Hysteresis and magnetocaloric effect at the magnetostructural phase transition of Ni-Mn-Ga and Ni-Mn-Co-Sn Heusler alloys

Hysteresis features of the direct and inverse magnetocaloric effect associated with first-order magnetostructural phase transitions in Ni-Mn-X (X $=$ Ga, Sn) Heusler alloys have been disclosed by differential calorimetry measurements performed either under a constant magnetic field, $H$, or by varying $H$ in isothermal conditions. We have shown that the magnetocaloric effect in these alloys crucially depends on the employed measuring protocol. Experimentally observed peculiarities of the magnetocaloric effect have been explained in the framework of a model that accounts for different contributions to the Gibbs energy of austenitic ${g}_{A}$ and martensitic ${g}_{M}$ phases. Obtained experimental results have been summarized by plotting a phase fraction of the austenite ${x}_{A}$ versus the driving force ${g}_{M}\ensuremath{-}{g}_{A}$. The developed approach allows one to predict reversible and irreversible features of the direct as well as inverse magnetocaloric effect in a variety of materials with first-order magnetic phase transitions.