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We present a first-principles study of the electronic and magnetic propertiesof epitaxial interfaces between the Heusler compounds Ti$_2$MnIn and Ni$_2$MnInand the III-V semiconductors, InSb and InAs, respectively. We use densityfunctional theory (DFT) with a machine-learned Hubbard $U$ correctiondetermined by Bayesian optimization. We evaluate these interfaces forprospective applications in Majorana-based quantum computing and spintronics.In both interfaces, states from the Heusler penetrate into the gap of thesemiconductor, decaying within a few atomic layers. The magnetic interactionsat the interface are weak and local in space and energy. Magnetic moments ofless than 0.1 $\mu_B$ are induced in the two atomic layers closest to theinterface. The induced spin polarization around the Fermi level of thesemiconductor also decays within a few atomic layers. The decisive factor forthe induced spin polarization around the Fermi level of the semiconductor isthe spin polarization around the Fermi level in the Heusler, rather than theoverall magnetic moment. As a result, the ferrimagnetic narrow-gapsemiconductor Ti$_2$MnIn induces a more significant spin polarization in theInSb than the ferromagnetic metal Ni$_2$MnIn induces in the InAs. This isexplained by the position of the transition metal $d$ states in the Heuslerwith respect to the Fermi level. Based on our results, these interfaces areunlikely to be useful for Majorana devices but could be of interest forspintronics.

First Principles Study of the Electronic Structure of the Ni$_2$MnIn/InAs and Ti$_2$MnIn/InSb interfaces