  Superlattices of correlated oxides have been used to explore interfacial
effects and to achieve additional control over the physical properties of
individual constituents. In this work, we present a first-principles
perspective of the strain and thickness effects in
La$_{2/3}$Sr$_{1/3}$MnO$_3$/YBa$_2$Cu$_3$O$_{7}$ (LSMO/YBCO) superlattices. Our
findings indicate that the presence of epitaxial strain and LSMO leads to a
reduction of buckling parameters of the interfacial CuO$_2$ planes, as well as
the transfer of electrons from LSMO to YBCO. In addition, the change in Cu-3$d$
valence is slightly dependent on the LSMO layer thickness. More interestingly,
the in-plane ferromagnetic ground state within the CuO$_2$ planes near the
interface is induced due to the local moments centered at the copper atoms.
These local moments are decoupled from the charge transfer and, according to
our calculations, appear mainly due to the Mn $3d$-O $2p$-Cu $3d$ hybridization
being restricted to the interfacial region. The induced net magnetic ordering
in interfacial copper atoms may have implications in the control of the
superconducting state in the LSMO/YBCO superlattices.
