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Abstract
Fano resonance arises from the interference of a localized discrete state coupled to the continuum states, which has become an indispensable probe in physical and chemical sciences. Compared with plenty of studies in the artificial meta-structures, Fano resonances in single crystals were rarely reported. Herein, we performed a comprehensive study on Fano resonances of KTa1-xNbxO3 (KTN) ferroelectric single crystals using temperature dependent Raman spectroscopy. The Fano asymmetric q factors were fitted for KTN crystals with various Nb concentrations. We found that the q factors were strongly correlated to Curie temperature Tc and ferroelectric polarization arrangement in different phase regions. In addition, the regulation of dopant transition metals on the Fano effect was also investigated in Cu:KTN and Fe:KTN crystals.
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1. Introduction
Optical resonances are everywhere in our daily life. Fano resonance is a universal phenomenon associated with wave propagation and interference, which has been observed in many fields [1–3]. Fano resonance effect was first discovered in the research about asymmetrical absorption spectra of noble gases, and the first theoretical explanation was given by Fano and Cooper in 1961 [4]. In theory, Fano resonance can be considered as the result of coherent scattering between a discrete vibrational state and background continuous states, thus leading to a transition from symmetric Lorentz shapes to asymmetric Fano shapes. Owing to the coupling between discrete and continuous configurations, the asymmetric peaks and dips are formed on each side of the wave shape, where an asymmetric factor q was proposed to evaluate the coupling intensity [5]. Since the asymmetric spectra (q values) of Fano resonance are very sensitive to the dielectric properties of medium, it has great potential for applications in optical sensors [6], single-particle spectroscopy [7], Fano lasing devices [8], and superconductor studies [9].
In recent years, Fano resonances have been widely investigated, especially in the artificial material systems with flexible structural parameter tunability, such as semiconductor nano-structures, plasmonic nano-antennas, and photonic crystals [10]. Some novel resonant effects were discovered, e.g. electromagnetically induced transparency (EIT), Borrmann effect, parity-time symmetry breaking, and so on. In contrast, Fano resonance in single crystals was rarely studied, since pure crystal with perfect periodicity usually displays only sharp Lorentz-shape vibrational peaks (discrete state). However, this case could be broken in ferroelectric/anti-ferroelectric crystals or relaxor ferroelectrics. In these crystals, the macroscopic polarization derives from the octahedral displacement of central metal. There always exists a small difference for displacement distance of central metal in each unit-cell, yielding a diffuse continuous state in vibrational spectrum and correlated Fano resonance in Raman spectrum. Therefore, it would be an effective strategy to construct and strengthen Fano coupling in disordered crystals. According to previous reports, this has been observed in BaTiO3 [11], Ba(Ti, Zr)O3 [12], Pr:SrTiO3 [13], KNbO3 [14], CaCu3Ti4O12 [15], etc.
Perovskite KTa1-xNbxO3 (KTN) crystal is a mixed crystal of KTaO3 and KNbO3. Its Curie temperature could be adjusted continuously with the regulation of Ta/Nb ratio. Therefore, KTN crystals could exist as cubic, tetragonal or orthorhombic phases at room temperature, depending on the Ta/Nb ratio [16]. Benefitting from this impressive feature, KTN crystal possesses rich ferroelectric domains [17–19] and exhibits newfangled optical response [20–26]. All these could be attributed to the fluctuation of Nb displacement distances, corresponding to the continuous states in vibrational spectrum. Accordingly, KTN crystal would be an excellent platform to study Fano resonance in single crystals. Herein, we made a comprehensive study on Fano resonances of KTN crystals with different Ta/Nb ratios using temperature dependent Raman spectroscopy. Based on the nonlinear fitting analysis, we found that the asymmetric q factors were strongly correlated to Curie temperature Tc and ferroelectric polarization arrangement in different phase regions. Moreover, the dopant transition metals effect on Fano resonance was also studied in Cu:KTN and Fe:KTN crystals.
