Ferromagnetic amorphous oxides in the EuO-TiO2system studied by the Faraday effect in the visible region and the x-ray magnetic circular dichroism at the EuM4,5andL2,3edges

Abstract

Amorphous Eu${}_{2}$TiO${}_{4}$ and EuTiO${}_{3}$ 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 4$f$-5$d$ 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 Eu${}_{2}$TiO${}_{4}$ and EuTiO${}_{3}$. The Eu ${M}_{4,5}$ edge x-ray magnetic circular dichroism (XMCD) signals, measured for the amorphous Eu${}_{2}$TiO${}_{4}$, 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 4$f$ spin magnetic moment of 6.6${\ensuremath{\mu}}_{\mathrm{B}}$ per Eu${}^{2+}$ ion. These results confirm that the ferromagnetic properties exclusively arise from 4$f$ spins of Eu${}^{2+}$. In addition, for both the amorphous Eu${}_{2}$TiO${}_{4}$ and EuTiO${}_{3}$, 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 5$d$ magnetic polarization of Eu${}^{2+}$ is involved in the process to cause the ferromagnetic interaction between Eu${}^{2+}$ ions. We further discuss the origin of ferromagnetism in the amorphous system on the basis of the energy diagram of Eu 4$f$ and 5$d$ levels deduced from the Faraday effect in the visible region. From the wavelength dependence of Faraday rotation angles of the amorphous EuO-TiO${}_{2}$ 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 5$d$ levels in the former is on the same order as that in the latter, which explains an enhanced ferromagnetic exchange interaction between Eu 4$f$ and 5$d$ states.