Abstract
The enhancement of functionality of perovskite ferroelectrics by local structure is one of current interests. By the Lidoping to KTa_{1−x}Nb_{x}O_{3} (KTN), the large piezoelectric and electrooptic effects were reported. In order to give new insights into the mechanism of doping, the microscopic origin of the Fano resonance induced by the local structure was investigated in 5%Lidoped KTN single crystals by Raman scattering. The coupling between the continuum states and the transverse optical phonon near 196 cm^{−1} (Slater mode) caused a Fano resonance. In the vicinity of the cubictetragonal phase transition temperature, T_{CT} = 31 °C, the almost disappearance of the Fano resonance and the remarkable change of the central peak (CP) intensity were observed upon heating. The local symmetry of the polar nanoregions (PNRs), which was responsible for the symmetry breaking in the cubic phase, was determined to E(x, y) symmetry by the angular dependence of Raman scattering. The electric field induced the significant change in the intensity of both CP and Fano resonance. From these experimental results, it is concluded that the origin of the Fano resonance in Lidoped KTN crystals is the coupling between polarization fluctuations of PNRs and the Slater mode, both belong to the E(x, y) symmetry.
Introduction
The leadbased ferroelectrics have been extensively used in our daily lives for their colossal piezoelectricity and giant dielectric response; however, its future applicability is highly limited because of the toxic nature of lead. Therefore, the advancements of lead free ferroelectrics materials are an imperative matter in applied physics. In order to enhance the functionality of lead free ferroelectrics, the role of local structure is very important^{1}. In the midst of lead free ferroelectrics, the investigation of Lidoped KTa_{1−x}Nb_{x}O_{3} (KTN) has fascinated much scientific attention owing to their enormous quadratic electrooptic coefficient^{2,3,4}, good photorefractive effect^{5}, and excellent piezoelectric effect^{6}, which make them one of the potential candidates for not only optical but also electromechanical device applications.
KTN is the solid solution of KTaO_{3} and KNbO_{3}. The most important aspect of KTN is the offcenter displacements of Nb ions at the Bsite and therefore they induce polar naoregions (PNRs)^{7}. The physical origin of the offcenter displacements of Nb ions was rationalized by the pseudo JahnTeller effect (PJTE)^{8}. A light scattering study also explained the offcenter displacements of Nb ions in KTN by eight site model, in which Nb ions displace among the equivalent [111] directions^{9}. As widely reported by various kinds of measurements^{10,11,12,13,14,15,16,17}, one offcenter displacement interacts with the neighboring offcenter displacements, leading to the local polar structure called PNRs in the paraelectric cubic phase of KTN crystals. The PNRs are characterized by various temperatures in the cubic phase. First, the Burns temperature, T_{B}^{18}, below which the dynamic PNRs appear. Second, the intermediate temperature, T*, at which the dynamic PNRs start to transform into static PNRs^{10,11,12}.
Recently, the effect of Lidoping in KTaO_{3} and KNbO_{3} is one of the interesting research fields in materials science. In K_{1y}Li_{y}TaO_{3} (KLT) and K_{1z}Li_{z}NbO_{3} (KLN), the substitutional Li ions occupy one of six offcenter sites along the [100] directions at the Asite^{19,20}, which can lead to the formation of random fields that enhance the appearance of PNRs. In KLT, there is a crossover at around critical concentration y = 0.022 between a freezing and a structural transition with a critical level of local polarization^{19}. Most recently, Rahaman et al. observed the effects of Lidoping on elastic properties, which enhanced the relaxor nature by the growth of PNRs of KTN^{21}. Therefore, the Lidoped KTN is an intriguing topic to investigate the Lidoping effects on precursor dynamical properties of a relaxor ferroelectric phase transition.
In KTN, the dynamical aspect of PNRs was extensively studied by inelastic light scattering^{10,11,13,14,22}. However, the microscopic origin of the Fano resonance at around 196 cm^{−1} in Lidoped KTN still remains fuzzy. The phenomenon of a Fano resonance results from the interaction between a discrete state and continuum states showing the asymmetry of the spectral line shape^{23}. The possible continuum states, which can interfere with the optical phonons and give rise to a Fano resonance, are the two acoustical phonon state^{24}, another transverse optic (TO) phonon via acoustic phonons^{25}, and the rapid polarization fluctuations with the frequency up to the Fano resonance frequency within micro polar regions^{26}, and nanoscopic polar regions^{27}. The Fano resonance was also observed in different types of materials from several physical origins by the various measurements^{28,29,30}. In this study, we investigated the microscopic origin of the Fano resonance in Lidoped KTN crystals using the temperature, angular, and electric field dependences of Raman scattering. The local symmetry breaking in the cubic phase was discussed on the basis of the existence of the first order Raman modes connecting with the evolution of the PNRs.