2. Results and discussion
2.1 Fano resonance effect and vibrational modes of KTN
Fano resonance represents a strong interference between a discrete mode and continuous modes of vibration, not a simple intensity superposition among multiple modes. Raman spectrum was adopted as a common probe to illuminate the Fano resonance. As shown in Fig. 1(a), Fig. 1(b), and Fig. 1(c), an asymmetric line pattern is generated when the discrete mode and continuous modes interact with each other, namely Fano resonance or Fano interference. In order to describe this asymmetric line shape quantitatively, we use the Fano formula Eq. (1) as follows,
where $I(\omega )$ is the measured Raman intensity, Ic is a constant parameter, Ib is a polynomial formula as ${I_b} = A{({\omega - {\omega_p}} )^3} + B{({\omega - {\omega_p}} )^2} + C({\omega - {\omega_p}} )+ D$, A, B, C and D are constants. $\varepsilon = \frac{{\omega - {\omega _p}}}{\varGamma }$ represents the dimensionless scale for energy reduction. $\varGamma $ and ${\omega _p}$ are the linewidth and frequency of the studied mode of Fano resonance in the Raman spectrum. q is the asymmetry factor, reflecting the strength of the coupling between the discrete and continuous states, which determines the line shape of the Fano resonance. Figure 1(d) depicts the Fano shape dependence on the q value. Unlike the symmetric Lorentz profile, the symmetry of the Fano lineshape is related to the value of the parameter q. The larger q value, the more dominant the discrete signal intensity in the spectrum will be. If the external perturbation was not coupled to the continuum state ($q \to \pm \infty$), the Fano lineshape becomes a symmetric Lorentz function $I(\omega )\propto \frac{1}{{1 + {\varepsilon ^2}}}$ . When q = 0, the Fano profile becomes a symmetric quasi-Lorentz antiresonance with $I(\omega )\propto \frac{{{{|\varepsilon |}^2}}}{{1 + {\varepsilon ^2}}}$, suggesting another limiting case that the external perturbation does not couple to the discrete state.
Fig. 1. Fano resonance effect in KTN crystal. (a-c) Schematic diagram of the generation of Fano resonance. (d) Fano line shape dependence on the asymmetry parameter q values. (e) The Raman spectra of KTN45 crystal under room temperature. (f-h) The vibrational diagram of TO2, TO3 and TO4 modes.
Then, we measured the Raman spectra of a c-cut KTa0.55Nb0.45O3 (KTN45) crystal under 633 nm excitation. It belongs to the tetragonal ferroelectric phase at room temperature. The incident light is along the c-axis. As shown in Fig. 1(e), there are three first-order peaks on the Raman spectrum, namely an asymmetric shape TO2 mode at 198 cm−1, a weak TO3 mode at 280 cm−1 and a TO4 mode at 570 cm−1 with wide bandwidth, respectively [27]. It is observed that there should be a strong Fano resonance between TO2 phonons and continuous polarization fluctuations in KTN ferroelectrics. Moreover, we applied the theoretical calculations on tetragonal KTN to simulate its vibrational phonon modes. Figures 1(f), 1(g) and 1(h) display the visualized vibrations of TO2, TO3 and TO4 modes, where the green arrows represent the atomic vibrational direction and the Ta/Nb atoms, O atoms and K atoms are plotted by blue, red, purple balls, respectively. Clearly, TO2 and TO4 modes are the transverse polar optic modes, while TO3 is the nonpolar optical mode. As mentioned above, the Fano resonance in ferroelectrics is strongly correlated to polarization fluctuations, where the spontaneous polarization of KTN originates from Nb5+ displacement in (NbO6) octahedron. According to Landau theory, there exist two underlying anharmonic potential surface minimum valleys in Gibbs free energy curve, corresponding to positive P and negative -P states. Consequently, the Nb5+ displacement would be switched with the external electric field or temperature fluctuations. However, the amplitude of Nb5+ displacement is not totally the same in different unit-cells depending on the chemical environment, and there would be an uncertain Nb-O bond length. In contrast, KTaO3 is always a cubic phase and Ta-O bond length could be considered as a solid constant. Note that the difference between d(Nb-O) and d(Ta-O) is compatible with the Fano resonance mechanism, that is, the broad Nb-O vibrations provide the continuous background and the Ta-O vibrations provide a sharp discrete state [12]. This is the microscopic origin of Fano resonance at 198 cm−1 in KTN crystals.
