Element-specific magnetic hysteresis loops observed in hexagonal ErFeO₃ thin films

Figures 1(a) and (b) show the XAS spectra of Er M_4,5-edge and Fe L_2,3-edge measured at 5.5 K, respectively. The XAS spectra are obtained as the sum spectra of different helicities and each spectrum is normalized by the maximum intensity. A 2:1 L₃/L₂ edge jump and 2nd order diffraction of the Er M_4,5-edge are subtracted from all Fe L_2,3-edge data before normalization. Since the 2nd order diffraction of the Er M₅–edge is well separated from the Fe L_2,3-edge, we rescaled our XAS spectra of the Er M_4,5-edge and subtracted them from the Fe XAS spectra. For the Er M_4,5-edge, almost the same XAS spectra are obtained for other temperatures. The spectrum shows good agreement with the theoretical dipole excitation spectrum of the ground level from the Hund's rule [26]. The M₅-edge exhibits a characteristic triplet profile, which has been reported in other Er compounds. This triplet peak originates from the optical selection rules ${\rm{\Delta }}J=0,\,\,\,\pm 1.$ Regarding the M₄-edge, splitting is not visible since this contribution is more obvious in the 3d_5/2 group for Er ions. In the case of the Fe L_2,3-edge, the spectrum shape is different from α-Fe₂O₃ or γ-Fe₂O₃ which has O_h Fe³⁺ site or a mixture of O_h and T_d Fe³⁺ sites [27]. This result is not surprising since Fe³⁺ has a coordination number of five to form corner-linked fivefold trigonal bipyramids and is located at a low symmetry site [6]. The point group of the Fe³⁺ site is lower than D_3h with energy splitting of a'₁, e', and e'. This energy splitting explains our XAS spectra and similar profiles have been reported in other materials [28, 29]. Figures 1(c) and (d) exhibit the XAS spectra of Er and Fe for different helicities measured at 5.5 K, respectively. The M₅-edge shows a large difference, which produces a strong XMCD results, as shown in figure 1(e). The obtained XMCD spectra are similar to the Er XMCD spectra observed in metallic systems. Although the difference between each helicity for the Fe spectra is much smaller than that of the Er M₅-edge, it exhibits a distinct difference, and the XMCD spectrum is shown in figure 1(f). Although the obtained Fe L₃-edge XMCD spectra having two positive peaks and a negative peak are similar to those of the h-YbFeO₃ thin film [28], this characteristic profile has also been reported in materials containing more than two Fe sites [30]. This result suggests the possibility of having two sites for Fe ions. Further experiments are needed to clarify this point. The temperature dependences of the XMCD spectra for Er and Fe are summarized in figure 2. The obtained features of the XMCD spectra do not change as a function of temperature. With an increasing temperature, the magnitude of the XMCD intensity decreases monotonically and becomes almost zero above the Néel temperature of 120 K. This phase transition temperature coincides well with previously reported SQUID measurement [21]. The negative sign of the XMCD in the L₃ edge for Fe ions indicates that the spin moment direction is parallel to the external magnetic field.

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Using sum-rule analysis, the ratio of the orbital moment (m_o) to spin (m_s) can be obtained from the XMCD spectrum and its integration spectrum [26, 31–35]. According to the XMCD sum rules, the orbital and spin magnetic moments for the Fe 3d state can be determined. Since we did not measure the incident angle dependence of XMCD, we cannot obtain the exact value of the angular-dependent magnetic dipole moment. Therefore, we only calculate m_o by using the following equation:

$$\begin{eqnarray*}&&{m}_{o}=-\displaystyle \frac{4}{3}\displaystyle \frac{\displaystyle {\int }_{{L}_{2}+{L}_{3}}d\omega ({\mu }^{+}-{\mu }^{-})}{\displaystyle {\int }_{{L}_{2}+{L}_{3}}d\omega \left({\mu }^{+}+{\mu }^{-}\right)}\left(10-n\right),\end{eqnarray*}$$

where n is the 3d electron occupation number and we assumed that n = 5. The obtained m_o values are summarized in table 1. The magnitude of m_o decreases with temperature. It can be seen that m_o for Fe is relatively small over the whole temperature range. Such a small value is reasonable and reported in many Fe systems since the ionic state of Fe³⁺ is half-filled [36–39]. To understand the precise contribution from the spin, it is necessary to conduct angular dependence experiments. We also applied the sum rules for the Er 4f state. The obtained m_o values are tabulated in table 1 assuming that n = 11. The m_o value of Er decreases monotonically with an increasing temperature. The inverse of the orbital moment for Er obeys the Curie-Weiss law with the Curie temperature of −12.7 K. This temperature coincides well with the paramagnetic component obtained from a superconducting quantum interference device magnetometer (SQUID) experiment [21]. This suggests the possibility that the paramagnetic component that we have observed in the SQUID experiments originates from the Er ion.