Methods
The K_{0.95}Li_{0.05}Ta_{0.73}Nb_{0.27}O_{3} (KLTN/0.05/0.27) and K_{0.95}Li_{0.05}Ta_{0.74}Nb_{0.26}O_{3} (KLTN/0.05/0.26) single crystals used in the present study were grown by the top seeded solution growth technique at NTT Corporation. The crystals were cut having the size of 4.0 × 3.2 × 1.2 mm^{3} and 4.0 × 3.18 × 1.0 mm^{3} with the largest faces perpendicular to the [100] direction, respectively. In KLTN/0.05/0.26 crystal, the platinum electrodes were deposited on the faces perpendicular to the [100] direction to apply the electric field. The temperature and electric field dependences of Raman spectra were measured using a double monochromator (HoribaJY, U1000) with the resolution of 1 cm^{−1} at a back scattering geometry. The Porto’s notation like ā(cc)a (VV) and ā(bc)a (VH) is used to denote the scattering configurations, where ā and a represent the direction of propagation of incident and scattered light, respectively. In the case of VV scattering the directions of the polarization of incident and scattered light are parallel to each other represented by, for example, cc. However, in the case of VH scattering the directions of the polarization of incident and scattered light are perpendicular to each other, for example, along c and b axes, respectively, represented by bc. A diode pumped solid state (DPSS) laser with a wavelength of 532 nm was used to excite the samples. The temperature of the samples was controlled by the heating/cooling stage (Linkam, THMS600) with ±0.1 °C accuracy over all temperatures.
For the angular dependence of Raman scattering, the KLTN/0.05/0.27 crystal was put on the xyz mapping stage (Tokyo Instruments) inside the Linkam installed in the optical reflection microscope (Olympus). The linearly polarized light from DPSS was incident to the sample through a polarization rotation device (Sigma Koki) equipped with a broadband halfwaveplate (Kogakugiken). When the polarization direction of incident light is inclined θ/2 with respect to the optical axis of the waveplate, the waveplate rotates polarization plane of incidence θ degree. On the other hand, the polarization direction of scattering light, propagating in opposite direction of incident light, is rotated by −θ degree. For better understanding the configurations of scattering, a typical illustration of the experimental scattering geometry is shown in Fig. 1. The strong elastic scattering was highly reduced by two volume Bragg gratings so called “ultra narrowband notch filters” (OptiGrate). The inelastic scattering light was dispersed by a singlemonochromator (Lucir) and the dispersed component was detected using a charge coupled device (CCD, Andor).
Results
Temperature dependence of Raman scattering spectra
In the analysis of Raman scattering spectra, the reduced intensity, I^{r}(ω), was calculated from the Stokes component of Raman scattering intensity by the following equation.
where is the BoseEinstein population factor, in which k_{B} is the Boltzmann constant and ħ is the Dirac constant. I(ω) is the observed Raman scattering intensity. By the reduced intensity, the effect of phonon population on spectra can be avoided. The temperature dependence of reduced ā(cc)a (VV) and ā(bc)a (VH) Raman spectra of a Lidoped KTN i.e., K_{0.95}Li_{0.05}Ta_{0.73}Nb_{0.27}O_{3} (KLTN/0.05/0.27) single crystal is shown in Fig. 2. The existence of a prominent first order TO_{2} mode at about 196 cm^{−1} in both VV and VH spectra and a TO_{3} mode at around 277 cm^{−1} at 26 °C demonstrates that the symmetry of the KLTN/0.05/0.27 single crystal is not cubic Pm3m symmetry at room temperature (RT). The detailed mode assignment of the KTN single crystals were studied in Refs. 31, 32, 33, 34. According to the phase diagram of KTN^{35,36}, a cubic phase is indeed expected for the nondoped KTN/0.27 crystal at RT. However, Lidoping raises the cubictetragonal phase transition temperature (T_{CT}) and the tetragonal phase with P4mm symmetry was reported at RT in KLTN/0.05/0.27^{21}. By Raman scattering, the effect of Lidoping on the phase transition of the KTN crystals was also reported by Prater et al.^{37}.
