Functional dependence of d-state bonding and magnetovolume effects in Heusler alloys

Accurate first-principles prediction of transition-metal Heusler alloys requires a balanced description of d-state bonding and, in magnetic members, magnetovolume coupling. Here, we systematically compare the Perdew-Burke-Ernzerhof (PBE) generalized-gradient approximation, the strongly constrained and appropriately normed (SCAN) meta-generalized-gradient approximation, and the regularized-restored SCAN (r²SCAN) functional for representative half-Heusler semiconductors and magnetic full-Heusler alloys. For the half-Heusler compounds examined here, PBE generally overestimates the equilibrium lattice constants, whereas SCAN yields systematically smaller values, and r²SCAN provides the best overall agreement with experiment. Bonding and charge-density analyses associate the reduced lattices predicted by SCAN with stronger directional d-state bonding tendencies, which are further reflected in stiffer elastic and vibrational responses. In magnetic full-Heusler alloys, the equilibrium lattice is governed by competition between bonding-driven contraction and magnetovolume expansion. The contraction tendency dominates for most compounds in the present dataset, whereas the moment enhancement predicted by SCAN and r²SCAN in selected Fe-based alloys can partially offset or even overcome this contraction. Energy-landscape calculations further reveal strong compound-dependent behavior: SCAN and r²SCAN over-stabilize a high-spin state in Fe₂VSn, but yield a more pronounced tetragonal minimum in Ni₂MnGa that is closer to the experimental martensitic distortion. These results show that functional accuracy in Heusler alloys depends on the combined treatment of d-state bonding, spin polarization, and structural anisotropy, providing a physical basis for property-specific functional selection in transition-metal intermetallics.