Ferroelectric and Spectroscopic Properties of Ho³⁺/Yb³⁺ Co-Doped Pb(Mg_1/3Nb_2/3)O₃-32PbTiO₃ Crystal

Abstract

In order to design a new multifunctional crystal with excellent ferroelectric and spectroscopic properties, experiments were carried out for Ho³⁺/Yb³⁺ co-doped Pb(Mg_1/3Nb_2/3)O₃ -32PbTiO₃ ferroelectric crystal using the flux method, the coercive field Ec of which is 11.86 kV/cm. Up-conversion luminescence emission bands, including an intense green emission band at 553 nm, a red band at 663 nm, and a weak infra-red band at 755 nm, are generated at 980 nm excitation. The main spectroscopic parameters, including radiative transition probability A(J′ − J), radiative lifetimes τ_rad, and branching ratios β, were predicted by applying Judd–Ofelt treatment. The obtained J-O intensity parameters are Ω₂ = 0.531 × 10⁻²⁰ cm², Ω₄ = 1.738 × 10⁻²⁰ cm², Ω₆ = 0.530 × 10⁻²⁰ cm². The radiative lifetime of ⁵I₇ level is 5.45 ms. The fluorescence lifetime of is ⁵F₅ is 92.568 μs. The investigations show that Ho³⁺/Yb³⁺ co-doped Pb(Mg_1/3Nb_2/3)O₃-0.32PbTiO₃ crystal is a new type of multifunctional crystal integrating ferroelectric and spectroscopic properties, which has a potential application in the developing innovative multifunctional devices and lasers.

1. Introduction

In recent decades, relaxor ferroelectric single crystals represented by (1−x) Pb(Mg_1/3Nb_2/3)O₃-xPbTiO₃ [PMN-PT] and Pb(Zn_1/3Nb_2/3)O₃-xPbTiO₃ [PZN-PT] have triggered a revolution. They are regarded as potential materials in the medical ultrasonic probe, underwater acoustic transducer, and ultrasonic motor owing to their excellent electric properties [1,2,3]. However, the low coercive field Ec limits their applications in high-power devices. It is urgent to develop a new-type ferroelectric single crystal with high coercive field Ec.

In addition, PMN-PT and PZN-PT relaxor ferroelectric crystals do not contain luminescent activators, which limits their application in optical devices and opto-electric couplers. Rare earth (RE) ions (Er³⁺, Ho³⁺, Eu³⁺, Tb³⁺, Tm³⁺, and Sm³⁺), as well-known activators with optical emission in the infrared and visible wavelength ranges, have been widely doped into the host material to design luminescent materials. In addition, RE ions are used in the electricity fields owing to their unique chemical properties. Therefore, new ferroelectric crystals doped with RE ions, such as Pb(Sm_1/2Nb_1/2)O₃-Pb(Mn_1/3Nb_2/3)O₃-PbTiO₃ [4], Sm doped Pb(Mn_1/3Nb_2/3)O₃-PbTiO₃ [5], Ho³⁺ doped PZN-PT [6], Pb(Sc_1/2Nb_1/2)O₃-Pb(Mn_1/3Nb_2/3)O₃-PbTiO₃ doping with Ho³⁺ and Ho³⁺/Yb³⁺ [7], and Pb(Ho_1/2Nb_1/2)O₃-Pb(Mn_1/3Nb_2/3)O₃-PbTiO₃ [8], have successfully grown in the last five years. Rare earth ions as solid solutions and impurity ions enter PMN-PT and PZN-PT crystals.

