Combining Quasiparticle Self-Consistent $GW$ and Machine-Learned DFT+$U$ to Assess Half-Metallicity in Co- and Ni-Based Heuslers

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 semi-local and hybrid functionals are compared to quasiparticle self-consistent $GW$ (QP$GW$). We also consider DFT with machine-learned Hubbard $U$ corrections [npj Computational Materials 6, 180 (2020)] with a new Bayesian optimization (BO) objective function to determine the $U$ values that yield the closest agreement with the QP$GW$ band structure and magnetic moments. We find that DFT+$U$(BO) can adequately reproduce the key 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, Co$_2$TiSn and Co$_2$ZrAl are the most likely to be half-metals.