2D ferromagnetism at finite temperatures under quantum scrutiny

TL;DR

This paper solves the quantum Heisenberg model for 2D honeycomb lattices to determine the conditions under which long-range magnetic order persists at finite temperatures, considering quantum fluctuations and anisotropic interactions.

Contribution

It provides a quantum mechanical analysis of 2D ferromagnetism at finite temperatures, extending beyond zero-temperature ab-initio predictions, and offers a practical tool for calculating Curie temperatures.

Findings

Long-range magnetic order persists at finite temperature with easy-axis anisotropy.

Validation on monolayer CrI3, CrBr3, and MnSe2 confirms the model.

Provides a tool for estimating Curie temperatures of 2D magnetic materials.

Abstract

Recent years have seen a tremendous rise of two-dimensional (2D) magnetic materials, several of which verified experimentally. However, most of the theoretical predictions to date rely on ab-initio methods, at zero temperature and fluctuations-free, while one certainly expects detrimental quantum fluctuations at finite temperatures. Here we present the solution of the quantum Heisenberg model for honeycomb/hexagonal lattices with anisotropic exchange interaction up to third nearest neighbors and in an applied field in arbitrary direction, that answers the question whether long-range magnetization can indeed survive in the ultrathin limit of materials, up to which temperature, and what the characteristic excitation (magnon) frequencies are, all essential to envisaged applications of magnetic 2D materials. We find that long-range magnetic order persists at finite temperature for materials with overall easy-axis anisotropy. We validate the calculations on the examples of monolayer CrI3, CrBr3 and MnSe2. Moreover, we provide an easy-to-use tool to calculate Curie temperatures of new 2D computational materials.