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.

Structural, magnetic and electronic properties of stoichiometric Co ₂ YZ Heusler alloys ( Y = Cr, Fe, Mn and Z = Al, Si, Ge) have been studied by means of ab initio calculations and Monte Carlo simulations. The investigations were performed in dependence on different levels of approximations in DFT (FP and ASA modes, as well as GGA and GGA + U schemes) and external pressure. It is shown that in the case of the GGA scheme the half-metallic behavior is clearly observed for compounds containing Cr and Mn transition metals, while Co ₂ Fe Z alloys demonstrate the pseudo half-metallic behavior. It is demonstrated that an applied pressure and an account of Coulomb repulsion ( U ) lead to the stabilization of the half-metallic nature for Co ₂ YZ alloys. The strongest ferromagnetic inter-sublattice (Co– Y ) interactions together with intra-sublattice (Co–Co and Y – Y ) interactions explain the high values of the Curie temperature obtained by Monte Carlo simulations using the Heisenberg model. It is observed that a decrease in valence electrons of Y atoms (i.e. Fe substitution by Mn and Cr) leads to the weakening of the exchange interactions and to the reduction of the Curie temperature. Besides, in the case of the FP mode Curie temperatures were found in a good agreement with available experimental and theoretical data, where the latter were obtained by applying the empirical relation between the Curie temperature and the total magnetic moment.

The structural, electronic and magnetic properties of Fe_100-xGa_x alloys are studied computationally in the composition range up to $x\le$ 31.25 at.% and experimentally about 27 at.%. Ga content. Using ab initio calculations, it is shown that as Ga content increases, the lattice parameters are found to increase for all types of structures, as opposed to the magnetic moment behavior. The phase diagram is plotted as a function of energy. In agreement with experimental results, the following sequences of phase transformations are observed: D0₃→A2 ( $6.25\le x\le 18.75$ at.%), D0₃→L1₂→A2 ( $18.75<x\le 21.875$ at.%), and L1₂→D0₁₉→B2→A2 ( $21.875<x\le 31.25$ at.%). It is found that the L1₂ cubic structure possesses the largest degree of spin polarization. Experimental studies of Fe-Ga as cast alloys at a constant heating rate and isothermal annealing carried out by means of in situ neutron diffraction and vibrating sample magnetometry demonstrate the sequence of phase transitions of the I and II order.

The stability of the nonmodulated martensitic phase, the austenitic Fermi surface, and the phonon dispersion relations for ferromagnetic ${\mathrm{Ni}}_2\mathrm{MnGa}$ are studied using density functional theory. Exchange-correlation effects are considered with various degrees of precision, starting from the simplest local spin density approximation (LSDA), then adding corrections within the generalized gradient approximation (GGA), and finally, including the meta-GGA corrections within the strongly constrained and appropriately normed (SCAN) functional. We discuss a simple procedure to reduce a possible overestimation of magnetization and underestimation of nesting vector in SCAN by parametrically decreasing self-interaction corrections.

The structural and magnetic properties of Co-doped Ni–Mn–In Heusler alloys are investigated in the framework of density functional theory and the Monte-Carlo method. The first principles calculations of the equilibrium properties (crystalline structure and magnetic ordering) indicate that the ferromagnetic state is favorable in the austenite structure, whereas the ferrimagnetic order is stable in the martensite structure. The strong competition of ferro- and antiferromagnetic exchange interactions arise from the austenite-martensite crossover. The temperature dependences of total magnetization are calculated by means of the proposed Hamiltonian model with the ab initio magnetic exchange couplings and magnetostructural interrelation. The calculated properties are in good agreement with the experimental ones.