Ferroelectric Properties and Spectroscopic Characterization of Pb(Mg 1/3 Nb 2/3 )O 3 -32PbTiO 3 :Er 3+ /Sc 3+ Crystal

: An Er 3+ /Sc 3+ co-doped 0.68Pb(Mg 1/3 Nb 2/3 )O 3 -0.32PbTiO 3 ferroelectric single crystal was grown by high-temperature ﬂux method. The remnant polarization Pr is 27.97 µ C/cm 2 and the coercive ﬁeld Ec is 8.26 kV/cm for [100] oriented crystal. Green (524 and 551 nm) and red (654 nm) emission bands are generated at the 980 nm excitation, which corresponds to the 2 H 11/2 → 4 I 15/2, 4 S 3/2 → 4 I 15/2 and 4 F 9/2 → 4 I 15/2 transitions of Er 3+ , respectively. Judd–Ofelt theory has been applied to predict the spectroscopic characteristics of the as-grown crystals. The obtained J–O intensity parameters Ω t ( t = 2, 4 and 6) are Ω 2 = 0.76 × 10 − 20 cm 2 , Ω 4 = 1.0 × 10 − 20 cm 2 , Ω 6 = 0.55 × 10 − 20 cm 2 . Spectroscopic characteristics, including optical transition probabilities, branching ratio, and radiative lifetime of Er 3+ in the crystal, are determined. The calculated radiative lifetimes of 4 I 13/2 and 4 I 11/2 energy levels are 2.82 ms and 2.61 ms, respectively. These investigations provide possibilities for the crystal Pb(Mg 1/3 Nb 2/3 )O 3 -0.32PbTiO 3 :Er 3+ /Sc 3+ to be a new type of multifunctional crystal integrating electricity-luminescence.

Ferroelectric single crystals represented by Pb(Mg 1/3 Nb 2/3 )O 3 -PbTiO 3 (PMN-PT) are well-known multifunctional materials owing to their excellent piezoelectric, ferroelectric properties, and ultra-high electromechanical coupling factors [7][8][9]. Rare earth (RE) ions as well-known luminescent activators with optical absorption and emission in the infrared and visible wavelength ranges have been widely used as dopants to design luminescent materials. Therefore, doping rare earth ions into relaxer-based ferroelectric single crystals will make the crystals simultaneously possess electrical-mechanical-optical properties, which have potential applications in developing innovative multifunctional devices. Our team members have successfully grown RE ions (Er 3+ , Ho 3+ , and Yb 3+ ) doped PMN-PT and PSN-PMN-PT single crystals and investigated their electric and optic properties systematically [14][15][16][17][18][19]. It is found that the addition of rare-earth ions not only improves the electrical properties of the crystals but also makes them obtain optical absorption and up-conversion luminescence properties. For example, XI, Z reported that the remnant polarization Pr of PSN-PMN-PT increased from 24.2 to 30.99 µC/cm 2 by the modification

Crystal Growth
PMN-32PT:Er 3+ /Sc 3+ single crystals were grown by the high-temperature flux method. The process is as follows: Firstly, MgO and Nb 2 O 5 powders with 99.99% purity were mixed at a molar ratio of 1:1 and calcinated at 1000 • C for 6 h to form the columbite precursor MgNb 2 O 6 . Secondly, MgNb 2 O 6 , PbO, and TiO 2 powders were mixed according to the stoichiometric composition of 0.68PZN-0.32PT, and excessive 80 wt% PbO powders as the solvent of high-temperature solution were added to the mixtures. 2 wt% Er 2 O 3 and 2 wt% Sc 2 O 3 were also added to the mixtures and wet-milled for 12 hours in the alcohol. Then the slurry mixtures were dried at 80 • C for 24 h in a drying oven; and the dried mixture powders were filled into a platinum crucible which was placed in a corundum pot with the same shape, the space between the platinum crucible and the corundum crucible was filled with Al 2 O 3 powders. Thirdly, the crucibles were sealed and placed in the crystal growth furnace with an automatic temperature controller, which was set from room temperature to 1330 • C at the rate of 3 • C/min, held for 12 h, and fell from 1330 • C to 650 • C at the rate of 0.01 • C/min, then cooled to room temperature spontaneously. Finally, the as-grown single crystals PMN-32PT:Er 3+ /Sc 3+ together with Pt crucible were boiled in nitric acid solution with the concentration of 50% until the crystals were separated from the platinum crucible. The as-grown crystals were obtained after the cleaning process in an ultrasonic cleaner when the crystals were removed from the platinum crucible. Finally, ferroelectric single crystal PMN-32PT:Er 3+ /Sc 3+ was cut into thin slices along the exposed surface.

