⇦Chinese Physics Letters, 2023, Vol. 40, No. 12, Article code 127801 Observation of Enhanced Faraday Effect in Eu-Doped Ce:YIG Thin Films Han-Xu Zhang (张晗旭)1, Sen-Yin Zhu (朱森寅)1, Jin Zhan (湛劲)1, Xian-Jie Wang (王先杰)1, Yi Wang (王一)1, Tai Yao (姚泰)2, N. I. Mezin3, and Bo Song (宋波)1,2,4,5* Affiliations 1School of Physics, Harbin Institute of Technology, Harbin 150001, China 2National Key Laboratory of Science and Technology on Advanced Composites in Special Environments, Harbin Institute of Technology, Harbin 150001, China 3A.A. Galkin Donetsk Institute for Physics and Engineering, Rosa Luxemburg Str. 72, 83114 Donetsk, Ukraine 4Zhengzhou Research Institute, Harbin Institute of Technology, Zhengzhou 450046, China 5Frontiers Science Center for Matter Behave in Space Environment, Harbin Institute of Technology, Harbin 150001, China Received 5 September 2023; accepted manuscript online 17 October 2023; published online 22 November 2023 *Corresponding author. Email: songbo@hit.edu.cn Citation Text: Zhang H X, Zhu S Y, Zhan J et al. 2023 Chin. Phys. Lett. 40 127801    Abstract Ce:YIG thin films are taken as an ideal candidate for magneto-optical devices with giant Faraday effect in the near-infrared range, but it is hindered by a limited Ce$^{3+}$/Ce$^{4+}$ ratio and a high saturation driving field. To address this issue, Eu doping can increase the Faraday rotation angle by $\sim$ 40% to $1.315\times 10^{4}$ deg/cm and decrease the saturation driving field by $\sim$ 38% to 1.17 kOe in Eu$_{0.75}$Ce$_{1}$Y$_{1.25}$Fe$_{5}$O$_{12}$ compared to Ce$_{1}$Y$_{2}$Fe$_{5}$O$_{12}$ pristine. The mechanism is attributed to the conversion of Ce$^{4+}$ to Ce$^{3+}$ and the weakening of ferrimagnetism by Eu doping. This work not only provides strategies for improving Ce$^{3+}$/Ce$^{4+}$ ratio in Ce:YIG, but also develops (Eu,Ce):YIG with a promising Faraday rotation angle for magneto-optical devices.
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 DOI:10.1088/0256-307X/40/12/127801 © 2023 Chinese Physics Society Article Text Yttrium iron garnet (YIG) single crystals and thin films have been widely utilized in magneto-optical devices such as optical isolators[1-3] and magneto-optical switches,[4] owing to the Faraday effect, which denotes that the rotation angle $\theta_{\scriptscriptstyle{\rm F}}$ with respect to the vibration direction is proportional to the applied magnetic field and propagation distance when light passes through a medium. However, potential applications of YIG single crystals in magneto-optical devices are severely hindered[5] due to their low Verdet constant ($\sim$ $2\times 10^{3}$ rad$\cdot$T$^{-1}\cdot$m$^{-1})$,[6] which typically results in a small Faraday rotation angle ($\sim$ 200$^\circ$/cm @1550 nm).[7] To meet the criteria of 45$^\circ$ deflection and lowest energy consumption in practical applications, a magneto-optical medium with a sufficient Faraday rotation angle and an accessible applied magnetic field is highly required. Numerous initiatives, including Bi/Ce doping,[8-13] surface structure modification,[14-17] modulation coherence,[18] and silicon-based integrated devices,[19,20] have been devoted to address these issues. Bi:YIG has attained the largest $\theta_{\scriptscriptstyle{\rm F}}$ in a visible range ($2\times 10^{5}$ deg/cm @525 nm),[9,21] although $\theta_{\scriptscriptstyle{\rm F}}$ in near-infrared is only $\sim$ $-3\times 10^{3}$ deg/cm. In contrast, Ce:YIG, a promising candidate, has garnered growing attention in the near-infrared[8] region with a peak $\theta_{\scriptscriptstyle{\rm F}}$ of $-1.4\times 10^{4}$ deg/cm @1127 nm.