Self-consistently renormailzed spin-wave theory of layered ferromagnets on honeycomb lattice

TL;DR

This paper introduces a self-consistent renormalized spin-wave theory for layered honeycomb ferromagnets, accounting for surface and bulk differences, and applies it to chromium-based van der Waals magnets to analyze temperature-dependent magnetization.

Contribution

The authors develop a mean-field self-consistent spin-wave approach that includes layer-specific effects, enabling detailed study of magnetic properties in layered honeycomb ferromagnets.

Findings

Magnetization decreases with temperature, showing dimensionality effects.

Ordering temperature is reduced in lower-dimensional systems.

Sensitivity of ordering temperature to anisotropy increases as dimensionality decreases.

Abstract

We develop a self-consistently renormalized spin-wave theory, within a mean-field approximation, for the two-dimensional Heisenberg ferromagnet with perpendicular easy-axis anisotropy on the honeycomb lattice, as well as its few-layer and bulk extensions. In this method, the magnetization dependence on temperature is found as the solution of the self-consistency equation. Furthermore, we account for the physical difference of surface and bulk layers by treating the layers as separate sublattices. Thus, the method can be readily generalized to study various magnetic phenomena in a broad range of systems, including those comprising magnetically inequivalent sublattices. Using our theory, we calculate the temperature-dependent magnetization for two chromium-based layered van der Waals insulating magnets, Cr$_2$Ge$_2$Te$_6$ and CrI$_3$, employing various sets of Heisenberg exchange and single-ion anisotropy values reported for these materials in the existing literature. As expected, we observe a strong dimensionality effect where the ordering temperature is reduced and its sensitivity on the anisotropy is enhanced with the decrease of dimensionality.