Ferromagnetic shape memory alloys ${\mathrm{Ni}}_{2+x}{\mathrm{Mn}}_{1-x}\mathrm{Ga}$ were studied in the range of compositions $0.16⩽x⩽0.36$. The experimental phase diagram, constructed from differential scanning calorimetry, transport, and magnetic measurements, exhibits distinctive feature in a compositional interval $0.18⩽x⩽0.27$, where martensitic and magnetic transitions merge in a first-order magnetostructural phase transition ferromagnetic $\text{martensite}\leftrightarrow \text{paramagnetic}$ austenite. Observed in this interval of compositions a nonmonotonous behavior of the magnetostructural phase transition temperature was ascribed to the difference in the exchange interactions of martensitic and austenitic phase and to the competition between increasing number of valence electron and progressive dilution of the magnetic subsystem which occur in the presence of a strong magnetoelastic interaction. Based on the experimental phase diagram, the difference between Curie temperature of martensite $T_C^M$ and Curie temperature of austenite $T_C^A$ was estimated. Influence of volume magnetostriction was considered in theoretical modeling in order to account for the existence of the magnetostructural phase transition over a wide range of compositions.

On the basis of Monte Carlo simulations using the Potts model Hamiltonian, we investigate the complex temperature dependence of magnetization of ferromagnetic $\text{Ni-Mn-}X$ $\left(X=\text{In},\text{Sn},\text{Sb}\right)$ Heusler alloys, in which part of the Mn atoms, which occupy the $X$ sites, interacts antiferromagnetically with the Mn atoms on the Mn sublattice. It is shown that this antiferromagnetic exchange is responsible for metamagnetic behavior and a series of magnetic phase transitions in the Heusler alloys. For an optimal choice of parameters of the model Hamiltonian, which have partially been obtained from ab initio calculations, we are able to describe the physics associated with the coupled martensitic-magnetic phase transition. The simulations lead to a qualitative agreement with the experimental magnetization curves and their dependence on temperature and composition.

First-principles calculations of magnetic exchange parameters of the austenitic and martensitic phases of Ni-Mn-Ga allow one to characterize this Heusler system across the phase diagram in agreement with experimental trends. The ab initio investigations have been combined with Monte Carlo simulations for a detailed description of the magnetic, martensitic, and magnetocaloric properties of ${\text{Ni}}_{2+x}{\text{Mn}}_{1-x}\text{Ga}$ $\left(0.18\le x\le 0.27\right)$ Heusler alloys, which undergo a first-order magnetostructural phase transition. For these alloys, the calculated temperature dependence of the magnetic and lattice contributions to the total specific heat as well as the evaluation of the isothermal magnetic entropy $\Delta S_{mag}\left(T,H_{ext}\right)$ and adiabatic temperature $\Delta T\left(T,H_{ext}\right)$ changes around the magnetostructural transition in an external magnetic field agree fairly well with the experimental data. In particular, results for $\Delta S_{mag}\left(T,H_{ext}\right)$ and $\Delta T\left(T,H_{ext}\right)$ may be used to speculate about designing new magnetic Heusler alloys with better magnetocaloric properties, i.e., larger $\Delta T\left(T,H_{ext}\right)$ values.

Monte Carlo simulations were used for a detailed description of magnetic, martensitic and magnetocaloric properties of Ni_2+x Mn_1−x Ga (0.18 ⩽ x ⩽ 0.24) and Ni₅₀Mn₃₄In₁₆ Heusler alloys, which undergo a first-order magnetostructural phase transition. In the simulations we made use of magnetic exchange parameters which were obtained by ab initio calculations. Results of magnetic and lattice contributions to the total specific heat as well as the change in the isothermal magnetic entropy ΔS _mag and the adiabatic temperature ΔT _ad changes around the magnetic and magnetostructural transitions in an external magnetic field agree fairly well with available experimental data.