  We report remarkably low residual resistivity, giant residual resistivity
ratio, 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 and
Co$_2$FeSi grown on (001) SrTiO$_3$. This unusual behavior is not observed in
films deposited on other cubic oxide substrates of comparable lattice
parameters. The scaling of the resistivity with thickness of the films allow
extraction of interface conductance, which can be attributed to a layer of
oxygen vacancies confined within 1.9 nm of the interface as revealed by
atomically resolved electron microscopy and spectroscopy. The high mobility
transport observed here at the interface of a fully spin polarized metal is
potentially important for spintronics applications.