[22] However, since Ce$^{4+}$ makes no contribution toward Faraday effect owing to its vacant 4$f$ orbitals, it is impossible to further raise the $\theta_{\scriptscriptstyle{\rm F}}$ in Ce:YIG. Due to the lower energy transition of Ce$^{3+}$(4$f)$–Fe$^{3+}$(tetrahedral) dipole, which benefits the magneto-optical effect,[23,24] increasing the $\theta_{\scriptscriptstyle{\rm F}}$ by tuning the Ce$^{3+}$/Ce$^{4+}$ ratio is a promising strategy. In addition, it remains an extremely challenging task to simultaneously raise $\theta_{\scriptscriptstyle{\rm F}}$ and to lower the saturation driving field. Inspired by europium's (Eu) weak deoxidation properties and magnetic characteristics,[25,26] it is anticipated that Eu doping may be a feasible technique to increase Ce$^{3+}$/Ce$^{4+}$ ratio, and to decrease the saturation driving field. Nevertheless, experimentation has not yet been conducted. In this study, well-oriented Eu$_{x}$Ce$_{1}$Y$_{2-x}$Fe$_{5}$O$_{12}$ ($x=0$, 0.3, 0.5, 0.75, 1) thin films were deposited on Gd$_{3}$Ga$_{5}$O$_{12}$ (GGG) substrates. The Faraday effect was improved from 0.48 to 0.86 by adjusting the ratio of Ce$^{3+}$/Ce$^{4+}$. At $x=0.75$, $\sim$ $40$% enhancement in the Faraday rotation angle and $\sim$ $38$% reduction in the saturation driving field were concurrently achieved over all the samples. Results and Discussion. Using a power-adjustable 532 nm continuous-wave laser as the light source, the Faraday hysteresis loop was measured by employing a custom-built Faraday rotation measuring system. According to Malus's law, the relationship between the Faraday rotation angle $\theta_{\scriptscriptstyle{\rm F}}$ and the collected light intensity $I_{\scriptscriptstyle{H}}$ can be calculated using the equation: \begin{equation} \theta_{\scriptscriptstyle{\rm F}}(H)=\arcsin ({{I_{\scriptscriptstyle{H}} \sin^{2}\alpha}/{I_{\alpha}}})^{1/2}-\alpha , \tag {1} \end{equation} where $I_{\scriptscriptstyle{H}}$ denotes the light intensity when an external magnetic field $H$ is applied, $\alpha$ represents the angle between the polarization direction of the analyzer prism and the extinction direction, and $I_{\alpha}$ implies the light intensity when an external magnetic field of zero strength is applied at a preset angle $\alpha$. In a typical measurement, $\alpha$ is set to 2$^\circ$, determined based on a comprehensive assessment of the relative change in light intensity [($I_{\scriptscriptstyle{H}}-I_{\alpha})/I_{\alpha}$] and the absolute change [$(I_{\scriptscriptstyle{H}}-I_{\alpha})/I$]. Here, $I$ depicts the light intensity in the absence of an external magnetic field when $\alpha$ is set to 90$^\circ$ according to the formula $I_{\alpha }=I\sin^{2}\alpha$. The relative change represents the ability of the system to distinguish the signal from the laser output noise, and the absolute change represents the ability of the system to distinguish the signal from the dark noise.
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Fig. 1. Changes in the relative sensitivity and absolute sensitivity of measuring light intensity for (a) the forward Faraday rotation angle and (b) the reverse Faraday rotation angle at different preset angles, showing the local amplification of $\alpha =0.2^\circ$–4$^\circ$.
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Fig. 2. (a) XRD patterns of Eu$_{x}$Ce$_{1}$Y$_{2-x}$Fe$_{5}$O$_{12}$ ($x = 0$, 0.3, 0.5, 0.75, 1) thin films, (b) AFM image of Eu$_{0.75}$Ce$_{1}$YIG, (c) Ce $3d$, (d) Fe $2p$ high-resolution XPS spectra of Eu$_{x}$Ce$_{1}$Y$_{2-x}$Fe$_{5}$O$_{12}$, and (e) variation of lattice constants as a function of Eu contents for Eu$_{x}$Ce$_{1}$Y$_{2-x}$Fe$_{5}$O$_{12}$.