Characterization Procedure
Micro morphology and element content of the as-grown crystal was performed by scanning electron microscope (FEI Quanta 400 FEG) quipped with Energy Dispersive Spectrometer (EDS). The X-ray diffraction (XRD) data were collected on an X-ray Diffractometer (Bruker D8 ADVANCE, Hannover, Germany) with Cu Ka radiation at the room temperature. The ferroelectric hysteresis loops were investigated by aix-ACCT TF2000 analyzer. The UV-VIS-NIR absorption spectra were detected by UV-VIS-NIR spectrophotometer (CARY50000, Agilent, Santa Clara, CA, USA). The up-conversion luminescence spectrum was measured by the Steady-State Spectrometer (FLS980, Edinburgh, England). Figure 1a shows the macroscopic morphology of as-grown PMN-32PT:Er 3+ /Sc 3+ crystals. It can be seen from the figure that the crystals present light yellow, the shape of which is irregular polyhedron or pseudo-cube with the size of 6 mm × 4 mm × 4 mm, similar to that of pure PMN-PT crystals reported in [15]. Figure 1b shows SEM image of PMN-32PT:Er 3+ /Sc 3+ crystals at 1000 times magnification. There are obvious steps like growth stripes in the local area of the crystal surface, and the step edges are arranged in a linear parallel manner, which also exists in undoped PMN-PT crystal as shown in Figure 1c. The doping of rare earth ions has little effect on the crystal growth, due to the good tolerance of the crystal. Figure 1d shows an SEM image of PMN-32PT:Er 3+ /Sc 3+ crystals at 5000 times magnification. It can be seen from Figure 1d that there are some corrosion pits with extremely irregular shapes in the crystal. The formation of corrosion pits is caused by the corrosion of wrapped PbO and various salt residues resulting from hot nitric acid during the separation of crystals. An energy dispersive spectrometer (EDS) was carried out at four random locations in the flat region of the crystal surface. Figure  1e,f shows a location and corresponding EDS spectrum. The spectrum shows that Pb, Mg, Nb, Ti, and O are the main elements in the single crystal. In addition, Er and Sc were also found, indicating that Er 3+ and Sc 3+ diffuse into the PMN-32PT. Table 1 shows the weight percentage of every element. wt% of Sc 3+ and Er 3+ are 0.13% and 2.21%, respectively.