Investigations have shown that some new-type ferroelectric crystals have higher coercive field Ec. It was reported that the coercive field E_C of Ho³⁺/Yb³⁺ co-doped PZN-PT crystal is about 9.26 kV/cm [9], which is higher than that of PZN-PT:Ho³⁺ (Ec~5.9 kV/cm) [6] and Pb(Sm_1/2Nb_1/2)O₃-Pb(Zn_1/3Nb_2/3)O₃-PbTiO₃ (Ec~ 3.61 kV/cm) [4] crystals. In addition, some new-type ferroelectric crystals own excellent luminescence properties. It was reported that an intense green emission band at 552 nm were observed in Ho³⁺ and Ho³⁺/Yb³⁺ co-doped Pb(Sc_1/2Nb_1/2)O₃-Pb(Zn_1/3Nb_2/3)O₃-PbTiO₃ by 980 nm laser excitation. The emission intensity of Ho³⁺/Yb³⁺ co-doped Pb(Sc_1/2Nb_1/2)O₃-Pb(Zn_1/3Nb_2/3)O₃-PbTiO₃ was increased by three orders of magnitude compared to the single doping of Ho³⁺ ions. In this case, the Yb³⁺, as an optical sensitive ion, enhances the luminescence intensity [7].

In order to provide an understanding of the spectroscopic properties of the new-type ferroelectric crystals doped with rare earth ions, it is necessary to apply Judd–Ofelt treatment on them. The main spectroscopic characteristics, including radiative transition probability, radiative lifetimes, branching ratios, and emission cross section, can be obtained by applying Judd–Ofelt theory. Judd–Ofelt treatment is widely applied to predict the spectroscopic characteristics for laser crystals [10,11,12,13,14,15,16,17,18,19]. However, relevant Judd–Ofelt treatment on the new-type ferroelectric crystals doping with rare earth ions could not be found in the previous literature.

In this work, Ho³⁺/Yb³⁺ were doped into PMN-32PT ferroelectric single crystals to form a new system. Judd–Ofelt treatment is performed on the PMN-32PT:Ho³⁺/Yb³⁺ ferroelectric crystal for the first time. Oscillator and spectral strength parameters, including Judd–Ofelt parameters Ω_t (t = 2, 4, and 6), radiative transition probabilities A(J′ − J), branching ratio β, and radiative lifetime τ_rad, were predicted. This investigation will provide a theoretical basis for the luminescence mechanism. In addition, the effect of Ho³⁺/Yb³⁺ ions on the ferroelectric properties of PMN-32PT crystal has been studied. Our research is as follows: Firstly, the experiments were carried out for Ho³⁺/Yb³⁺ co-doped Pb(Mg_1/3Nb_2/3)O₃-32PbTiO₃ ferroelectric crystal using the flux method. Secondly, the main characteristics, including XRD, EDS, hysteresis loops, absorption, and up-conversion luminescence emission spectra of the crystals, were investigated. Finally, the spectroscopic parameters of PMN-32PT:Ho³⁺/Yb³⁺ crystal were predicted by applying the Judd–Ofelt treatment.

2. Materials and Methods

2.1. Crystal Growth

PMN-32PT:Ho³⁺/Yb³⁺ crystal was grown by the high-temperature flux method. The process is shown in Figure 1:

Step 1: PbO, MgO, Nb₂O₅, Ho₂O₃, Yb₂O₃, and TiO₂ powders with 99.99% purity were used as starting materials. MgO and Nb₂O₅ powders were mixed at a molar ratio of 1:1 and calcinated at 1000 °C for 6 h to form the precursor MgNb₂O₆.

Step 2: MgNb₂O₆, PbO, and TiO₂ powders were mixed according to the stoichiometric composition 0.68PMN–0.32PT. Meanwhile, the 2 mol% Ho₂O₃ and Yb₂O₃, together with excessive 80 wt% PbO powders, were also added to the mixtures.

Step 3: The mixtures were wet-milled for 12 h in the alcohol and dried at 80 °C for 24 h in a drying oven. Then, the dried mixture powders were poured into a platinum crucible which was placed in a corundum pot.

Step 4: The crucibles were 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. Two weeks later, the as-grown PMN-32PT:Ho³⁺/Yb³⁺ crystals were obtained.

