Curie Temperature of Emerging Two-Dimensional Magnetic Structures

TL;DR

This paper uses the XXZ Heisenberg model and Monte Carlo simulations to accurately predict the Curie temperature of 2D magnetic materials, revealing a universal linear relationship and improving estimation methods for new 2D magnetic materials.

Contribution

It introduces a combined modeling and simulation approach to predict Curie temperatures, establishing a universal linear dependence and offering a faster estimation method for 2D magnetic materials.

Findings

Calculated Tc of chromium trihalides and Cr2Ge2Te6 matches experimental data.

Identified a universal linear relationship between Tc and magnetic interactions.

Provided a simplified prediction method for Tc without extensive simulations.

Abstract

Recent realizations of intrinsic, long-range magnetic orders in two-dimensional (2D) van der Waals materials have ignited tremendous research interests. In this work, we employ the XXZ Heisenberg model and Monte Carlo simulations to study a fundamental property of these emerging 2D magnetic materials, the Curie temperature (Tc). By including both onsite and neighbor couplings extracted from first-principles simulations, we have calculated Tc of monolayer chromium trihalides and Cr2Ge2Te6, which are of broad interests currently, and the simulation results agree with available measurements. We also clarify the roles played by anisotropic and isotropic interactions in deciding Tc of magnetic orders. Particularly, we find a universal, linear dependence between Tc and magnetic interactions within the parameter space of realistic materials. With this linear dependence, we can predict Tc of general 2D lattice structures, omitting the Monte Carlo simulations. Compared with the widely used Ising model, mean-field theory, and spin-wave theory, this work provides a convenient and quantitative estimation of Tc, giving hope to speeding up the search for novel 2D materials with higher Curie temperatures.