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We report remarkably low residual resistivity, giant residual resistivityratio, free-electron-like Hall resistivity and high mobility ($\approx$ 10$^4$cm$^2$V$^{-1}$s$^{-1}$) charge transport in epitaxial films of Co$_2$MnSi andCo$_2$FeSi grown on (001) SrTiO$_3$. This unusual behavior is not observed infilms deposited on other cubic oxide substrates of comparable latticeparameters. The scaling of the resistivity with thickness of the films allowextraction of interface conductance, which can be attributed to a layer ofoxygen vacancies confined within 1.9 nm of the interface as revealed byatomically resolved electron microscopy and spectroscopy. The high mobilitytransport observed here at the interface of a fully spin polarized metal ispotentially important for spintronics applications.

Two-dimensional electron-gas-like charge transport at magnetic Heusler alloy-SrTiO$_3$ interface