2.2 Fano resonance in KTN crystal with various Ta/Nb ratio
As we know, the Curie temperature Tc of perovskite-type ferroelectrics is related to the central B-site off-center distance in the oxygen octahedra. Therefore, the Tc of KTN crystal could be adjusted continuously by changing Ta/Nb ratio. When the Tc is lower than the room temperature, the displacement of central B-sites would be zero and therefore the spontaneous polarization disappears completely. As a result, Fano resonance effect would be changed consequently.
To study the relationship between crystalline phases and Fano resonance, we measured the Raman scattering spectroscopy of KTN crystals with different Nb contents at room temperature. Figure 2(a) shows that there are three possible crystalline phases at room temperature, namely cubic, tetragonal, and orthorhombic. We grew eight KTN crystals with x = 0.22, 0.36, 0.40, 0.41, 0.42, 0.43, 0.44, 0.45, respectively. The orange dashed line represents room temperature (25 ℃) and the purple dot corresponds to the composition of the sample we prepared. At room temperature, the former two samples are cubic phase and the latter six samples are tetragonal phase. Their Raman spectra are displayed in Fig. 2(b). It is observed that the damping of the Fano line shapes become larger with increasing Nb content, which indicated that Curie temperature Tc could greatly affect the Fano resonance owing to the changed polarization arrangement. Then, we measured the Raman spectra of KTN samples with different Curie temperatures, as depicted in Fig. 2(c). Fano resonance is observed in the ferroelectric phase (Tc = 41 ℃, 70 ℃, 99 ℃) and disappears in the paraelectric KTN crystal. This could be attributed to the absence of continuous states in paraelectric KTN crystals.
Fig. 2. Fano resonance of KTN crystals at room temperature. (a) Phase diagram of KTa1-xNbxO3. (b) Raman scattering spectra of KTN crystals with different Nb components. (c) Raman scattering spectra of ferroelectric and paraelectric KTN crystals under 25 ℃.
2.3 Temperature dependent Fano resonance in KTN crystal
Besides Curie temperature and Ta/Nb ratio, the polarization states could be also changed by the external temperature fluctuations. Next, we took KTN42 crystal (x = 0.42, Tc = 40 ℃) as an example to study the relationship between phase transition and Fano resonance. The measurement temperature was adjusted from −70 ℃ to 80 ℃. KTN42 crystal belonged to orthorhombic phase below −30 ℃ and changed to tetragonal phase from −30 ℃ to 40 ℃. When the external temperature further improves, it became cubic phase. Figure 3(a) shows the Raman spectrum of KTN42 under different temperatures. It could be observed that the line shape gradually flattens out as the increased temperature, and then totally disappeared when T > Tc. The experimental data could be well fitted by the Fano formula in Eq. (1). Based on the fitting results, we obtained the asymmetry parameter q, linewidth Γ, and vibrational frequency ωp, as shown in Fig. 3(b), Fig. 3(c), and Fig. 3(d). As the temperature gradually increases, the asymmetry parameter q reduces from 1.3 to 0.3. This is comparable to that of orthorhombic KNbO3 (q = 0.75 at 300 K) [14], CaCu3Ti4O12 (q = 1.02 at 300 K) and SrCu3Ti4O12 (q = 2.02 at 300 K) [15], but smaller than that of Pr:SrTiO3 (q = 4∼18 at 300 K for different Pr content) [13]. In addition, the trend of the FWHM is opposite of q factor, which increases from 6 cm−1 to 17 cm−1. The central position of TO2 mode moves from 191.5 cm−1 to 189.1 cm−1. It is observed that there are two clear turning points for three parameters around −30 ℃ and 40 ℃, corresponding to phase transition from orthorhombic to tetragonal phase, and transition from tetragonal phase to final cubic phase. Similar trends were also observed in other KTN crystals. These results indicate that the Fano resonant behaviors of KTN crystal are strongly dependent on the external temperature and the associated ferroelectric polarization.
