Spin diffusion and relaxation in three-dimensional isotropic Heisenberg antiferromagnets

TL;DR

This paper develops a theoretical framework for understanding spin diffusion and relaxation in three-dimensional isotropic Heisenberg antiferromagnets above the Neel temperature, incorporating critical dynamics and scaling behavior.

Contribution

It introduces a diagrammatic kinetic theory for critical dynamics in antiferromagnets, analyzing the scaling of diffusion and relaxation coefficients near the phase transition.

Findings

Kinetic coefficients are singular in the fluctuation region.

Critical indices for diffusion and relaxation are calculated.

Scaling behavior aligns with dynamic scaling theory and renormalization group predictions.

Abstract

A theory is proposed for kinetic effects in isotropic Heisenberg antiferromagnets at temperatures above the Neel point. A metod based on the analysis of a set of Feynman diagrams for the kinetic coefficients is developed for studying the critical dynamics. The scaling behavior of the generalized coefficient of spin diffusion and relaxation constant in the paramagnetic phase is studied in terms of the approximation of coupling modes. It is shown that the kinetic coefficients in an antiferromagnetic system are singular in the fluctuation region. The corresponding critical indices for diffusion and relaxation processes are calculated. The scaling dimensionality of the kinetic coefficients agrees with the predictions of dynamic scaling theory and a renormalization group analysis. The proposed theory can be used to study the momentum and frequency dependence of the kinetic parameters, and to determine the form of the scaling functions. The role of nonlocal correlations and spin-liquid effects in magnetic systems is briefly discussed.