Macroscopic and Microscopic Morphology of the Crystals
temperature. The ferroelectric hysteresis loops were investigated by aix-ACCT TF2000 analyzer. The UV-VIS-NIR absorption spectra were detected by UV-VIS-NIR spectrophotometer (CARY50000, Agilent, California). The up-conversion luminescence spectrum was measured by the Steady-State Spectrometer (FLS980, Edinburgh, England). Figure 1a shows the macroscopic morphology of as-grown PMN-32PT:Er 3+ /Sc 3+ crystals. It can be seen from the figure that the crystals present light yellow, the shape of which is irregular polyhedron or pseudo-cube with the size of 6 mm × 4 mm × 4 mm, similar to that of pure PMN-PT crystals reported in [15]. Figure 1b shows SEM image of PMN-32PT:Er 3+ /Sc 3+ crystals at 1000 times magnification. There are obvious steps like growth stripes in the local area of the crystal surface, and the step edges are arranged in a linear parallel manner, which also exists in undoped PMN-PT crystal as shown in Figure 1c. The doping of rare earth ions has little effect on the crystal growth, due to the good tolerance of the crystal. Figure 1d shows an SEM image of PMN-32PT:Er 3+ /Sc 3+ crystals at 5000 times magnification. It can be seen from Figure 1d that there are some corrosion pits with extremely irregular shapes in the crystal. The formation of corrosion pits is caused by the corrosion of wrapped PbO and various salt residues resulting from hot nitric acid during the separation of crystals. An energy dispersive spectrometer (EDS) was carried out at four random locations in the flat region of the crystal surface. Figure 1e,f shows a location and corresponding EDS spectrum. The spectrum shows that Pb, Mg, Nb, Ti, and O are the main elements in the single crystal. In addition, Er and Sc were also found, indicating that Er 3+ and Sc 3+ diffuse into the PMN-32PT. Table 1 shows the weight percentage of every element. wt% of Sc 3+ and Er 3+ are 0.13% and 2.21%, respectively.    Figure 2a shows the XRD patterns of the exposed flat surface of a PMN-32PT:Er 3+ /Sc 3+ crystal. It can be seen from the figure that there are only two diffraction peaks corresponding to the crystal planes (100) and (200) at the range of 10 •~6 0 • , respectively, and no other impurity peaks, which indicates that the crystal grows basically along the [100] orientation. Figure 2b shows the XRD patterns of PMN-32PT:Er 3+ /Sc 3+ and PMN-32PT crystals powders for comparison. we can see that the diffraction peak positions are consistent with each other. The doping of rare earth ions does not make the crystal produce a new phase. They both present pure perovskite structure (ABO 3 ) without pyrochlore phase or any other second phase, which indicates that Er 3+ /Sc 3+ ions have been diffused into the lattice of the single crystal PMN-32PT. Figure 2c shows the enlarged view of the diffraction peaks of the strongest peak, we can see that the diffraction peak position of the PMN-32PT:Er 3+ /Sc 3+ crystals is offset to the small angle. This phenomenon can be explained by the Bragg equation: 2dsinθ = kλ, where d is the interplanar spacing, θ is the diffraction angle, λ is the wavelength of X-ray, and k is the diffraction order. In the experiment, λ = 1.5406 Å, for the same k, the larger interplanar spacing, the smaller diffraction angle. When the Mg 2+ (r(Mg 2+ ) = 0.72 Å) or Nb 5+ (r(Nb 5+ ) = 0.64 Å) ions are replaced by larger Er 3+ (r(Er 3+ ) = 0.88 Å) ions, d becomes larger and the diffraction angle θ decreases. The deviation of the diffraction peak to a small angle further indicates that Er 3+ diffuses into the PMN-32PT crystal lattice.

XRD Patterns
Crystals 2021, 11, x FOR PEER REVIEW 4 of 12 PMN-32PT:Er 3+ /Sc 3+ (5000 × SEM morphology) (e) a location for EDS (f) EDS spectrum of a location on PMN-32PT:Er 3+ /Sc 3+ crystals surface.  Figure 2a shows the XRD patterns of the exposed flat surface of a PMN-32PT:Er 3+ /Sc 3+ crystal. It can be seen from the figure that there are only two diffraction peaks corresponding to the crystal planes (100) and (200) at the range of 10°~60°, respectively, and no other impurity peaks, which indicates that the crystal grows basically along the [100] orientation. Figure 2b shows the XRD patterns of PMN-32PT:Er 3+ /Sc 3+ and PMN-32PT crystals powders for comparison. we can see that the diffraction peak positions are consistent with each other. The doping of rare earth ions does not make the crystal produce a new phase. They both present pure perovskite structure (ABO3) without pyrochlore phase or any other second phase, which indicates that Er 3+ /Sc 3+ ions have been diffused into the lattice of the single crystal PMN-32PT. Figure 2c shows the enlarged view of the diffraction peaks of the strongest peak, we can see that the diffraction peak position of the PMN-32PT:Er 3+ /Sc 3+ crystals is offset to the small angle. This phenomenon can be explained by the Bragg equation: 2dsinθ = kλ, where d is the interplanar spacing, θ is the diffraction angle, λ is the wavelength of X-ray, and k is the diffraction order. In the experiment, λ = 1.5406 Å, for the same k, the larger interplanar spacing, the smaller diffraction angle. When the Mg 2+ (r(Mg 2+ ) = 0.72 Å) or Nb 5+ (r(Nb 5+ ) = 0.64 Å) ions are replaced by larger Er 3+ (r(Er 3+ ) = 0.88 Å) ions, d becomes larger and the diffraction angle θ decreases. The deviation of the diffraction peak to a small angle further indicates that Er 3+ diffuses into the PMN-32PT crystal lattice.

