Ferromagnetic amorphous oxides in the EuO-TiO${}_2$ 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 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${\mu }_{\mathrm{B}}$ 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.

Figure 1

Schematic energy diagram of the 5$d$ and 4$f$ states for Eu${}^{2+}$ in EuTiO${}_3$ crystal (c-ETO), EuO crystal, and amorphous EuTiO${}_3$ (a-ETO) (from left to right). The 5$d$ crystal-field splitting is drawn based on the energy level scheme described in Refs. 14 and 16. The larger crystal-field splitting for a-ETO compared to c-ETO results in the smaller energy separation between the 4$f$ levels and the lower levels of 5$d$ states.

Figure 2

Temperature dependence of magnetization of a-ETO (a) and a-2ETO thin films (b) deposited on Kapton foils (triangles), measured at an external magnetic field ($H$) of 100 Oe using SQUID magnetometer. From temperature derivative of magnetization curves, Δ$M$/Δ$T$ (squares), the Curie temperature is determined to be 6.0 K for a-ETO and 15 K for a-2ETO, in agreement with those of our previous samples deposited on SiO${}_2$ glass substrates, as described in Ref. 11.

Figure 3

Magnetic-field dependence of magnetization of a-2ETO thin film deposited on SiO${}_2$ glass substrate, measured at 2 K using SQUID magnetometer. The magnetic field ($H$) is applied along the directions parallel (in plane) and perpendicular (out of plane) to the sample surface.

Figure 4

(a) Room-temperature optical absorption spectra in the visible region for 100-nm-thick a-ETO and a-2ETO thin films. (b) Wavelength dependence of the Verdet constant at room temperature for a-ETO and a-2ETO.

Figure 5

Eu $L_{2,3}$ edge XAS (a) and XMCD (b) of a-ETO thin film and Eu $L_{2,3}$ edge XAS (c) and XMCD (d) of a-2ETO thin film, measured at 1.9 K under an external magnetic field ($H$) of 1.9 T. The positions of the major peak and satellite for the Eu $L_3$ edge XAS are indicated by the vertical dashed lines.

Figure 6

Fit of Eu $L_3$ edge XAS of a-2ETO thin film with the superposition of two Lorentzians and two arctangent functions.

Figure 7

Eu $M_{4,5}$ edge XAS (a) and XMCD (b) of a-2ETO thin film, measured at 10 K under an external magnetic field of 1.9 T.

Figure 8

(a) Experimental XAS at the Eu $M_{4,5}$ edges for the a-2ETO thin film (solid curve) and the weighted sum of the theoretical XAS for Eu${}^{2+}$ and Eu${}^{3+}$ (broken curve). The experimental data were recorded at 10 K under an external magnetic field of 1.9 T. (b) Theoretical XAS of Eu${}^{2+}$ and Eu${}^{3+}$ obtained by atomistic multiplet calculations.

Figure 9

(a) Temperature dependences of the Eu $M_5$ edge XMCD signal amplitude (squares) and SQUID magnetization data (solid line), measured for a-2ETO under an external magnetic field ($H$) of 1.9 T applied perpendicular to the surface. Inset shows the Eu $M_5$ edge XMCD signals for the same sample at various temperatures between 15 and 150 K. (b) $H$ dependences of the Eu $M_{4,5}$ edge XMCD signals (squares) and SQUID magnetization data (solid line), measured for a-2ETO at 10 K. The XMCD signals are plotted with the sign reversed.

Figure 10

(a), (b) Temperature dependences of the Eu $L_3$ edge XMCD signals (triangles) and SQUID magnetization data (solid line), measured for the a-2ETO (a) and a-ETO (b) under an external magnetic field ($H$) of 0.1 T applied perpendicularly to the surface. The respective inset shows the Eu $L_3$ edge XMCD signals recorded at various temperatures between 1.9 and 187 K. (c), (d) $H$ dependences of the Eu $L_3$ edge XMCD signals (triangles) and SQUID magnetization data (solid line), measured for a-2ETO (c) and a-ETO (d) at 2 K.