To investigate the temperature dependence of a central peak (CP), which is related to the relaxation process of dynamic PNRs, all spectra were fitted by the combination of a Lorentzian CP, damped harmonic oscillator (DHO) model, and a third order polynomial with the Fano function as follows^{22,38}
where I_{B} = P(ω − ω_{TO2})^{3} + Q(ω − ω_{TO2})^{2} + R(ω − ω_{TO2}) + S, A_{CP} and Γ_{CP} are intensity and FWHM (full width at half maximum) of the CP, respectively. The A_{i}, Г_{i}, and ω_{i} are intensity, damping, and frequency of the ith Raman mode, respectively. The I_{0} is intensity of the Fano resonance (TO_{2} mode), q is the asymmetry parameter characterises the coupling strength between the phonon and continuum states, ε = 2(ω − ω_{TO2})/Γ_{TO2} is the reduced energy, where Γ_{TO2} is the FWHM of the Fano resonance. P, Q, R, and S are the constants. Figure 3a shows the fit result using equation (2). Since the Raman modes were best resolved at the lowest temperature, therefore, the fitting procedure was started with the spectrum measured at the lowest temperature. The best fit in the preceding temperature was taken as the initial data for the next higher temperature. The temperature dependence of the reduced intensity, A_{CP}, and FWHM, Г_{CP}, of the CP observed in the VV scattering spectrum is shown in Fig. 3b. As can be seen in Fig. 3b, the A_{CP} begins to increase below the intermediate temperature, T* ∼ 100 °C, upon cooling, reflecting the sudden growth of the volume fraction of PNRs^{10,11,21}. In Fig. 3b, the temperature dependence of Г_{CP}, which is inversely proportional to the relaxation time, becomes narrower remarkably towards the T_{CT} upon cooling, implying the slowing down of the relevant polarization fluctuations of PNRs. Therefore, the anomaly at around 100 °C must reflect a significant change in the dynamical properties of the KLTN/0.05/0.27 crystal upon cooling. It is significant that both A_{CP} and Г_{CP} exhibit clear anomaly in the vicinity of the T_{CT} = 31 °C. Moreover, the first order TO_{1} mode in the VV spectra completely vanished at T_{CT} upon heating (Fig. 3c), which can be the clear indication of the phase transition of the KLTN/0.05/0.27 single crystal. The similar variation of the intensity and the Г_{CP} of the CP associated with the precursor dynamics was also observed in Pb(Zn_{1/3}Nb_{2/3})O_{3} (PZN) single crystal^{38}. The values of the characteristic temperatures T_{CT} and T* are in good agreement with the values reported in ref. 21.
It is worth noting that the temperature dependence of the reduced intensity, I_{0}, of the Fano resonance decreases rather fast in the vicinity of the T_{CT} upon heating, while it is still intense above the T_{CT} (Fig. 4a,b), indicating the symmetry breaking caused by the dynamic PNRs. In a typical relaxor, the breaking of symmetry in the cubic phase due to the existence PNRs with rhombohedral R3m symmetry was also studied by Raman scattering^{39,40}. It is also significant that the Г_{TO2} shows the noticeable change associated with these precursor effects, therefore, the Fano resonance might be correlated with the PNRs. Since the polarization fluctuations of the PNRs give rise to the CP, hence, the coupling between the CP and the TO_{2} phonon can cause a Fano resonance near 196 cm^{−1} in Lidoped KTN crystals. The schematic illustration of the coupling phenomenon between CP and TO_{2} phonon is shown in Fig. 5.
