Modeling of full-Heusler alloys within tight-binding approximation: Case study of Fe₂MnAl

Heusler alloys have been known for about a century, and predictions of magnetic moment values using Slater-Pauling rule have been successful for many such materials. However, such a simple counting rule has been found not to always work for all Heusler alloys. For instance, Fe₂CuAl has been found to have magnetic moment of 3.30 μ_B per formula unit although the Slater-Pauling rule suggests the value of 2 μ_B. On the other hand, a recent experiment shows that a non-stoichiometric Heusler compound Fe₂Mn_0.5Cu_0.5Al possesses magnetic moment of ~4 μ_B, closer to the Slater-Pauling prediction for the stoichiometric compound. Such discrepancies signify that the theory to predict the magnetic moment of Heusler alloys in general is still far from being complete. Motivated by this issue, we propose to do a theoretical study on a full-Heusler alloy Fe₂MnAl to understand the formation of magnetic moment microscopically. We model the system by constructing a density-functional-theory-based tight-binding Hamiltonian and incorporating Hubbard repulsive as well as spin-spin interactions for the electrons occupying the d-orbitals. Then, 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 the experimental data.