frequency proportional to q^2. This suggests a form for the correlation function which modifies the spin diffusion coefficients obtained in a moments calculation by Cowan and Mullin, who used a standard Gaussian ansatz for the second derivative of the correlation function.