Curie temperature of emerging two-dimensional magnetic structures

Recent realizations of intrinsic, long-range magnetic orders in two-dimensional (2D) van der Waals materials have ignited tremendous research interest. 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 (T-c). By including both on-site and neighbor couplings extracted from first-principles simulations, we have calculated T-c of monolayer chromium trihalides and Cr2Ge2Te6, which are of broad interest currently, and the simulation results agree with available measurements. We also clarify the roles played by anisotropic and isotropic interactions in deciding T-c of magnetic orders. Particularly, we find a universal, linear dependence between T-c and magnetic interactions within the parameter space of realistic materials. With this linear dependence, we can predict T-c 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 T-c, giving hope to speeding up the search for novel 2D materials with higher Curie temperatures.