Fig. 3. Temperature dependent Fano resonance in KTN crystal. (a) Raman spectra of the KTN42 crystal fitted by Fano formula. The purple circles are experimental data and the red lines are fitting lines. (b) Asymmetry parameter q, (c) linewidth Γ, and (d) vibrational frequency ωp of KTN42 crystal under different temperatures.
2.4 Fano resonance and ferroelectric polarization
In order to give a direct elaboration for Fano resonance and ferroelectric polarization, we studied the light transmittance and scattering of KTN crystals. The ferroelectric polarization distribution manifests as the domains and domain walls in the ferroelectrics. As well known, domain walls can cause light scattering, which reduces the transmittance of the crystal [28]. When the temperature gradually approaches the Curie temperature, the domain walls gradually disappear and the transmittance ratio of ferroelectric crystal could be improved. This provides a simple method to study the relations between Fano resonance and ferroelectric polarization. In terms of KTN crystals, the phase transition often requires a structural distortion of the Ta/Nb-O octahedra over a certain spatial and temporal range, leading to the presence of strain in the sample, which manifests itself as the generation of domain walls.
To avoid the unnecessary liquid nitrogen volatilization, a high-Tc KTN45 (x = 0.45, Tc = 99 ℃, dimensions: 10 mm × 10 mm × 1 mm) was selected and the external temperature was adjusted from 30 ℃ to 120 ℃. Here, we observed the synchronous change among the Fano resonance and the transmittance of the KTN crystal during the heating process. At the temperature of 30 ℃, KTN crystal was opaque with a cloudy region due to strong domain walls scattering. At the same time, the Fano resonance of TO2 mode was very strong with a large q value, as shown in Fig. 4(a). As the temperature increased, the transmittance of the crystal gradually improved and the Fano resonance gradually weakened, as shown in Fig. 4(b)-Fig. 4(h). Figure 4(i) displays that all the cloudy regions disappeared and KTN crystal became transparent at 100 °C. At this time, the Fano resonance also became absent when the temperature rose above the Curie temperature. These phenomena suggest that the Fano resonance is indeed related to the ferroelectric domains and polarization fluctuations.
Fig. 4. Fano resonance and ferroelectric polarization. (a) The temperature dependent Raman spectra of KTN45 crystal. (b-i) Photograph of KTN45 crystal under different temperatures.
2.5 Transition metal doping effect on Fano resonance
As mentioned above, the Fano resonance in KTN crystal originates from the difference between d(Nb-O) and d(Ta-O), where the broad Nb-O vibrations provide the continuous background. Therefore, it is possible to modulate the continuous background via doping other transition metals at the B site. Here, we measured and fitted the Raman spectra of Cu:KTN and Fe:KTN. Figures 5(a) and 5(b) display that both Cu:KTN and Fe:KTN single crystals exhibited Fano resonance, indicating the Fano coupling mechanism in them should be the same with pure KTN crystal. The fitted asymmetric parameters q of Cu:KTN and Fe:KTN gradually reduced with the increased temperature, which is also similar to pure KTN. However, the q values are slightly different for Cu:KTN and Fe:KTN crystals. As shown in Fig. 5(c), Fe:KTN possesses higher q values from -50 to 60 ℃, than other crystals, but that of Cu:KTN are slightly smaller than pure KTN crystals.