Hysteresis Loops
Polarization versus Electric field (P-E) hysteresis loop is a common characteristic of all ferroelectric materials. Figure 3a shows P-E hysteresis loops of the PMN-32PT:Er 3+ /Sc 3+ crystals along [100] at room temperature. It can be seen from the figure that the hysteresis loop tends to be saturated as the applied electric field in-

Hysteresis Loops
Polarization versus Electric field (P-E) hysteresis loop is a common characteristic of all ferroelectric materials. Figure 3a shows P-E hysteresis loops of the PMN-32PT:Er 3+ /Sc 3+ crystals along [100] at room temperature. It can be seen from the figure that the hysteresis loop tends to be saturated as the applied electric field increases from 2 to 14 kV/cm. When the electric field increases to 14 kV/cm, the P-E hysteresis loop is saturated. The obtained remnant polarization (Pr) is 27.97 µC/cm 2 and the coercive field E C is 8.26 kV/cm, which is higher than that of PMN-32PT crystal (Pr~19.43 µC/cm 2 , E C~3 .83 kV/cm) shown in Figure 3b. The E C is also higher than that of PMN-32PT:Er 3+ (E C~6 .37 kV/cm) and PMN-32PT:Ho 3+ (E C~4 .31 kV/cm) crystals reported in literature [16] and [17]. The enhancement of the coercive field is attributed to the domain wall pinning by defects [17]. The higher coercive field makes the ferroelectric single crystals PMN-32PT:Er 3+ /Sc 3+ become a potential material for high-power piezoelectric device applications.

