Influence of crystal field on anisotropic x-ray magnetic linear dichroism at theCo2+L2,3edges

Abstract

We expand the previous theoretical treatment for the strong anisotropy of the x-ray magnetic linear dichroism (XMLD) in a crystal field of cubic point-group symmetry to the more general case of tetragonal point-group symmetry. For the cubic symmetry, there are only two fundamental spectra, which have the same shape for rotation of either linear light polarization $\mathbf{E}$ or magnetization direction $\mathbf{H}$. For the tetragonal symmetry, the XMLD is a linear combination of four fundamental spectra, with a different shape for linear dichroism (rotation of $\mathbf{E}$) and magnetic dichroism (rotation of $\mathbf{H}$). However, only one extra spectrum is required to relate the linear and magnetic dichroism. The validity of the theory is demonstrated using a $\mathrm{Co}{\mathrm{Fe}}_{2}{\mathrm{O}}_{4}(011)$ thin film on $\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_{3}$, which has both tetrahedrally distorted symmetry and large magnetic anisotropy. The XMLD at the Co ${L}_{2,3}$ edges was found to exhibit a strong dependence on the relative orientation of external magnetic field, x-ray polarization, and crystalline axes. The large variations in the peak structure as a function of angle are not caused by the spin-orbit-induced magnetocrystalline anisotropy but arise from the symmetry of the measurement geometry. The results are compared with calculated spectra using atomic multiplet theory for ${\mathrm{Co}}^{2+}$ ${d}^{7}\ensuremath{\rightarrow}2{p}^{5}{d}^{8}$ in octahedral and tetragonal crystal field symmetry. Although the magnitude of the dichroism is strongly influenced by the temperature, its spectral shape remains largely unaffected. The measured fundamental spectra are also robust against incomplete magnetization. The influence of the tetragonal distortion is revealed by small differences between the linear and magnetic dichroism. It is shown that the magnetic dichroism spectra can be transferred from $\mathrm{Co}{\mathrm{Fe}}_{2}{\mathrm{O}}_{4}$ to CoO. Therefore, the rich structure in the ${\mathrm{Co}}^{2+}$ ${L}_{3}$ XMLD provides a sensitive probe to determine the orientation of the spin axis with respect to the crystalline axes, hence offering a valuable tool for experimentalists for the study of exchange bias in Co oxides. In contrast, the ${\mathrm{Co}}^{2+}$ ${L}_{2}$ edge, where the fundamental spectra have similar spectral shape but with opposite sign, does not allow an unambiguous determination.