Angular dependence of Raman scattering spectra
For better understanding the physical origin of the Fano resonance in Lidoped KTN crystals, we analyzed the angular dependence of both VV and VH spectra in the cubic phase as shown in Fig. 6a,b, respectively. The angular dependence of Raman spectra shows the periodic variation with the rotation of the plane of polarization, and the variation of the intensity was out of phase between VV and VH spectra. We are mainly concerned about the microscopic origin of the Fano resonance. The angular dependence of Raman spectra was analyzed on the basis of Raman tensor calculations assuming the local symmetry of PNRs to clarify the physical origin of the CP and the Fano resonance in the cubic phase. According to the neutron pair distribution function analysis, the local symmetry of the PNRs of the Pb(Mg_{1/3}Nb_{2/3})O_{3} (PMN) crystal was reported as rhombohedral R3m^{41}. The R3m symmetry has three Raman active modes, A_{1}(z), E(y), and E(x) with the following Raman tensors^{42}:
The angular dependence of Raman integrated intensity was fitted by the following expression
where θ is the rotation angle of the experimental coordinates and is the transformation matrix for the modification of the Raman tensor components^{42}. Since the local rhombohedral regions are oriented randomly along the eight equivalent polarization directions, thus the angular dependence was calculated in the multidomain states in which the contributions of all eight domains are summed up equaly^{42}. The angular dependence of observed Raman intensity of the CP, I_{CP}, and the Fano resonance, I_{TO2}, in both VV and VH spectra in the cubic phase are plotted in Fig. 6c,d, respectively. It is worth noting that the change of the intensity of the CP and the Fano resonance with the rotation of the plane of polarization in the cubic phase of the Lidoped KTN crystal is similar to the behaviour of PNRs of PMN with the E(x, y) symmetry^{42}. Hence, on the analysis of the angular dependence of Raman results of the Lidoped KTN crystals, we excluded the A_{1}(z) symmetry of PNRs. For the E(x, y) symmetry of PNRs, one can obtain the values of the intensity of the cc (VV) and bc (VH) components after the transformation of the Raman tensor component using the equation (4) given by
The change of the intensity of the CP and the Fano resonance observed at both VV and VH spectra is well fitted by the theory via equations (5) and (6) as shown in Fig. 6c,d, respectively. The fitted curves reproduce the observed intensity variations rather well, implying that the CP and the Fano resonance in the cubic phase stem from the E(x, y) symmetry of PNRs with a rhombohedral R3m symmetry. Since both the CP and the TO_{2} phonon belong to the same symmetry, therefore, the CP and the TO_{2} phonon can be coupled with each other resulting in a Fano resonance in Lidoped KTN single crystal.
Electric field induced Raman scattering spectra
In order to clarify the origin of the Fano resonance, the electric field dependence of Raman scattering spectra of the KLTN/0.05/0.26 single crystal was investigated above and below the T_{CT} = 21 °C. The lower value of the T_{CT} of the KLTN/0.05/0.26 crystal than that of the KLTN/0.05/0.27 crystal occurs by the lower Nb concentrations. Figure 7a shows the electric field dependence of Raman spectra of the KLTN/0.05/0.26 crystal in both VV and VH scattering measured at 25 °C. It is interesting to note that the application of the electric fields causes the increase of the intensity for the VH spectra in the cubic phase, while no noticeable change appears for the VV spectra. In KTN, the relaxor like behaviour is originated from the correlated motion of the offcenter Nb ions. These displacements are along equivalent [111] directions, and each one can switch between several equivalents or symmetry related sites as shown in Fig. 7c^{7,13}. The motion between these various orientations affects the offdiagonal components of the polarizability tensors, and therefore influences the intensity of the VH scattering. In this study, the electric field was applied along the a i.e., [100] direction, which is orthogonal to the bc scattering plane. As a result, Nb ions became constrained for moving in this plane i.e., amongst four equivalent positions (Fig. 7d). Such a motion enhances the intensity of the VH scattering, while preventing that of the VV one. This effect is clearly seen in Fig. 7b, where the I_{0} increases with increasing electric field in the VH spectrum, while in the VV spectrum the I_{0} does not exhibit any appreciable change by the electric field. The switching of the Nb ions amongst four equivalent sites under the moderate electric fields can be the evidence of the dynamical response of local polarizations in the PNRs. Recently, the dynamic response of the PNRs under an electric field in the cubic phase of KTN was reported in Ref. 43. It is also expected that the restriction of the Nb ions to four sites results in a [100] timeaveraged polarizations with the application of the sufficient applied field, and resulting in a crystal transforms into a lower tetragonal P4mm symmetry. Since the applied electric filed was not as high as that can induce the phase transition of the KLTN/0.05/0.26 crystal at 25 °C, therefore the Raman spectra below 2.75 kV/cm was not same as observed spectra in the tetragonal phase, as presented in Fig. 2.
