Longitudinal magnon transport properties in the easy-axis XXZ Heisenberg ferromagnet on the face-centered cubic lattice

TL;DR

This paper investigates how magnons contribute to longitudinal spin and thermal transport in an easy-axis XXZ ferromagnet on a face-centered cubic lattice, revealing activated behavior, a magnon gap's importance, and an analog of the Wiedemann-Franz law.

Contribution

It provides a detailed theoretical analysis of magnon transport properties in a complex lattice, highlighting the role of the magnon gap and establishing an analog of the Wiedemann-Franz law.

Findings

Both spin and thermal conductivities show activated temperature dependence at low temperatures.

A magnon gap is essential for the convergence of transport conductivities.

An analog of the Wiedemann-Franz law for magnon transport is identified at low temperatures.

Abstract

We present a detailed investigation of longitudinal magneto-thermal transport in the $S=1/2$ ferromagnetic XXZ model with easy-axis exchange anisotropy ($\Delta>1$) on a face-centered cubic lattice consisting of four sublattices. We employ linear spin-wave theory and the Kubo formalism to evaluate the longitudinal spin and thermal conductivities, both of which exhibit activated temperature dependence in the low-temperature regime, and to determine their magnetic-field dependence. Our analysis indicates that a magnon gap is crucial for ensuring the convergence of these conductivities. Furthermore, by examining the ratio of thermal conductivity to spin conductivity, we identify an analog of the Wiedemann-Franz law for magnon transport at low temperatures. Finally, we demonstrate that these results can be generalized to systems with arbitrary spin.