  Layered ruthenates are a unique class of systems which manifests a variety of
electronic and magnetic features emerged from competing energy scales. At the
heart of such features lies the multi-orbital physics, especially, the
orbital-selective behavior. Here, we propose that the SrRuO3-SrTiO3
heterostructure is a highly tunable platform to obtain the various emergent
properties. Employing the density functional theory plus dynamical mean-field
theory, we thoroughly investigate the orbital-dependent physics of the system
and identify the competing magnetic fluctuations. We show that the epitaxial
strain drives the system towards multi-orbital or orbital selective Mott phases
from the Hund metal regime. At the same time, the two different types of static
magnetism are stabilized, ferromagnetism and checkerboard antiferromagnetism,
from the competition with the spin-density wave instability.