Figures 3(a) and (b) show the magnetic field dependences of the XMCD intensity. At 150 K, both Er and Fe ions exhibit linear behaviors which are typical for paramagnetic materials. Below 120 K, the magnetic field dependences behave differently for the Er and Fe ions. Fe exhibits obvious hysteresis loops below 120 K. With a decreasing temperature, the magnetization and the coercive field H_c increase monotonically until 50 K, which indicates the existence of ferromagnetism along the c-axis. Below 20 K, the shapes of the magnetic hysteresis loops show sudden changes, and the coercive field decreases with a decreasing temperature. However, the Er ion still contains a paramagnetic linear component with an apparent magnetic hysteresis loop below 120 K. This result leads to the conclusion that the paramagnetic contribution that appears in macroscopic measurements is caused by the Er ion. After subtracting the linear component χH at different temperatures, it exhibits well-saturated hysteresis loops in the temperature range of 10 to 75 K. Figure 3(e) shows the temperature dependence of the coercive field for both the Fe and Er ions. Regarding Er ions, we plotted the values obtained from the subtracted hysteresis loops. The magnitude of the coercive field for Er ions takes the same value as that of Fe ions. Figures 3(c) and (d) show the magnitudes of XMCD intensity for the Fe and Er ions obtained at 1 T, respectively. We also collected XMCD intensity as a function of temperature at several different energies (695, 708.7, 740 eV for Fe L₃–edge and 1380, 1402, 1425 eV for Er M₅–edge) and plotted them on the same figures. Fe ions exhibit a maximum value at 20 K and further decreasing the temperature weakens the XMCD intensity. On the other hand, the XMCD intensity of Er ion monotonically increases with a decreasing temperature. Such a difference is derived from a paramagnetic linear component of the Er ion. Since the XMCD intensity corresponds to the magnetic moment, the magnitude of XMCD intensity obtained at 0 T which represents the spontaneous magnetization is plotted in figure 3(f). Regarding Er ions, these values are calculated from the subtracted hysteresis loops. After subtraction, the behavior of Er is similar to that of Fe ions. These results suggest that the magnetic properties of Er ions are strongly influenced by the Fe magnetic moment through the exchange field, which makes the magnetic ordering temperature of Er higher than that of normal rare-earth containing materials. Another thing that we would like to mention is the directions of the overall magnetic moments for both elements. On the h-YbFeO₃ thin film, spontaneous magnetization reversal is observed by several authors and explains this phenomenon as the result of the cancellation of the magnetic moment [19, 28], which is different from our current situation. The Dzialoshinskii-Moriya interaction induces the canting of Fe ions from the ab plane, which creates an exchange field on the Er ion. This exchange field causes the canting of the Er ion. As a result, the magnetic moments of Er and Fe cant in the same direction from the ab plane and produce weak ferromagnetism. This model is consistent with previous SQUID and Mössbauer experiments [21]. Mössbauer spectroscopy suggests that the magnetic moment of Fe ions is inclined around 10 ° from ab plane at 5 K. Since Fe³⁺ ion possesses a magnetic moment of 5 μ_B, such a canting produces around 0.87 μ_B/f.u. along the c-axis, which is lower than the magnetization obtained from SQUID experiment (shown in figure 3(g)). It means that Er ion is also inclined from the ab plane and aligned parallel to the Fe ion. A sudden change in the shape of the hysteresis loop probably originates from a strong anisotropy that has the easy magnetization axis along the in-plane direction. To understand the spin configuration of h-ErFeO₃, DFT calculation is desired and we are planning to perform it and publish the result in elsewhere.

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Figure 4 shows the Mössbauer spectra measured at different temperatures. Paramagnetic spectra consisting of a doublet are observed above 150 K. The isomer shift and quadrupole splitting are 0.37 and 2.01 mm s⁻¹, respectively. The value of the isomer shift suggests that the Fe ions are in a high-spin Fe³⁺ state. With decreasing temperature, the Mössbauer spectrum starts to change its shape below 110 K. This temperature coincides well with the XMCD experiments. Below 30 K, well-resolved magnetically ordered spectra with a hyperfine field of 43.3 T at 5.7 K are observed. Although the M-H hysteresis loops of Er and Fe ions obtained from XMCD measurements show drastic changes below 20 K, there is almost no difference between 30 and 5.7 K. This means that the magnetic structure does not change at approximately 20 K. The intensity ratio of the six absorption lines at 5.7 K is close to 3:4:1:1:4:3, which indicates that the hyperfine field lies approximately in the plane of the film. All these results are quite similar to previously reported work which used a 98% ⁵⁷Fe-enriched ErFeO₃ thin film [21]. This result clearly suggests that at a depth of 2 nm below the surface, the magnetic properties and structure are already recovered to be the same as those in the bulk h-ErFeO₃. Therefore, we can conclude that the current XMCD data obtained in the total electron yield mode with a larger probing depth reflect the bulk property. In the bulk h-ErFeO₃, the direction of the magnetic moment of Fe on the same c-plane forms a triangular lattice and its magnetization is cancelled. The magnetic moment is canted from the ab plane at 10 °, which produces weak ferromagnetism along the c-axis. The same picture can be applied for the present study and it agrees with our XMCD results.

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