Electronic and magnetic properties of (1 1 1)-oriented CoCr$_2$O$_4$ epitaxial thin film*

We report on the fabrication of high quality (1 1 1)-oriented ferrimagnetic normal spinel CoCr$_2$O$_4$ epitaxial thin films on single crystal Al$_2$O$_3$ substrates. The structural, electronic and magnetic properties were characterized by $in$-$situ$ reflection high energy electron diffraction, atomic force microscopy, X-ray diffraction, X-ray photoemission spectroscopy, SQUID magnetometry and element resolved resonant X-ray magnetic scattering. The comprehensive characterization reveals that no disorder in the cation distribution or multivalency issue is present in the samples. As a result, Kagom\'e and triangular layers are naturally formed via this specific growth approach. These findings offer a pathway to fabricate two dimensional Kagom\'e heterostructures with novel quantum many-body phenomena by means of geometrical design.