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We present a first-principles approach for the computation of the magneticGibbs free energy of materials using magnetically constrained supercellcalculations. Our approach is based on an adiabatic approximation of slowlyvarying local moment orientations, the so-called finite-temperature disorderedlocal moment picture. It describes magnetic phase transitions and howelectronic and/or magnetostructural mechanisms generate a discontinuous(first-order) character. We demonstrate that the statistical mechanics of thelocal moment orientations can be described by an affordable number of supercellcalculations containing noncollinear magnetic configurations. The applicabilityof our approach is illustrated by firstly studying the ferromagnetic state inbcc Fe. We then investigate the temperature-dependent properties of atriangular antiferromagnetic state stabilizing in two antiperovskite systemsMn$_3$AN (A = Ga, Ni). Our calculations provide the negative volume expansionof these materials as well as the ab initio origin of the discontinuouscharacter of the phase transitions, electronic and/or magnetostructural, ingood agreement with experiment.

Ab initio calculation of the magnetic Gibbs free energy of materials using magnetically constrained supercells