Step 5: The as-grown single crystals PMN-32PT:Ho³⁺/Yb³⁺ together with Pt crucible were boiled in nitric acid solution until the crystals were separated from the crucible. Then, PMN-32PT:Ho³⁺/Yb³⁺ crystal was cut into thin slices along the exposed surface. Finally, the silver paste was daubed on two sides as the electrodes and annealed at 550℃ for 2 h before testing ferroelectric properties.

2.2. Characterization Procedure

The X-ray diffraction data was collected by X-Ray Diffractometer (Bruker D8 ADVANCE, Germany) with Cu Ka radiation. Energy dispersive system (EDS) spectrum was obtained by a scanning electron microscope (Gemini SEM 500). The ferroelectric hysteresis loops were measured by aix-ACCT TF2000 analyzer. The absorption spectra were detected by UV-VIS-NIR spectrophotometer (UV3600PLUS, HIMADZU, JAPAN). The luminescence spectrum and the fluorescence lifetime were measured by Steady-State Spectrometer (FLS980, Edinburgh, England).

3. Results and Discussion

3.1. XRD Patterns

Figure 2 shows the XRD patterns of Ho³⁺/Yb³⁺ co-doped PMN-32PT crystal powders together with undoped PMN-32PT for comparison. One can see that the diffraction peaks of PMN-32PT:Ho³⁺/Yb³⁺ are consistent with PMN-32PT crystal. They are both pure perovskite structure (ABO₃) without any other phase. The enlarged view of (111) and (200) peaks is shown in Figure 2b,c. It can be seen that (111) and (200) peaks occur splitting, which indicates that Ho³⁺/Yb³⁺ diffuse into the PMN-32PT crystal lattices and induces the transition from rhombohedral phase into the tetragonal and rhombohedral phase. The tetragonal and rhombohedral phase coexist in the PMN-32PT:Ho³⁺/Yb³⁺ crystal.

3.2. EDS Spectrum

Figure 3a shows energy dispersive system (EDS) of three random points on the surface of PMN-32PT:Ho³⁺/Yb³⁺ crystals. The EDS spectrums of the three points are presented in Figure 3b–d. It can be seen from the figures that the chemical composition of the single crystal is Pb, Mg, Nb, Ti, and O. In addition, the Ho and Yb are also found, which indicates that Ho³⁺ and Yb³⁺ ions diffuse into single crystals. The element content of the crystals obtained by EDS is shown in

Table 1. The element content of the PMN-32PT: Ho³⁺/Yb³⁺ crystals obtained by EDS.

	O	Pb	Mg	Ti	Nb	Ho	Yb
A1 (wt%)	6.49	68.76	1.19	5.59	14.82	1.59	1.55
A2 (wt%)	6.61	68.75	1.14	5.57	14.86	1.59	1.47
A3 (wt%)	6.77	66.00	1.07	6.25	16.69	1.68	1.54

. It is noticed that the element distribution of the crystal is homogeneity. According to the tested niobium and titanium content, the calculated chemical composition is close to the PMN-32PT. The weight content of Ho³⁺ and Yb³⁺ is about 1.62 wt% and 1.52 wt%, respectively.

