Half-metallic Heusler compounds are of significant interest for spintronics. For device fabrication, compounds that can be epitaxially grown on III-V semiconductors are particularly attractive. We present a first-principles investigation of four Co-based and two Ni-based Heusler compounds that are lattice-matched to InAs. The results of density functional theory (DFT) using semilocal and hybrid functionals are compared with quasiparticle self-consistent $GW$ ($\mathrm{QP}GW$). We also assess DFT with machine-learned Hubbard $U$ corrections, as proposed in M. Yu et al. [npj Comput. Mater. 6, 180 (2020)]. Here, the $U$ values that yield the closest agreement with the $\mathrm{QP}GW$ band structure are determined using an updated Bayesian optimization (BO) objective function that considers the atomic magnetic moments in addition to the band structure. We find that $\mathrm{DFT}+U$(BO) can adequately reproduce the key $\mathrm{QP}GW$ features in most cases. Our results reveal a strong method dependence of the degree of spin polarization at the Fermi level and, in some cases, even the dominant spin channel (majority or minority). Of the materials studied here, ${\mathrm{Co}}_2\mathrm{TiSn}$ and ${\mathrm{Co}}_2\mathrm{ZrAl}$ are the most likely to be half-metals.

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• Density of states
• Electronic structure
• Magnetism
• First-principles calculations