Fig. 5. Fano resonance of transition metal doped KTN crystal. (a) Raman spectrum of Cu:KTN crystal. (b) Raman spectrum of Fe:KTN crystal. (c) The comparison of Fano asymmetric parameter q for different KTN crystals.
We have proposed that the Fano coupling intensity is strongly sensitive to the polarization distribution. Therefore, the changed q values indicate that Fe and Cu-doping could greatly modulate the polarization distributions and fluctuations in KTN crystals, which could be attributed two possible aspects: (i) Curie temperature. The Cu- and Fe-doping would greatly change the Curie temperature of KTN crystal. For example, the Curie temperature Tc of 0.1%Cu:KTa0.628Nb0.372O3 is 15 ℃ [29], which is higher than that of pure KTa0.628Nb0.372O3 (Tc ∼ 10.3 ℃). The Curie temperature of 0.5% Fe: KTa0.47Nb0.53O3 is 118℃ [30], which is comparable to pure KTa0.47Nb0.53O3 (Tc ∼ 117.1 ℃). Therefore, the ferroelectric distribution of Cu:KTN and Fe:KTN would be quite different to that in pure KTN crystals. Consequently, the asymmetric q values in Fano resonance were also changed with the changed Tc. (ii) Vacancy defects. As we know, the introduction of Fe2+ and Cu2+ would result in many Vo defects and VK defects [31]. These vacancies would play a strong pinning effect on the domain walls and affect the displacement distances of Nb atoms would be greatly regulated in Fe:KTN and Cu:KTN crystals. Therefore, the asymmetric q values for them were also changed in Fano resonances. According to the previous report, a similar trend is also found in Li:KTN crystal [32]. These results indicate that Fe- and Cu-doping could greatly modulate the polarization fluctuations in KTN crystals. In other words, Fano resonance could be applied as a sensitive probe to detect the ferroelectric domains and polarization.
3. Conclusion
In summary, a comprehensive study on Fano resonances of KTN crystals was made via temperature dependent Raman spectroscopy. Based on the Fano formula fitting, we obtained their asymmetric q factors, which were strongly correlated to Curie temperature Tc and ferroelectric polarization arrangement in different phase regions. In addition, the Cu-doping and Fe-doping effects on Fano resonance were also observed and analyzed. Our work not only provides some new insights for old KTN crystals but also gives helpful inspirations for Fano physics and Fano optics, especially in ferroelectric-based functional materials.
Funding
National Natural Science Foundation of China (51890863, 51972179, 52002220, 52025021, 52072189); Future Plans of Young Scholars at Shandong University.
Disclosures
The authors declare no competing of interests.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. M. F. Limonov, “Fano resonance for applications,” Adv. Opt. Photonics 13(3), 703–771 (2021). [CrossRef]
2. M. F. Limonov, M. V. Rybin, A. N. Poddubny, and Y. S. Kivshar, “Fano resonances in photonics,” Nat. Photonics 11(9), 543–554 (2017). [CrossRef]
3. Y. Yu, W. Xue, E. Semenova, K. Yvind, and J. Mork, “Demonstration of a self-pulsing photonic crystal Fano laser,” Nat. Photonics 11(2), 81–84 (2017). [CrossRef]