Judd-Ofelt Analysis
The analyses of the optical unpolarized absorption spectra of laser crystals by using the Judd-Ofelt theory have been reported in much literature [20][21][22][23][24][25][26][27][28][29]. Firstly, the Judd-Ofelt model was applied to the unpolarized absorption bands to determine their experimental oscillation strength. The experimental oscillation strength (f exp ) associated with a 4f-4f transition from the ground state (J) to an excited state (J ) can be obtained from analysis of the D(λ)dλ of absorption bands using the following formula: where m is the electron mass, c is the speed of light in vacuum, e is the electron charge, N 0 is the erbium concentration, L is the thickness of the sample, λ is the mean wavelength of the specific absorption band, and D(λ) is optical density. From the absorption spectra shown in Figure 4, only seven optical absorption bands from the ground state 4 I 15/2 of erbium ions in the total spectrum were explored. The values of experimental polarized oscillator strengths f exp of these seven bands were obtained from Formula (1). The results are listed in Table 2 along with the values of the main parameters.  (3) and (4), and the theoretical oscillator strength f cal is the sum of them, they are given by the followings: where J and J are the angular momentums of the initial and final level, respectively; h is the Planck constant; n is the average refractive index which can be express as n = (2n o + n e )/3. The values of n o (λ) and n e (λ) used here were derived from reference [12]; where N is a number of is absorption bands. In this paper N = 7. Table 2 shows the f cal and f exp that result from the above-mentioned analysis together with the δ rms and the effective J-O parameters Ω t (t = 2, 4 and 6) for the PMN-32PT:Er 3+ /Sc 3+ crystals. We can see that the values of theoretical oscillator strength f cal are practically closed to those of experimental oscillator strength f exp and the δ rms between which is 0.38 × 10 −6 for PMN-32PT:Er 3+ /Sc 3+ . Based on our previous work reported in the literature [10], Judd-Ofelt analysis was also carried out for absorption spectra of PMN-32PT:Er 3+ in this paper and the calculated results are shown in Table 3. The first column of Table 4 shows the δ rms of Er 3+ in some laser crystals for comparison. It can be seen that the obtained δ rms is lower than that of several laser crystals containing Er 3+ [22][23][24]26]. The low RMS deviation indicates that our fitting is effective. The obtained effective J-O parameters Ω t (t = 2, 4 and 6) are Ω 2 = 0.76 × 10 −20 cm 2 , Ω 4 = 1.0 × 10 −20 cm 2 , Ω 6 = 0.55 × 10 −20 cm 2 for the crystals PMN-32PT:Er 3+ /Sc 3+ and Ω 2 = 1.77 × 10 −20 cm 2 , Ω 4 = 1.50 × 10 −20 cm 2 , Ω 6 = 0.79 × 10 −20 cm 2 for PMN-32PT:Er 3+ . As well known, Judd-Ofelt parameters Ω t (t = 2, 4, and 6) are important for the investigation of the local structure and bonding in the vicinity of rare-earth ions. They characterize the interaction of rare-earth ions with the host crystals. In addition, the spectroscopic quality factor, defined by Ω 4 /Ω 6 , is critically important in predicting the stimulated emission for the active laser medium. For comparative study, the J-O parameters and Ω 4 /Ω 6 of other crystals are also listed in Table 4. In this work, the values of Ω 4 /Ω 6 are 1.82 and1.90 for PMN-32PT:Er 3+ /Sc 3+ and PMN-32PT:Er 3+ , respectively, which are smaller than that of LiNbO 3 [26][27][28]. Still, it is larger than that of other crystals reported in the literature [20][21][22][23][24][25]. The high spectroscopic quality factor Ω 4 /Ω 6 indicates the ferroelectric single crystal PMN-32PT:Er 3+ /Sc 3+ and PMN-32PT:Er 3+ can be promising laser crystal.  