Orbital polarization inNiFe2O4measured byNi−2px-ray magnetic circular dichroism

Abstract

We report a comprehensive study of the x-ray magnetic circular dichroism (XMCD) at the Ni ${L}_{2,3}$ edges of ${\mathrm{NiFe}}_{2}{\mathrm{O}}_{4}$ (trevorite), a ferrimagnetic compound which belongs to the class of strongly correlated $3d$ systems. The measured XMCD line shape is in good agreement with full-multiplet calculations for a ${3d}^{8}$ ground state including an octahedral crystal field of $10Dq=1.2$ eV. Using the XMCD sum rules, we find for the nickel an orbital to spin magnetic moment ratio of $L/S=0.27\ifmmode\pm\else\textpm\fi{}0.07,$ which means that the orbital contribution to the magnetic moment is 12\ifmmode\pm\else\textpm\fi{}2 %. The size of the error bar is not due to the neglect of band structure and hybridization, but due to Coster-Kronig transitions which give a transfer of spectral weight in the dichroism near the ${L}_{2}$ edge. Using the sum rules for the isotropic x-ray absorption spectrum, we obtain the expectation value of the spin-orbit interaction, which can be converted into an $L/S$ ratio of 0.34\ifmmode\pm\else\textpm\fi{}0.11. All sum-rule results were corrected for the influence of core-valence exchange interaction, which gives rise to jj mixing between the two absorption edges. The correction is done by comparing the calculated sum-rule results with the correct ground-state values calculated as a function of crystal-field strength. The 2-eV shoulder of the ${L}_{3}$ line shows a strong positive dichroism, which can be attributed to a spin-flip state. From the overall agreement between the experimental and theoretical results, we conclude that a localized model provides a good description for the orbital magnetization.