To clarify the effects of the electric field on the Fano resonance of the Lidoped KTN crystals, we also performed the field induced Raman scattering in the ferroelectric phase where the polarization fluctuations of PNRs were frozen into nanodomain states, while the growth into macrodomains was blocked by the random fields. The electric field dependence of the I_{0} and the A_{CP} measured at 2 °C is displayed in Fig. 8. It is important to note that the I_{0} and the A_{CP} exhibit the anomalous change at E = 1.5 kV/cm. In Lidoped KTN, without the external electric field there was no driving force for switching the nanodomain states to ferroelectric macrodomains in the tetragonal phase. Since the applied electric field along [100] direction stabilizes a tetragonal phase, therefore, the electric filed induced sudden increase of the I_{0} and the A_{CP} is caused by the alignment of the random nanodomain states along the field direction. Hence, the field induced change at 1.5 kV/cm can be the transition from random nanodomain states to a macrodomain state. By the applied electric field, such a transition from nanodomain states to a macrodomain state was also observed in typical relaxor ferroelectrics^{44,45} Since the proposed microscopic origin of the Fano resonance in Lidoped KTN single crystal is the coupling between CP and TO_{2} mode, it is expected that the electric filed effect on CP and TO_{2} mode should be the similar fashion. From the Fig. 8, it is apparent that the intensity of CP and TO_{2} mode exhibits the similar dependences on the electric field. These results strongly support the coupling between the CP and the TO_{2} mode.
Discussion
In the present study, the attention has been paid to clarify the microscopic origin of the Fano resonance in Lidoped KTN single crystals. The physical origin of the Fano resonance is discussed on the basis of different types of models and finally one model is chosen which reproduces the observed results appropriately. The Fano resonances reported in different types of materials may result from several different physical origins^{24,25,26,27,28,29,30}. In BaTiO_{3} single crystals, the Fano resonance at around 175 cm^{−1} was attributed to the interference effect arising from the coupling of a single phonon state to a two acoustical phonon state through the anharmonic terms in the potential function^{24}. In that case, the variation of the intensity of the acoustical mode and the Fano resonance should be the same in the wide temperature range. However, in Lidoped KTN crystals, the intensity of the 2TA mode did not exhibit any appreciable change in the cubic phase (Fig. 3c), whereas the intensity of the Fano resonance showed the noticeable temperature dependence (Fig. 4a,b). Therefore, the coupling between the TO_{2} phonon and the two acoustic phonons cannot be the origin of the Fano resonance in Lidoped KTN crystals.
Pinczuk et al. also suggested that the interference in BaTiO_{3} crystals at about 175 cm^{−1} can be due to the anharmonic coupling of the lowest frequency TO phonon with the higher frequency TO phonon via acoustic phonons^{25}. In Lidoped KTN crystals, the lowest frequency TO phonon vanished at the T_{CT}, whereas the Fano resonance still existed above the T_{CT} (Fig. 3c), and this fact again rules out the coupling of the lowest frequency TO phonon with the higher frequency TO phonon via acoustical phonons as the origin of our observation.
In the relaxor Ba(Zr_{1/2}Ti_{1/2})O_{3} (BZT), the Fano resonance at around 155 cm^{−1} was caused by the interaction between the Ti and the Zr sublattices^{28}. Interestingly, the Fano resonance in BZT persists up to 627 °C, which is far above the T_{B} ~ 177 °C at which dynamic PNRs start to appear. This is contrary to what was observed in the present observation, because the Fano resonance in Lidoped KTN crystals disappeared slightly above the T* at which the dynamic to static transition of PNRs begins.