4. U. Fano and J. W. Cooper, “Line profiles in the far-UV absorption spectra of the rare gases,” Phys. Rev. 137(5A), A1364–A1379 (1965). [CrossRef]
5. U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124(6), 1866–1878 (1961). [CrossRef]
6. M. Vinod, G. Raghavan, and V. Sivasubramanian, “Fano resonance between coherent acoustic phonon oscillations and electronic states near the bandgap of photoexcited GaAs,” Sci. Rep. 8(1), 17706 (2018). [CrossRef]
7. B. Zhen, S. L. Chua, J. Lee, A. W. Rodriguez, X. Liang, S. G. Johnson, J. D. Joannopoulos, M. Soljacic, and O. Shapira, “Enabling enhanced emission and low-threshold lasing of organic molecules using special Fano resonances of macroscopic photonic crystals,” Proc Natl Acad Sci USA 110(34), 13711–13716 (2013). [CrossRef]
8. Y. Yu, A. Sakanas, A. R. Zali, E. Semenova, K. Yvind, and J. Mørk, “Ultra-coherent Fano laser based on a bound state in the continuum,” Nat. Photonics 15(10), 758–764 (2021). [CrossRef]
9. M. F. Limonov, A. I. Rykov, S. Tajima, and A. Yamanaka, “Raman scattering study on fully oxygenated YBa2CuO7 single crystals: x-y anisotropy in the superconductivity-induced effects,” Phys. Rev. Lett. 80(4), 825–828 (1998). [CrossRef]
10. Y. Zhang, X. Hu, Y. Fu, H. Yang, and Q. Gong, “Ultrafast all-optical tunable Fano resonance in nonlinear ferroelectric photonic crystals,” Appl. Phys. Lett. 100(3), 031106 (2012). [CrossRef]
11. A. Chaves, R. S. Katiyar, and S. P. S. Porto, “Coupled modes with A1 symmetry in tetragonal BaTiO3,” Phys. Rev. B 10(8), 3522–3533 (1974). [CrossRef]
12. D. Wang, J. Hlinka, A. A. Bokov, Z. G. Ye, P. Ondrejkovic, J. Petzelt, and L. Bellaiche, “Fano resonance and dipolar relaxation in lead-free relaxors,” Nat. Commun. 5(1), 5100 (2014). [CrossRef]
13. V. Dwij, B. K. De, S. Tyagi, G. Sharma, and V. Sathe, “Fano resonance and relaxor behavior in Pr doped SrTiO3: A Raman spectroscopic investigation,” Physica B: Condensed Matter 620, 413265 (2021). [CrossRef]
14. A. M. Quittet, M. I. Bell, M. Krauzman, and P. M. Raccah, “Anomalous scattering and asymmetrical line shapes in Raman spectra of orthorhombic KNbO3,” Phys. Rev. B 14(11), 5068–5072 (1976). [CrossRef]
15. D. K. Mishra and V. G. Sathe, “Evidence of the Fano resonance in a temperature dependent Raman study of CaCu3Ti4O12 and SrCu3Ti4O12,” J. Phys.: Condens. Matter 24(36), 369501 (2012). [CrossRef]
16. X. Wang, J. Wang, Y. Yu, H. Zhang, and R. I. Boughton, “Growth of cubic KTa1−xNbxO3 crystal by Czochralski method,” J. Cryst. Growth 293(2), 398–403 (2006). [CrossRef]
17. Y. Wang, X. Meng, H. Tian, C. Hu, P. Xu, P. Tan, and Z. Zhou, “Dynamic evolution of polar regions in KTa0.56Nb0.44O3 near the para-ferroelectric phase transition,” Cryst. Growth & Des. 19(2), 1041–1047 (2019). [CrossRef]
18. X. Li, Q. Yang, X. Zhang, S. He, H. Liu, and P. Wu, “Heating-rate-dependent dielectric properties of KTa0.58Nb0.42O3 crystal in paraelectric phase,” Cryst. Growth & Des. 20(4), 2578–2583 (2020). [CrossRef]