3.3. Hysteresis Loops

Figure 4a shows the ferroelectric hysteresis loop of Ho³⁺/Yb³⁺ doped PMN-32PT single crystal. It can be seen from the figure that the hysteresis loop of PMN-32PT: Ho³⁺/Yb³⁺ single crystal gradually becomes saturation when the external electric field was increased from 4 kV/cm to 16 kV/cm. The spontaneous polarization (Ps) and residual polarization (Pr) of Ho³⁺/Yb³⁺ doped PMN-32PT crystal is 22.52 μC/cm² and 20.85 μC/cm², respectively, which is similar with that of undoped PMN-PT crystals (Ps~23.29 μC/cm², Pr~19.38 μC/cm²) shown in Figure 4b. However, the coercive field (E_c~11.86 kV/ cm) of PMN-32PT:Ho³⁺/Yb³⁺ crystal is higher than that of undoped PMN-PT crystals (E_c~3.92 kV/cm). The enhancement in coercive field in the crystals could be attributed to the distorted lattice and oxygen vacancy to pin the domain wall motion [7,8]. As the radius of doping ions Ho³⁺(0.089 nm) and Yb³⁺(0.086 nm) are close to that of the cations (Mg²⁺: r~0.072 nm; Nb⁵⁺: r~0.064 nm; and Ti⁴⁺: r~0.0605 nm) located the B-site, Ho³⁺ and Yb³⁺ ions preferentially occupy the B-site and distort the crystal lattice (demonstrated in XRD results). Large lattice distortion induces high stress, which limits the domain switching, resulting in the Ec increase. On the other hand, considering the different valence states among Ho³⁺, Yb³⁺, Mg²⁺, Nb⁵⁺, and Ti⁴⁺, some charged ions such as oxygen vacancies will be formed for compensating charge balance. The combination of doped cations (Er³⁺or Yb³⁺) and oxygen vacancies form defect dipoles. The defect dipole is consistent with each other in the short range, which act as pinning points to prevent the domain moving. Therefore, the coercive field was enhanced.

3.4. UV-VIS-NIR Absorption

Figure 5 shows the absorption spectra of the PMN-32PT:Ho³⁺/Yb³⁺ single crystal at 300 K. Seven absorption peaks were observed in the range of 450 nm~2200 nm. The peaks located at 451 nm, 541 nm, 643 nm, 1152 nm, and 1943 nm correspond to the transitions ⁵G₆/⁵F₁→⁵I₈ (451 nm), ⁵F₄/⁵S₂→⁵I₈ (541 nm), ⁵F₅→⁵I₈ (643 nm), ⁵I₆→⁵I₈ (1152 nm), and ⁵I₇ →⁵I₈ (1943 nm) of Ho³⁺ ions, respectively. The peaks at 902 nm and 974 nm correspond to the transition absorption of Yb³⁺ ions. The special line at 800–860 nm is caused by the switching from infrared detectors to visible light detectors. The obtained absorption spectra of PMN-32PT:Ho³⁺/Yb³⁺ single crystal is very similar to that of PSN-PMN-PT:Ho³⁺/Yb³⁺ crystal [7], which have similar structure. The number of observed absorption peaks is limited by the energy band gap of the host crystals. Hence, only five absorption bands of Ho³⁺ in the spectrum are explored. It is less than that of laser crystals LiNbO₃:In³⁺/Ho³⁺ [11], YAlO₃:Ho³⁺ [12], YAG:Ho³⁺ [13], and Gd₃(Al,Ga)₅O₁₂:Ho³⁺/Yb³⁺ [14]. It seems that it is necessary to apply the Judd–Ofelt treatment to analyze the absorption spectrum shown in Figure 5.

3.5. Judd–Ofelt Analysis

Figure 6 shows the main steps of Judd– Ofelt treatment on the PMN-PT:Ho³⁺/Yb³⁺ crystal:

Step 1: The experimental oscillation strength, f_exp (J→J′), of Ho³⁺ in the PMN-32PT crystal are obtained by Equation (1). There are only five optical absorption bands from the ground state ⁵I₈ of Ho³⁺ ions in the spectrum shown in Figure 5. The experimental oscillation strength f_exp (J→J′) of these five bands are obtained from analysis of the five integral absorption coefficients ∫α(λ)dλ.

$$f_{\mathit{exp}}^{}(J\to J^{\prime })=\frac{m{c}^2}{\pi e^2{\overline{\lambda }}^2{N}_0}{\displaystyle \int \alpha (\lambda )}d\lambda$$

(1)

where J is the ground state ⁵I₈, J′ is the excited state, c is the speed of light in vacuum, m and e are the electron mass and charge, respectively, and N₀ is the holmium concentration. In this paper, $\overline{\lambda }$ is the average wavelength of the J→J′ transition. α(λ) is absorption coefficient, which obtained from absorption spectra testing.

