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.

A review is given of experimental and theoretical works concerning the investigation of magnetic and structural phase transitions and of the magnetocaloric effect in Ni-Mn- X ( X= Ga, In, Sn, Sb)...

We present ab initio calculations of magnetic exchange parameters of stoichiometric Heusler compound Ni${}_2$MnSn and a few nonstoichiometric Ni${}_2$Mn${}_{1+x}$Sn${}_{1-x}$ cases. Use of the exchange parameters in subsequent Monte Carlo simulations allows us to evaluate the magnetization curves as a function of temperature and composition as well as the critical temperatures of the magnetic phase transitions. The latter are compared to those obtained from a mean-field approximation using the Heisenberg model. We find that the variation of the experimental Curie temperatures of nonstoichiometric alloys can be explained theoretically if we assume that the main impact of disorder is the intermixing of manganese and tin on their corresponding sublattices and the simultaneous appearance of strong antiferromagnetic trends which originate from the nearest-neighbor Mn-Mn interactions on different sublattices. The Curie temperatures of the Ni-Mn-Sn alloys which have been obtained from the Monte Carlo simulations are in qualitative agreement with the experimental transition temperatures.

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.

The structural and magnetic properties of functional Ni-Mn-$Z$ ($Z=\text{Ga}$, In, Sn) Heusler alloys are studied by first-principles and Monte Carlo methods. The ab initio calculations give a basic understanding of the underlying physics which is associated with the strong competition of ferro- and antiferromagnetic interactions with increasing chemical disorder. The resulting $d$-electron orbital dependent magnetic ordering is the driving mechanism of magnetostructural instability which is accompanied by a drop of magnetization governing the size of the magnetocaloric effect. The thermodynamic properties are calculated by using the ab initio magnetic exchange coupling constants in finite-temperature Monte Carlo simulations, which are used to accurately reproduce the experimental entropy and adiabatic temperature changes across the magnetostructural transition.