Realistic finite temperature simulations for magnetic and transport properties of ferromagnet

Accurately modeling the magnetic and transport properties of ferromagnetic materials at finite temperatures remains a significant challenge in materials science. In this study, we present a comprehensive simulation approach that combines first-principles calculations with Monte Carlo simulations to investigate body-centered cubic (bcc) iron (Fe). We calculate the magnetic exchange coupling constants (Jij) while incorporating thermal lattice vibrations effects, achieving a more realistic temperature-dependent behavior of Jij and the Curie temperature of bcc Fe. Our Monte Carlo simulations employ the classical Heisenberg model enhanced with a quantum fluctuation-dissipation relation, wherein thermal spin fluctuations effects of magnons obey Bose-Einstein statistics. This approach successfully reproduces the spontaneous magnetization curve across a wide temperature range. Our method addresses well-known discrepancies in spontaneous magnetization between the ordinary classical Heisenberg model and experimental results, particularly in the low-temperature regime where spontaneous magnetization follows Bloch’s 3/2 power law in experimental data. Additionally, we demonstrate that our approach accurately reproduces the electrical resistivity and specific heat of bcc Fe, whereas the ordinary classical Heisenberg model fails to capture these temperature-dependent properties. Our findings highlight the importance of considering both thermal lattice vibrations and thermal spin fluctuations effects with Bose-Einstein statistics when modeling ferromagnetic materials, thus enabling more precise predictions of magnetic and transport properties at finite temperatures.