Step 2: The theoretical oscillator strength, f_cal (J→J′), of Ho³⁺ in the PMN-PT crystal is given by Equation (2):

$$f_{cal}^{}(J\to J\prime )=\frac{8{\pi }^{2}mc}{3h(2J+1)n^2\overline{\lambda }}({\chi }_{ed}{S}_{ed}+{\chi }_{md}{S}_{md})$$

(2)

where h is the Planck constant and n is the refractive index of the host. n = (2n_o + n_e)/3 for crystals. The values of n_o(λ) and n_e(λ) used here for PMN-PT were derived from reference [15]. χ_ed and χ_md are the refractive index factors of electric dipole transition and magnetic dipole transition, respectively; they are given by Equations (3) and (4). S_ed and S_md are the line strengths for the electric dipole and magnetic dipole transitions, respectively. They are given by Equations (5) and (7).

$${\chi }_{ed}=\frac{n{\left(n^2+2\right)}^2}{9}$$

(3)

$${\chi }_{md}=n^3$$

(4)

$$S_{md}(J\to J\prime )={(h/4\pi mc)}^2{\left|\langle 4f^N(SL)J\Vert L+2S\Vert 4f^N\left(S^{\prime }{L}^{\prime }\right)J\prime \rangle \right|}^2$$

(5)

$$\mathrm{Selection}\mathrm{rule}\mathrm{of}{S}_{\mathit{md}}\mathrm{transitions}:\Delta l=0;\Delta S=0;\Delta L=0;\Delta J=0,\pm 1;\Delta M=0,\pm 1$$

(6)

$$S_{ed}(J\to J\prime )={{\displaystyle \sum _{t=2,4,6}{\Omega }_t\left|\langle 4{\mathrm{f}}^N(SL)J|\left|U^{(t)}\right||4{\mathrm{f}}^N(S^{\prime }{L}^{\prime })J^{\prime }\rangle \right|}}^2$$

(7)

$$\mathrm{Selection}\mathrm{rule}\mathrm{of}{S}_{\mathit{ed}}\mathrm{transitions}:\Delta l=\pm 1;\Delta S=0;\left|\Delta L\right|\le 6;\left|\Delta J\right|\le 6;$$

(8)

where the reduced matrix elements of the unit tensor operator, U^(t)(t = 2, 4, and 6), are almost insensitive to the ion environment. The values used here were derived from reference [13]. In addition, (L + 2S) is the magnetic dipole operator which depends on ∆J:

$$J^{\prime }=J\to \left|\langle 4f^N\left(SL\right)J\Vert L+2S\Vert 4f^N(\left(S^{\prime }{L}^{\prime }\right)J^{\prime }\rangle \right|={\left[\frac{2J+1}{4J(J+1)}\right]}^{1/2}\times \left[S(S+1)-L(L+1)+3J(J+1)\right]$$

(9)

$$J^{\prime }=J-1\to \left|\langle 4f^N\left(SL\right)J\Vert L+2S\Vert 4f^N(\left(S^{\prime }{L}^{\prime }\right)J^{\prime }\rangle \right|={\left[\frac{\left({(S+L+1)}^2-J^2\right)\left(J^2-{(L-S)}^2\right)}{4J}\right]}^{1/2}$$

(10)

$$J^{\prime }=J+1\to \left|\langle 4f^N\left(SL\right)J\Vert L+2S\Vert 4f^N(\left(S^{\prime }{L}^{\prime }\right)J^{\prime }\rangle \right|={\left[\frac{\left({(S+L+1)}^2-{(J+1)}^2\right)\left({(J+1)}^2-{(L-S)}^2\right)}{4(J+1)}\right]}^{1/2}$$

(11)

Step 3: The J-O intensity parameters, Ω_t (t = 2, 4, and 6), are found by least-squares fitting the measured experimental oscillation strength (f_exp) values given by Formula (1) to the calculated theoretical ones (f_cal) given by Equation (2). The three J-O intensity parameters Ω_t (t = 2, 4, and 6) characterize the efficiency of interaction of the rare earth ion Ho³⁺with the field PMN-PT ferroelectric crystal.