Figures 1(a) (positive rotation angle) and 1(b) (negative rotation angle) demonstrate the measurement system sensitivity to the relative and absolute changes in light intensity at various preset angles ($\alpha$) in order to detect small Faraday rotation angles. For larger preset angles $\alpha$ ($>$ 10$^\circ$), the relative change in light intensity approaches zero. Even if the absolute change in light intensity is greatest at 45$^\circ$, it is difficult to distinguish such variations from the signal noise. Conversely, at lower preset angles $\alpha$ ($ < $ $1^\circ$), the absolute change in light intensity approaches zero, making it indistinguishable from the dark noise. Notably, the relative change in light intensity for positive rotation angle [shown in the inset of Fig. 1(a)] has a peak which is due to the angle between the polarized light and polarizer larger than 90$^\circ$ but does not occur during the measurement of the negative rotation angle [as illustrated in the inset of Fig. 1(b)]. When the preset angle $\alpha$ is adjusted to 2$^\circ$, the system ensures accurate sensitivity to both relative and absolute changes in light intensity. The XRD patterns of Eu$_{x}$Ce$_{1}$Y$_{2-x}$Fe$_{5}$O$_{12}$ ($x =0$, 0.3, 0.5, 0.75, 1) [Fig. 2(a)] reveal that all as-obtained films display epitaxial crystallization on GGG (444) (ICDD-PDF-2:01-071-0701), which is consistent with prior findings.[27,28] No contribution from secondary phases is identified within the sensitivity of XRD measurement. The atomic force microscopy (AFM) image of the Eu$_{0.75}$Ce$_{1}$Y$_{1.25}$Fe$_{5}$O$_{12}$ film [Fig. 2(b)] exhibits an $R_{\rm a}$ of 0.447 nm throughout an area of $5.0\times 5.0$ µm$^{2}$, revealing a highly crystalline surface quality. To investigate the chemical environment of Ce [Fig. 2(c)], XPS spectra of Ce 3$d$ disclose that the main valences in (Eu,Ce):YIG are Ce$^{4+}$ (ca. 916.7 eV, 907 eV, and 902 eV for $3d_{3/2}$, 898.5 eV, 889.2 eV, and 882.2 eV for $3d_{5/2})$ and Ce$^{3+}$ (ca. 904.1 eV and 900.8 eV for $3d_{3/2}$, 885.3 eV and 880.4 eV for 3$d_{5/2}$), respectively.[29] For Fe $2p$ spectra [Fig. 2(d)], the primary valences are Fe$^{3+}$ (ca. 732.9 eV and 724.4 eV for 2$p_{1/2}$, 719 eV and 711 eV for 2$p_{3/2}$) and Fe$^{2+}$ (ca. 729.4 eV and 723 eV for 2$p_{1/2}$, 715.4 eV and 710.1 eV for 2$p_{3/2}$) caused by oxygen vacancies (V$_{\rm O})$, respectively. XPS results suggest that Ce$^{3+}$/Ce$^{4+}$ ratios gradually increase from 0.48, 0.60, 0.70 to 0.86 as Eu concentration increases ($x \leqslant 0.75$), whereas Fe$^{3+}$/Fe$^{2+}$ ratios grow from 1.58, 1.90, 2.58, to 3.38, corresponding to the Eu content of 0, 0.3, 0.5, and 0.75, respectively. At $x=1$, the Ce$^{3+}$/Ce$^{4+}$ ratio declines further to 0.83, while the ratio of Fe$^{3+}$/Fe$^{2+}$ decreases to 3.27. Calculated from XRD data, Fig. 2(e) displays lattice constants as a function of Eu doping concentration. It is widely known that Eu doping could promote the transition from Ce$^{4+}$ to Ce$^{3+}$, resulting in increase in Ce$^{3+}$ [$r$(Ce$^{3+}$) $>$ $r$(Ce$^{4+}$)] and reduction in Fe$^{2+}$ [$r$(Fe$^{2+}$) $>$ $r$(Fe$^{3+}$)]. Due to the limitation of the sampling step size of the x-ray diffractometer, the calculated lattice constant should have some inevitable errors. Consequently, the lattice constants of (Eu$_{0.3}$,Ce):YIG, (Eu$_{0.5}$,Ce):YIG, and (Eu$_{0.75}$,Ce):YIG are about 12.464 Å, 12.461 Å, and 12.466 Å, respectively, which are close to that of Ce:YIG. As revealed by the XPS data, at $x=1$, additional Eu doping could no longer