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

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.