Determination of Curie temperatures using spin models derived from first-principles calculations

Accurate modeling of magnetic materials is essential for understanding their fundamental properties and advancing technological applications. The widely used methods based on the magnetic force theorem often fall short due to neglecting effects from longitudinal spin fluctuations and struggling with predicting the high-temperature behavior of itinerant magnets, as demonstrated by the significant underestimation of the Curie temperature of nickel. In this work, we demonstrate accurate simulation of magnetic materials by combining high-throughput first-principles calculations with a comprehensive model spin Hamiltonian to predict magnetic phase transitions. The Hamiltonian explicitly includes long-range exchange interactions, longitudinal fluctuations, magnetic anisotropy, and biquadratic interactions. By using a moderately sized data set for parametrization, we achieve an optimal balance between accuracy and efficiency. We validate the method by successfully calculating the Curie temperature of strongly itinerant nickel, which closely matches experimental values and outperforms previous theoretical predictions. Additionally, we apply the method to $\mathrm{Fe}$, $\mathrm{Co}$, and $\mathrm{Cr}\mathrm{Te}$${}_{2}$, further demonstrating its reliability. This method provides a valuable tool for discovering and designing new magnetic materials, hopefully offering crucial insights that accelerate material innovation and device development.