Thermal conductivity in large-$J$ two-dimensional antiferromagnets: Role of phonon scattering

TL;DR

This paper investigates how phonon scattering affects thermal conductivity in large-$J$ 2D antiferromagnets like La$_2$CuO$_4$, using two theoretical methods to analyze magnon heat transport and scattering mechanisms.

Contribution

It compares Boltzmann and memory-function approaches to model magnon-phonon scattering, highlighting the importance of optical phonons in high-temperature thermal conductivity.

Findings

Both methods agree on relaxation rate behavior.

Optical phonons significantly influence magnon heat relaxation.

Additional scattering sources are incorporated into the models.

Abstract

Motivated by the recent heat transport experiments in 2D antiferromagnets, such as La$_2$CuO$_4$, where the exchange coupling $J$ is larger than the Debye energy $\Theta_{\rm D}$, we discuss different types of relaxation processes for magnon heat current with a particular focus on coupling to 3D phonons. We study thermal conductivity by these in-plane magnetic excitations using two distinct techniques, Boltzmann formalism within the relaxation-time approximation and memory-function approach. Within these approaches, a close consideration is given to the scattering of magnons by both acoustic and optical branches of phonons. A remarkable accord between the two methods with regards to the asymptotic behavior of the effective relaxation rates is demonstrated. Additional scattering mechanisms, due to grain boundaries, impurities, and finite correlation length in the paramagnetic phase, are discussed and included in the calculations of the thermal conductivity $\kappa(T)$. Again, we demonstrate a close similarity of the results from the two techniques of calculating $\kappa(T)$. Our complementary approach strongly suggests that scattering from optical or zone-boundary phonons is important for magnon heat current relaxation in a high temperature window of $\Theta_D\lesssim T \ll J$.