The inelastic light scattering study reported that the rapid polarization fluctuations with the frequency up to the Fano resonance frequency within micro and nanoscopic polar regions interfere with a polar TO phonon resulting in the Fano resonance in nonrelaxor SrTiO_{3} thin films^{26}, and SrTiO_{3} and Ca_{x}Sr_{1−x}TiO_{3} nanocubes^{27}, respectively. However, the situation in Lidoped KTN is perfectly different from the situation in refs. 26 and 27, where the micro and nanoscopic polar regions were arisen from incorporated impurities, most likely due to the oxygen vacancies. In contrast, the PNRs can be induced in KTN owing to the offcenter displacements Nb ions at the Bsite. In KTN and Lidoped KTN, the local polarization fluctuations of PNRs itself are much slower than that of the TO_{2} phonon frequency, and appear as the CP in a GHz frequency range^{10,11,21}. Furthermore, it is significant that the value of the q gradually increased towards the T_{CT} and became the maximum in the ferroelectric phase, where the local polarization fluctuations were totally absent. Therefore, the interference between the rapid polarization fluctuations within micro polar regions and the TO_{2} phonon in nonrelaxor SrTiO_{3} films cannot be the origin of the Fano resonance in Lidoped KTN crystals.
According to the theory, the q parameter is inversely proportional to the density of continuum states (ρ) and the interaction strength (V)^{46,47}. The Г_{TO2} of the Fano resonance is proportional to the ρV^{2}. It is interesting to note that both Г_{TO2} and q^{−1} increased approximately linearly with the temperature towards the T_{CT} in the ferroelectric phase as shown in Fig. 4d. These results reflect that the V does not vary strongly with the temperature, and the temperature dependence of both Г_{TO2} and q^{−1} was caused by the increase of the density of continuum states towards the T_{CT}. These results are similar to those observed in a ferroelectric semiconductor Sn_{2}P_{2}Se_{6}^{29}.
Since the Fano resonance in Lidoped KTN crystals is affected by the precursor dynamics in the cubic phase, there can be the correlation between the Fano resonance and PNRs. It is well established that the dynamic PNRs in KTN and Lidoped KTN crystals are observed as the CP^{10,11,13,21}. Therefore, to clarify the physical origin of the Fano resonance, it is worth to compare the variation of the intensity of the CP and the Fano resonance with the temperature, angular, and electric field dependences of Raman spectra. It is clearly seen that the CP and the Fano resonance intensities showed the similar dependences on temperature, angular, and electric field, which demonstrates that the Fano resonance is driven by the CP. On the basis of these results, it is concluded that the coupling between the CP and the TO_{2} phonon can be the origin of the Fano resonance in Lidoped KTN single crystals^{30}.
In summary, the microscopic origin of the Fano resonance in Lidoped KTN single crystals was investigated by the temperature, angular, and electric field dependences of Raman scattering. The breaking of local symmetry in the cubic phase due to the existence of PNRs with E(x, y) symmetry was observed by the intense first order Raman scattering, in which the first order scattering is forbidden in the cubic Pm3m symmetry. In the VH Raman spectra, the remarkable field dependence of the Fano resonance intensity in the cubic phase can be the dynamical response of local polarizations to the electric field. The CP and TO_{2} phonon intensities showed the similar dependences on temperature, angular, and electric field. From these experimental results, it is concluded that the origin of the Fano resonance in Lidoped KTN crystals is the coupling between the polarization fluctuations of PNRs and the TO_{2} phonon, both belong to the E(x, y) symmetry.
Additional Information
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Acknowledgements
The research was partly supported by the Marubun Research Promotion Foundation, the JSPS KAKENHI Grant Numbers 26790040 90134204, and the Murata Science Foundation. The one of the authors wish to thank to Mr. M. A. Helal for the support during experiments.
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Affiliations
Graduate School of Pure and Applied Sciences, University of Tsukuba, Tsukuba, Ibaraki 3058573, Japan
 M. M. Rahaman
 & S. Kojima
NTT Corporation Device Innovation Center, Nippon Telegraph and Telephone Corporation, Atsugi, Kanagawa 2430198, Japan
 T. Imai
 & T. Sakamoto
Faculty of Education, Shimane University, Matsue, Shimane 6908504, Japan
 S. Tsukada
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Contributions
M.M.R. and S.K. wrote the main manuscript text. T.I. and T.S. grew the single crystals. S.T. established the measurement system for the angular dependent Raman scattering, and M.M.R. and S.T. measured the temperature, angular, and field dependences of Raman scattering. All authors reviewed the manuscript and contributed the discussion of the results.
Competing interests
The authors declare no competing financial interests.
Corresponding authors
Correspondence to M. M. Rahaman or S. Kojima.
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