cause any beneficial effect on the transition from Ce$^{4+}$ to Ce$^{3+}$, but simply replaces Y$^{3+}$, leading to an increase in lattice constant (12.482 Å). To assess the optical absorption characteristics of as-deposited films, transmittance spectra within the range of 250–1000 nm were recorded [Fig. 3(a)]. Clearly, all (Eu,Ce):YIG films exhibit greater transmittance in the wavelength ranges of 250–400 and 700–1000 nm than Ce:YIG, notably in the latter, transmittance values over 90% were recorded. Transmittance and thickness data are used to compute the absorption coefficients of as-deposited Eu$_{x}$Ce$_{1}$Y$_{2-x}$Fe$_{5}$O$_{12}$ films in the range of 400–1000 nm, as shown in Fig. 3(b). Distinctly, owing to the unavoidable light absorption of Fe$^{2+}$,[12] Ce:YIG exhibits much higher absorption in 400–1000 nm compared to YIG. Since the absorption peaks of Eu$^{3+}$ are distributed around 400 nm,[30,31] the absorption coefficients slightly increase compared to Ce:YIG in 400–750 nm, but exhibit similar curves in 750–1000 nm after Eu doping.
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Fig. 3. (a) Transmittance in the range of 250–1000 nm, and (b) the absorption coefficient in the range of 400–1000 nm, for Eu$_{x}$Ce$_{1}$Y$_{2-x}$Fe$_{5}$O$_{12}$ films.
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Fig. 4. (a) Transition schematic diagrams of ion-doped YIG magnetic structure, (b)–(f) Variation of in-plane (IP) and out-of-plane (OP) hysteresis loops for Eu$_{x}$Ce$_{1}$Y$_{2-x}$Fe$_{5}$O$_{12}$ films, and (g) saturation magnetization and coercivity versus Eu contents.
To explore the impact of Eu doping on magnetic properties, the magnetic structure of the (Eu,Ce):YIG (111) crystal plane is schematically depicted in Fig. 4(a). Tetrahedral and octahedral Fe$^{3+}$ ions are denoted by red and green spheres, respectively, and the relative direction of magnetic moments is indicated by arrows [Fig. 4(a), left]. Ce$^{3+}$ (orange) and Ce$^{4+}$ (blue) coexist in Ce:YIG, and Fe$^{2+}$ (deep red and deep green) and then Ce doping appear [Fig. 4(a), middle]. In addition, Eu (purple) doping converts a portion of Ce$^{4+}$ to Ce$^{3+}$ and reduces Fe$^{2+}$ content [Fig. 4(a), right]. Figures 4(b)–4(f) show the magnetic hysteresis loops of (Eu,Ce):YIG thin films, excluding all possible paramagnetism signals from the GGG substrate. All the samples exhibit an in-plane magnetization easy axis, which attributes to the dominance of shape anisotropy.[27,32] According to Néel's theory, the magnetism of YIG is caused by tetrahedral (24$d$ site) Fe$^{3+}$ ions and octahedral (16$a$ site) Fe$^{3+}$ ions, whereas dodecahedral (24$c$ site) Y$^{3+}$ ions have no effect on magnetism.[33] Due to the super-exchange interaction, two kinds of Fe$^{3+}$ magnetic moments align in the opposite parallel directions, with a ratio of 3:2 [Fig. 4(a), left].[24] Further, as indicated in XPS studies, the transition of the closest tetrahedral and octahedral Fe$^{3+}$ into Fe$^{2+}$ due to oxygen vacancy (V$_{\rm O})$ weakens ferrimagnetism [Fig. 4(a), middle]. Interestingly, this observation is consistent with the experimental results, accordingly Ce:YIG exhibits a saturation magnetization ($M_{\rm s}$) of 117 emu/cm$^{3}$ [Fig. 4(b)], lower than that of YIG (140 emu/cm$^{3}$).