19. F. Huang, C. Hu, H. Tian, X. Meng, P. Tan, and Z. Zhou, “The effect of composition gradient on microdomain structure and the macro-ferroelectric/piezoelectric properties,” Cryst. Growth & Des. 19(9), 5362–5368 (2019). [CrossRef]
20. L. Falsi, M. Aversa, F. Di Mei, D. Pierangeli, F. Xin, A. J. Agranat, and E. DelRe, “Direct observation of fractal-dimensional percolation in the 3D cluster dynamics of a ferroelectric supercrystal,” Phys. Rev. Lett. 126(3), 037601 (2021). [CrossRef]
21. F. Xin, F. Di Mei, L. Falsi, D. Pierangeli, C. Conti, A. J. Agranat, and E. DelRe, “Evidence of chaotic dynamics in three-soliton collisions,” Phys. Rev. Lett. 127(13), 133901 (2021). [CrossRef]
22. D. Pierangeli, M. Ferraro, F. Di Mei, G. Di Domenico, C. E. de Oliveira, A. J. Agranat, and E. DelRe, “Super-crystals in composite ferroelectrics,” Nat. Commun. 7(1), 10674 (2016). [CrossRef]
23. E. DelRe, E. Spinozzi, A. J. Agranat, and C. Conti, “Scale-free optics and diffractionless waves in nanodisordered ferroelectrics,” Nat. Photonics 5(1), 39–42 (2011). [CrossRef]
24. F. Di Mei, L. Falsi, M. Flammini, D. Pierangeli, P. Di Porto, A. J. Agranat, and E. DelRe, “Giant broadband refraction in the visible in a ferroelectric perovskite,” Nat. Photonics 12(12), 734–738 (2018). [CrossRef]
25. L. Falsi, L. Tartara, F. Di Mei, M. Flammini, J. Parravicini, D. Pierangeli, G. Parravicini, F. Xin, P. DiPorto, A. J. Agranat, and E. DelRe, “Constraint-free wavelength conversion supported by giant optical refraction in a 3D perovskite supercrystal,” Commun. Mater. 1(1), 76 (2020). [CrossRef]
26. C. Li, X. Wang, Y. Wu, F. Liang, F. Wang, X. Zhao, H. Yu, and H. Zhang, “Three-dimensional nonlinear photonic crystal in naturally grown potassium-tantalate-niobate perovskite ferroelectrics,” Light. Sci. Appl. 9(1), 193 (2020). [CrossRef]
27. S. Kojima, M. M. Rahaman, R. Sase, T. Hoshina, and T. Tsurumi, “Vibrational dynamics of ferroelectric K(Ta1−xNbx)O3 studied by far-infrared spectroscopic ellipsometry and Raman scattering,” Jpn. J. Appl. Phys. 57(11S), 11UB05 (2018). [CrossRef]
28. C. Qiu, B. Wang, N. Zhang, S. Zhang, J. Liu, D. Walker, Y. Wang, H. Tian, T. R. Shrout, Z. Xu, L. Q. Chen, and F. Li, “Transparent ferroelectric crystals with ultrahigh piezoelectricity,” Nature 577(7790), 350–354 (2020). [CrossRef]
29. Q. Yang, X. Zhang, H. Liu, X. Wang, Y. Ren, S. He, X. Li, and P. Wu, “Dynamic relaxation process of a 3D super crystal structure in a Cu:KTN crystal,” Chin. Opt. Lett. 18(2), 021901 (2020). [CrossRef]
30. F. Huang, C. Hu, Z. Xian, X. Sun, Z. Zhou, X. Meng, P. Tan, Y. Zhang, X. Huang, Y. Wang, and H. Tian, “Photovoltaic properties in an orthorhombic Fe doped KTN single crystal,” Opt. Express 28(23), 34754–34760 (2020). [CrossRef]
31. Y. Wang, P. Tan, X. Meng, Z. Zhou, X. Huang, C. Hu, F. Huang, J. Wang, and H. Tian, “Manganese-doping enhanced local heterogeneity and piezoelectric properties in potassium tantalate niobate single crystals,” IUCrJ 8(2), 319–326 (2021). [CrossRef]
32. M. M. Rahaman, T. Imai, T. Sakamoto, S. Tsukada, and S. Kojima, “Fano resonance of Li-doped KTa1-xNbxO3 single crystals studied by Raman scattering,” Sci. Rep. 6(1), 23898 (2016). [CrossRef]
