Modeling of half-Heusler compound NiMnSb within tight-binding approximation

Heusler compounds are families of magnetic materials with general stoichiometry of either X₂YZ (full-Heusler compound) or XYZ (half-Heusler compound), with X and Y being transition metal elements, and Z a main-group element. Their various potentials for technology development make them be still relevant as a subject of both experimental and theoretical studies. Half-Heusler compounds are generally crystallized in the C1_b-type structure. The magnetic moments of such materials may be predicted using Slater-Pauling rule, giving m = (N_{valence electrons} - 18)μ_B per formula unit. However, this simple counting rule does not always work for all compounds in this group. This motivates us to perform a theoretical study to investigate the mechanism of magnetic moment formation microscopically. As a case study, we focus on NiMnSb, a particular half-Heusler compound, for which comparison between existing experimental results and theoretical predictions of its magnetic moment has not yet been quite convincing. We model the system by constructing a tight-binding-based Hamiltonian, incorporating Hubbard repulsive as well as spin-spin interactions for the electrons occupying the d-orbitals. We solve the model using Green's function approach, and treat the interaction terms within the mean-field approximation. At this stage, we aim to formulate the computational algorithm for the overall calculation process. Our final goal is to compute the total magnetic moment per unit cell of this system and compare it with available experimental data.