[12,34] The effect of Eu doping on magnetism can be ascribed to two aspects: (i) The magnetic moment of Eu$^{3+}$ is in the same direction as that of octahedral Fe$^{3+}$. (ii) It promotes the conversion of Ce$^{4+}$ to Ce$^{3+}$ and reduces the concentrations of both V$_{\rm O}$ and Fe$^{2+}$ [Fig. 4(a), right]. Hence, for $x \leqslant 0.5$, the magnetic moment of Eu plays a major role on decreasing the net magnetic moment of the thin film [Figs. 4(c) and 4(d)], whereas for $0.5 < x \leqslant 1$, the transition from Fe$^{2+}$ to Fe$^{3+}$ plays a crucial part in progressively increasing the net magnetic moment [Figs. 4(e) and 4(f)]. Figure 4(g) shows the magnetic moment at saturation and in-plane coercivity versus Eu contents. At $x=1$, the rapid rise in in-plane coercivity is attributed to an increase in the internal stress of the film induced by Eu$^{3+}$ that does not participate in the transition of Ce$^{4+}$ to Ce$^{3+}$. In general, Eu doping reduces the net magnetic moment and saturation field, achieving the desired outcome.
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Fig. 5. (a)–(e) Faraday hysteresis loops measured at room temperature for Eu$_{x}$Ce$_{1}$Y$_{2-x}$Fe$_{5}$O$_{12}$ films, and (f) changes in saturated Faraday rotation angle and saturated driving field versus Eu contents.
To verify the prediction of Eu doping on Ce:YIG Faraday effect enhancement, Figs. 5(a)–5(e) display the Faraday hysteresis loops of (Eu,Ce):YIG at 532 nm, and Fig. 5(f) shows the saturated Faraday rotation angle and saturated driving magnetic field versus Eu contents excluding the Faraday signal generated by the GGG substrate (10$^\circ$/cm @532 nm). As mentioned in prior XPS analysis, when $x \leqslant 0.75$, the saturated Faraday rotation angle of the film rises gradually to around $0.94\times 10^{4}$, $1.078\times 10^{4}$, $1.159\times 10^{4}$, and $1.315\times 10^{4}$ deg/cm, respectively, due to the transition from Ce$^{4+}$ to Ce$^{3+}$ with Eu doping. However, at $x=1$, the saturated Faraday rotation angle drops to $1.04\times 10^{4}$ deg/cm, which may be due to the expansion of the lattice constant and the rise in internal stress. Furthermore, according to previous magnetic analysis, Eu doping reduces the net magnetic moment, thus decreases the requirement for the applied magnetic field to drive magnetic moment deflection, results in a decrease in a saturated driving field (ca. 1.88 kOe, 1.30 kOe, 1.20 kOe, 1.17 kOe, and 1.02 kOe, respectively). In conclusion, well-oriented (Eu,Ce):YIG thin films have been deposited on GGG substrates, and a correlation between Eu doping concentration and an increase in Faraday rotation angle is established. Eu doping ($x=0.75$) produces a saturated Faraday rotation angle of $1.315\times 10^{4}$ deg/cm and a saturated driving field of 1.17 kOe, which are $\sim$ 40% more and $\sim$ 38% less than those of Ce$_{1}$Y$_{2}$Fe$_{5}$O$_{12}$ in its pristine state. The impressive performance could be attributed to the transition of Ce$^{4+}$ to Ce$^{3+}$ and the reduction of ferrimagnetism brought out by Eu doping. This dual-role approach is thought to provide opportunities and prospects for future development of Ce:YIG magneto-optical films. Acknowledgments. This work was supported by the National Science Fund for Distinguished Young Scholars (Grant No. 52225201), the National Natural Science Foundation of China (Grant Nos. 52072085 and 52271207), the National Key Research and Development Program of China (Grant No. 2023YFE0201000), the Fundamental Research Funds for the Central Universities (Grant No. HIT.BRET.2022001), the Heilongjiang Touyan Innovation Team Program, and the Science Foundation of National Key Laboratory of Science and Technology on Advanced Composites in Special Environments. 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