Realistic finite temperature simulations for the magnetic and transport properties of ferromagnets

Spontaneous magnetization cannot be accurately estimated using the ordinary classical Heisenberg model because the quantization effects are neglected, especially in low-temperature regions where experimental observations follow Bloch's 3/2 power law driven by magnon thermal excitation. The spontaneous magnetization of body-centered cubic (bcc) iron (Fe) is elucidated based on first-principles calculations by considering phonon and magnon fluctuation effects. The magnetic exchange coupling constants (J_ij) are derived while incorporating thermal lattice vibration effects, achieving a more realistic temperature dependence of J_ij of bcc Fe. Our Monte Carlo simulations showed that thermal lattice vibration effects reduced the Curie temperature from 1503 K to 1060.9 K, closely matching the experimental value of 1043 K. The temperature dependence of spontaneous magnetization is significantly improved when the quantization effects are considered, using Bose–Einstein statistics for thermal spin fluctuation effects. The well-known discrepancies in spontaneous magnetization between the ordinary classical Heisenberg model and experimental results are resolved, particularly in the low-temperature regime. Additionally, we elucidated finite-temperature electronic structures by accounting for thermal lattice vibration and thermal spin fluctuation effects. The temperature dependence of electrical resistivity is well reproduced by using the Kubo–Greenwood formula as a linear response theory with thermal lattice vibration and thermal spin fluctuation effects. Our findings highlight the importance of considering both thermal lattice vibration and thermal spin fluctuation effects with Bose–Einstein statistics when modeling ferromagnetic materials, thus enabling more precise predictions of magnetic and transport properties at finite temperatures.