Ferromagnetic amorphous oxides in the EuO-TiO₂ system studied by the Faraday effect in the visible region and the x-ray magnetic circular dichroism at the Eu M_4,5 and L_2,3 edges

Amorphous Eu₂TiO₄ and EuTiO₃ have been studied by a combination of the Faraday effect in the visible region and polarization-dependent x-ray absorption spectroscopy at the Eu M_4,5 and L_2,3 edges to examine the role of Eu 4f-5d exchange interactions on the ferromagnetic behavior. The bulk-sensitive x-ray absorption spectra (XAS) for Eu L_2,3 edges show that most of the europium ions are present as the divalent state in the amorphous Eu₂TiO₄ and EuTiO₃. The Eu M_4,5 edge x-ray magnetic circular dichroism (XMCD) signals, measured for the amorphous Eu₂TiO₄, dramatically increase upon cooling through the Curie temperature (16 K) determined by a superconducting quantum interference device (SQUID) magnetometer. Sum-rule analysis of the XMCD at Eu M_4,5 edges measured at 10 K yields a 4f spin magnetic moment of 6.6μ_B per Eu2 ⁺ ion. These results confirm that the ferromagnetic properties exclusively arise from 4f spins of Eu2⁺. In addition, for both the amorphous Eu₂TiO₄ and EuTiO₃, the temperature and magnetic-field dependence of Eu L_2,3 edge XMCD signals can be scaled with the corresponding magnetization measured by SQUID, indicating that the 5d magnetic polarization of Eu2⁺ is involved in the process to cause the ferromagnetic interaction between Eu2⁺ ions. We further discuss the origin of ferromagnetism in the amorphous system on the basis of the energy diagram of Eu 4f and 5d levels deduced from the Faraday effect in the visible region. From the wavelength dependence of Faraday rotation angles of the amorphous EuO-TiO₂ system in comparison with those of the divalent Eu chalcogenides as reported previously, it is found that the magnitude of crystal-field splitting of Eu 5d levels in the former is on the same order as that in the latter, which explains an enhanced ferromagnetic exchange interaction between Eu 4f and 5d states.