Step 4: The radiative transition probability A(J′-J), calculated radiative lifetimes τ_r and branching ratios β are obtained by Equations (12) to (14):

$$A\left(J^{\prime },J\right)=A_{ed}+A_{md}=\frac{64{\pi }^4{e}^2}{3h(2J+1){\overline{\lambda }}^3}({\chi }_{ed}{S}_{ed}+{\chi }_{md}{S}_{md})$$

(12)

$$\beta =\frac{A_{J\prime J}}{{\displaystyle \sum _{J^{\prime }}{A}_{J\prime J}}}$$

(13)

$$\tau =\frac{1}{{\displaystyle \sum _{J\prime }{A}_{\mathrm{JJ}\prime }}}$$

(14)

From Equations (1) to (11), the values of f_cal and f_exp, together with Ω_t (t = 2, 4 6) of Ho³⁺ ion in the field environment of PMN-PT crystal, have been obtained. They are listed in

Table 2. f_cal, f_exp, δ_rsm, and Ω_t(t = 2, 4, and 6) of PMN-32PT:Ho³⁺/Yb³⁺ crystal.

Transition	$\overline{\mathit{\lambda }}$/nm	fexp × 10−6	fcal × 10−6	Ωt (t = 2,4,6)/cm2
5I8→5F1/5G6	451	14.2203	14.2234	Ω2 = 0.531 × 10−20 Ω4 = 1.738 × 10−20 Ω6 = 0.530 × 10−20
5I8→5F4/5S2	541	6.9864	7.3646
⁵I₈→⁵F₅	643	5.4893	5.2341
⁵I₈→⁵I₆	1152	2.4753	1.0429
⁵I₈→⁵I₇	1943	2.2074	2.2074
δrsm = 1.063 × 10−6

. It can be found that the theoretical oscillator strength (f_cal) is consistent with the experiment oscillator strength f_exp. The root square deviation (δ_rsm) is 1.063 × 10⁻⁶. It indicates that the obtained oscillator strengths are highly reliable. The obtained values of Judd–Ofelt intensity parameter are Ω₂ = 0.531×10⁻²⁰ cm², Ω₄ = 1.738×10⁻²⁰ cm², and Ω₆ = 0.530 × 10⁻²⁰ cm² for Ho³⁺ ion in PMN-32PT crystal.

It is known that the spectroscopic quality factor is characterized by Ω₄/Ω₆. In

Table 3. The values of Ω_t (t = 2, 4, and 6) × 10⁻²⁰/cm² and Ω₄/Ω₆ of Ho³⁺ in laser crystals.

Crystal	Ω2	Ω4	Ω6	Ω4/Ω6	Reference
LiNbO3:In/Ho	1.069	13.575	10.076	1.347	[11]
YAlO3:Ho	1.087	3.18	1.879	1.69	[12]
YAG:Ho	0.101	2.086	1.724	1.210	[13]
Gd3(Al,Ga)5O12:Ho/Yb	0.475	2.434	1.761	1.382	[14]
CNGG:Ho	2.85	2.35	0.76	3.09	[16]
GdScO3:Ho	4.19	3.01	0.93	3.24	[17]
PMN-PT:Ho/Yb	0.531	1.738	0.530	3.273	This work

