  Magnetic anisotropy of epitaxially grown thin films is affected by the strain
from the substrates due to a combined effect of distorted electronic structure
and spin-orbit interaction (SOI). As an inverse process, one expects an
anisotropy of the electronic structure induced by magnetization in the presence
of SOI. We have studied the charge-density anisotropy induced by magnetization
in thin films of the ferromagnetic metal La$_{1-x}$Sr$_{x}$MnO$_3$ via x-ray
magnetic linear dichroism (XMLD). XMLD measurements on thin films with various
thicknesses have shown that the XMLD intensity is proportional to the square of
the ferromagnetic moment. Using the XMLD sum rule and cluster-model
calculation, it has been shown that more Mn 3$d$ electrons are distributed in
orbitals elongated along the direction parallel to the spin polarization than
in orbitals elongated in the direction perpendicular to it. The cluster-model
calculation has shown that the effect of tensile strain from the SrTiO$_3$
substrate on the XMLD spectra is also consistent with the observed XMLD
spectral line shapes.
