Complex magnetic phases are exploited in many important solid-state technologies, but their first principles modelling at finite temperature is a major challenge. We present a first-principles approach for the computation of the magnetic Gibbs free energy of materials using magnetically constrained supercell calculations [1]. Our method, based on an adiabatic approximation for the local moment orientations [2], describes magnetic phase transitions and how purely electronic and magnetovolume mechanisms generate a discontinuous (first-order) character. We will show its performance by studying the temperature-dependent properties of bcc Fe and of a triangular antiferromagnetic state in Mn$_3$AN (A = Ga, Ni) [3], among other materials. Our calculations explain the negative thermal expansion observed in these systems as well as the origin of first-order phase transitions with technological functionality in good agreement with experiment. Results obtained using two different density functional theory codes, the Vienna Ab Initio Simulation package (VASP) and the linear-scaling KKR-nano code suitable for thousands of atoms (https://jukkr.fz-juelich.de), will be shown.

[1] E. Mendive-Tapia, J. Neugebauer, T. Hickel, Phys. Rev. B \textbf{105}, 064425 (2022).

[2] B. Gyorffy et al., J. Phys. F: Met. Phys. \textbf{15} 1337 (1985).

[3] D. Boldrin et al., Phys. Rev. X \textbf{8} 041035 (2018).