, the J–O intensity parameters Ω_t (t = 2, 4, and 6) and the spectroscopic quality factor Ω₄/Ω₆ for PMN-32PT:Ho³⁺/Yb³⁺ are compared with the values obtained for some laser crystals containing Ho³⁺. The value of Ω₄/Ω₆ for Ho³⁺ in PMN-32PT crystal is 3.273, which is larger than that of laser crystals as well as LiNbO₃:In³⁺/Ho³⁺ [11], YAlO₃:Ho³⁺ [12], YAG:Ho³⁺ [13], and Gd₃(Al,Ga)₅O₁₂:Ho³⁺/Yb³⁺ [14]. It is close to that of CNGG:Ho³⁺ and GdScO₃:Ho³⁺ crystals [16,17]. The high spectroscopic quality factor indicates the PMN-32PT:Ho³⁺/Yb³⁺ is a promising laser crystal.

Table 4. The calculated results of the spectroscopic parameters of PMN-32PT:Ho³⁺/Yb³⁺crystal.

Transitions	λ/nm	${\left|{\mathbf{U}}^{(2)}\right|}^2$	${\left|{\mathbf{U}}^{(4)}\right|}^2$	${\left|{\mathbf{U}}^{(6)}\right|}^2$	Aed/s−1	Amd/s−1	A/s−1	$\mathit{\beta }$	τrad/ms
⁵I₇→⁵I₈	1986	0.0249	0.1344	1.5217	144	40	184	1.00	5.45
⁵I₆→⁵I₈	1172	0.0083	0.0383	0.6918	336	0	336	0.84	2.51
→⁵I₇	2859	0.0319	0.1366	0.9308	39	23	62	0.16
⁵I₅→⁵I₈	902	0	0.0092	0.0936	133	0	133	0.41	3.09
→⁵I₇	1653	0.0027	0.0226	0.8887	165	0	165	0.51
→⁵I₆	3920	0.0438	0.1705	0.5729	15	10	25	0.08
⁵I₄→⁵I₈	761	0	0	0.0077	17	0	17	0.09	5.36
→⁵I₇	1234	0	0.0033	0.1568	84	0	84	0.45
→⁵I₆	2172	0.0022	0.0281	0.664	70	0	70	0.38
→⁵I₅	4869	0.0312	0.1237	0.9099	11	4	15	0.08
⁵F₅→⁵I₈	648	0	0.4277	0.5686	5609	0	5609	0.78	0.14
→⁵I₇	961	0.0177	0.3298	0.4340	1335	0	1335	0.19
→⁵I₆	1448	0.0102	0.1212	0.4995	231	0	231	0.03
→⁵I₅	2297	0.0068	0.0271	0.1649	17	0	17	0.00
→⁵I₄	4348	0.0001	0.0059	0.004	0	0	0	0.00
⁵S₂→⁵I₈	547	0	0	0.227	2360	0	2360	0.53	0.22
→⁵I₇	755	0	0	0.4096	1619	0	1619	0.36
→⁵I₆	1027	0	0.0206	0.1541	349	0	349	0.08
→⁵I₅	1391	0	0.0043	0.1062	76	0	76	0.02
→⁵I₄	1947	0.0013	0.0279	0.2795	86	0	86	0.02
→⁵F₅	3527	0	0.011	0.0036	2	0	2	0.00
⁵F₄→⁵I₈	540	0	0.2402	0.7079	9000	0	9000	0.75	0.08
→⁵I₇	741	0	0.1988	0.0324	1589	0	1589	0.13
→⁵I₆	1000	0.0018	0.258	0.1697	960	0	960	0.08
→⁵I₅	1343	0.0012	0.1314	0.4655	351	0	351	0.03
→⁵I₄	1854	0.0001	0.0234	0.2587	50	0	50	0.00
→⁵F₅	3233	0.1944	0.0923	0.008	14	8	22	0.00

