  Magnetic multilayers of $(SrRuO_3)_m(SrMnO_3)_n$ were grown artificially
using the pulsed laser deposition technique on (001)-oriented $SrTiO_3$
substrates. The state of strain at the interfaces and the structural coherency
are studied in details utilizing asymmetrical $X$-ray diffraction and the $\sin
^2\psi $ method. First, the evolution of the lattice parameters, the
crystallinity and the epitaxy of the films are evaluated as a function of the
number of $SrMnO_3$ unit cells using $X$-rays diffraction and transmission
electron microscopy. Second, our results on the stress indicate that the
$SrRuO_3/SrMnO_3$ superlattices show a larger residual strain as compared to
the single layer film of $SrRuO_3$. This suggests that the lattice stiffening
from interfacial strain and inhibiting the dislocation by composition
modulation. Finally, these results bring insights on the interfacial stress
measurements of oxide multilayers that can be used to control the physical
properties at the level of the atomic scale.
