Calculation of magnetic moment of inverse-Heusler alloy Fe₂CuAl via first-principles-based tight-binding model

Heusler alloys have been known since the 19^th century and have fascinated researchers because of their wide range of applications, especially related to their magnetic properties. The magnetic moment of a few of these materials can be predicted by simply counting their valance electrons [this is called the Slater-Pauling (SP) rule]. However, this simple counting rule does not work in many other cases. Inverse-Heusler alloys are a sub-class of Heusler alloys, and in many cases also do not follow the SP rule. Fe₂CuAl (FCA) is an inverse-Heusler alloy for which the SP rule predicts a magnetic moment of 2.00 μB. However, experimental results give a magnetic moment of 3.30 μB. Motivated by this discrepancy, we study this material theoretically to gain a microscopic understanding of how the magnetic moment forms. For this purpose, we construct a first-principles-based tight-binding model incorporating an on-site Hubbard repulsion U between each d orbital and a Hund coupling J between different d orbitals of a given atom in the system. We use the Green's function technique and apply the mean-field approximation to solve the model. The results show the magnetic moment of FCA depends on U and J. We find that the magnetic moment given by the SP rule (2.00 μB) corresponds to a plateau in our magnetic moment vs J curves for various values of U, and that the experimental magnetic moment (3.30 μB) corresponds to a point on the curves rising above the plateau.