Based on the obtained J-O parameters Ω t (t = 2, 4, and 6), the radiative transition probability A(J-J ) of the electric and magnetic dipole transitions from an excited manifold J to a lower manifold J can be calculated by followings: Branching ratios β and radiative lifetimes τ r were calculated according to the following. The calculated electric and magnetic dipole spontaneous emission probabilities, radiative lifetimes, and branching ratios of Er 3+ ions in crystals PMN-32PT:Er 3+ /Sc 3+ and PMN-32PT:Er 3+ are summarized in Table 5. The radiative transitions of 4 F 9/2 → 4 I 15/2 (654 nm), 4 S 3/2 → 4 I 15/2 (551 nm), and 2 H 11/2 → 4 I 15/2 (524 nm) have larger fluorescence branching ratios in visible wavelength regions. The fluorescence branching ratios of them are 81%, 73%, and 70%, respectively. Moreover, the radiative lifetimes of 4 I 13/2 and 4 I 11/2 levels for the PMN-32PT:Er 3+ /Sc 3+ crystals are estimated to be 2.82 ms and 2.61 ms, respectively, which are longer than those of PMN-32PT:Er 3+ , KY(WO 4 ) 2 :Er 3+ /Yb 3+ [21], Gd 3 Ga 5 O 12 :Er 3+ /Pr 3+ [22], and Lu 2 O 3 :Er 3+ [29] shown in Table 6, indicating excellent energy storage capability for the PMN-32PT:Er 3+ /Sc 3+ crystals.   Figure 5a shows the up-conversion emission spectra of Er 3+ /Sc 3+ co-doped PMN-32PT crystals irradiated by a 980-nm laser with different pump power. Three emission bands are generated, corresponding to 2 H 11/2 → 4 I 15/2 (524 nm), 4 S 3/2 → 4 I 15/2 (551 nm), 4 F 9/2 → 4 I 15/2 (654 nm) transitions. These assignments are coinciding with the J-O analysis because these dipole transitions have large fluorescence branching ratios and high radiative quantum efficiencies. It can be seen from the spectrum that the green light has undergone Stark level splitting, 551 nm splitting into 540 nm, 551 nm, and 565 nm. This is due to the fact that each spectral branch of rare earth ions has a 2J+1 degeneracy, if the symmetry of the crystal field is low, then the degeneracy of the energy level will be canceled or partially canceled, resulting in energy level splitting. Figure 5b shows the dependence of emission intensities on pump power used to investigate the up-conversion mechanism and the number of photons in the up-conversion process. The up-converted emission intensity I up is proportional to IR excitation intensity I IR , I up ∝ I IR m where m is the number of pumping photons. The dependence emission intensity on pump power is quadratic and obtained m values are 1.92 2.21 and 2.27 for 4 F 9/2 → 4 I 15/2 (654 nm), 4 S 3/2 → 4 I 15/2 (551 nm), and 2 H 11/2 → 4 I 15/2 (524 nm), respectively. These values are close to 2, which indicates that two excitation photons contribute to one UC photon. excitation intensity IIR, Iup ∝ IIR m where m is the number of pumping photons. Th dependence emission intensity on pump power is quadratic and obtained m valu are 1.92 2.21 and 2.27 for 4 F9/2→ 4 I15/2 (654 nm), 4 S3/2→ 4 I15/2 (551 nm), and 2 H11/2→ 4 I15/2(52 nm), respectively. These values are close to 2, which indicates that two excitatio photons contribute to one UC photon. Finally, it should be stressed that all of the preceding results and discussio concentrate on the spectroscopic properties of Er 3+ . As no absorption and emissio bands corresponding to Sc 3+ are generated, spectroscopic properties of Sc 3+ cannot b investigated by Judd-Ofelt treatment. However, comparison results of the Judd-Ofe analysis carried out for Er 3+ doped PMN-32PT and Er 3+ /Sc 3+ co-doped PMN-32P crystals are given in Table 6, where the longer radiative lifetime fo PMN-32PT:Er 3+ /Sc 3+ crystal indicated that Sc 3+ ion doping improves the optical quali of the PMN-32PT:Er 3+ crystal, but the molecular mechanism needs to be further inve tigated.

Conclusions
PMN-32PT:Er 3+ /Sc 3+ single crystals were grown by using the high-temperatu flux method. The coercive field EC of PMN-32PT crystal was enhanced from 3.8 kV/cm to 8.26 kV/cm by Er 3+ /Sc 3+ ions modification. Moreover, seven optical absorp tion bands of Er 3+ are explored in the PMN-32PT crystal field. Based on the analysis Finally, it should be stressed that all of the preceding results and discussion concentrate on the spectroscopic properties of Er 3+ . As no absorption and emission bands corresponding to Sc 3+ are generated, spectroscopic properties of Sc 3+ cannot be investigated by Judd-Ofelt treatment. However, comparison results of the Judd-Ofelt analysis carried out for Er 3+ doped PMN-32PT and Er 3+ /Sc 3+ co-doped PMN-32PT crystals are given in Table 6, where the longer radiative lifetime for PMN-32PT:Er 3+ /Sc 3+ crystal indicated that Sc 3+ ion doping improves the optical quality of the PMN-32PT:Er 3+ crystal, but the molecular mechanism needs to be further investigated.

Conflicts of Interest:
The authors declare no conflict of interest.