Inverse magnetocaloric effect and phase separation induced by giant van Hove singularity in itinerant ferromagnetic metal

A thermodynamic theory based on Landau grand potential expansion for ferromagnetic-paramagnetic phase transitions is developed for an electronic phase-separated state. It is rigorously shown that ferromagnetic phase involved in the phase-separated state exhibits negative magnetic susceptibility in the vicinity of tricritical point. Thus, an entropy of the magnetically ordered phase may increase when the magnetic field is applied, which implies positive sign of the total magnetic entropy change $\mathrm{\ensuremath{\Delta}}S$ within magnetocaloric effect (MCE). The electronic phase separation and MCE are considered within the Hubbard model for face-centered cubic lattice with giant van Hove singularity of electron density of states at the band bottom. Within the Hartree-Fock approximation it is shown that such model of itinerant magnet exhibits the first-order ferromagnet-paramagnet phase transition with electronic phase separation and inverse magnetocaloric effect deep inside the phase-separated region. Temperature dependence of $\mathrm{\ensuremath{\Delta}}S$ for the mean-field solution of the nondegenerate Hubbard model is analyzed in detail for different band filling values. The possibility to control $\mathrm{\ensuremath{\Delta}}S$ sign by changing both temperature and band filling of magnetocaloric materials is demonstrated. This is important to interpret a lot of experimental data, possible technological applications, and further theoretical developments.