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

Anisotropic Charge Distribution Induced by Spin Polarization in La$_{0.6}$Sr$_{0.4}$MnO$_{3}$ Thin Films Studied by X-ray Magnetic Linear Dichroism