  Under various conditions of the growth process, when the presumably
unconventional superconductor Sr$_2$RuO$_4$ (SRO) contains micro-inclusions of
Ru metal, the superconducting critical temperature increases significantly. An
STEM study shows a sharp interface geometry which allows crystals of SRO and of
Ru-metal to grow side by side by forming a commensurate superlattice structure
at the interface. In an attempt to shed light as to why this happens, we
investigated the atomic structure and electronic properties of the interface
between the oxide and the metal micro-inclusions using density functional
theory (DFT) calculations. Our results support the observed structure
indicating that it is energetically favored over other types of Ru-metal/SRO
interfaces. We find that a $t_{2g}$-$e_g$ orbital mixing occurs at the
interface with significantly enhanced magnetic moments. Based on our findings,
we argue that an inclusion mediated interlayer coupling reduces phase
fluctuations of the superconducting order parameter which could explain the
observed enhancement of the superconducting critical temperature in SRO samples
containing micro-inclusions.