lists the results of calculated electric and magnetic dipole spontaneous emission probabilities, radiative lifetimes, and branching ratios for the main emission transitions of Ho³⁺ in the field of PMN-32PT environment. It can be found from Table 4 that the transition probability A(J′ − J) of the ⁵F₄/⁵S₂→⁵I₈ (547 nm and 540 nm), ⁵F₅→⁵I₈ (648 nm), and ⁵F₄/⁵S₂→⁵I₇ (741 nm and 755 nm) transitions is larger than that of other transitions. It can be predicted that there are three emissions which is consistent of an intense green, a red, and a weak NIR transition in the visible range. In addition, the radiative lifetime of ⁵I₇ energy level were calculated to be 5.45 ms, which is close to that of Gd₃(Al,Ga)₅O₁₂:Ho³⁺/Yb³⁺ (⁵I₇~5.87 ms) crystal [14]. It is longer than that of LiNbO₃:In³⁺/Ho³⁺ (⁵I₇~2.66 ms) [11] and NaGd(MoO₄)₂:Ho³⁺/Tm³⁺ (⁵I₇~4.02 ms) laser crystals [20].

Table 5. The radiative lifetimes of Ho³⁺ in different crystal.

Crystals	⁵I₇	⁵I6	⁵F5	Reference
PMN-PT: Ho3+/Yb3+	5.45	2.51	0.14	This paper
MgWO4: Ho3+	6.18	2.98	0.21	[21]
GdYTaO4: Ho3+	5.33	2.35	0.12	[22]
NaGd(MoO4)2: Ho3+/Tm3+	4.02	2.46	0.15	[20]
LiNbO3: Ho3+/In3+	2.66	1.32	0.09	[11]

lists the radiative lifetime of ⁵I₇, ⁵I₆, and ⁵I₅ of Ho³⁺ in different crystals for comparison. It can be seen that the radiative lifetime of Ho³⁺ in PMN-32PT crystal is shorter than that of MgWO₄:Ho³⁺ crystal [21], but larger than those of other crystals reported in [11,20,22]. The longer radiative lifetime indicates that the energy storage capacity is high. It is in favor of achieving population inversion. Therefore, PMN-32PT crystal is suitable to be used as an up-conversion host material.

3.6. Fluorescence Properties

The up-conversion emission spectra of PMN-32PT:Ho³⁺/Yb³⁺ crystals at 980 nm excitation are shown in Figure 7a. It consists of an intense green emission band at 553 nm, a red band at 663 nm, and a weak IR band at 755 nm. The three emission bands correspond to the ⁵F₄/⁵S₂→⁵I₈, ⁵F₅→⁵I₈, and ⁵F₄/⁵S₂→⁵I₇ transitions, respectively. This is consistent with the calculation results shown in Table 4 (the transition probability of ⁵F₄/⁵S₂→⁵I₈, ⁵F₅→⁵I₈, and ⁵F₄/⁵S₂→⁵I₇ are larger than that of other transitions).

In addition, the fluorescence decay curves for ⁵F₅→⁵I₈ transitions of Ho³⁺ in PMN-32PT at 663 nm with the excitation of 980nm are shown in Figure 7b. The decay curves exhibited multi-exponential behavior, it can be well fitted with dual exponential function, fluorescence lifetime obtained by Equation (15):

$${\tau }_f=\left(B_1{\tau }_1^2+B_2{\tau }_2^2\right)/\left(B_1{\tau }_1+B_2{\tau }_2\right)$$

(15)

where B₁ and B₂ are fitted parameters and τ₁ and τ₂ are measured decay lifetimes, the values of which are shown in

Table 6. The measured B₁, B₂, τ₁, and τ₂ of the fluorescence lifetime for PMN-32PT:Ho³⁺/Yb³⁺.

Transitions	$\mathit{\lambda }$ (nm)	${\mathit{\tau }}_1\left(\mathsf{\mu }\mathbf{s}\right)$	${\mathit{\tau }}_2\left(\mathsf{\mu }\mathbf{s}\right)$	B1	B2	${\mathit{\tau }}_{\mathit{f}}\left(\mathsf{\mu }\mathbf{s}\right)$
5F5→5I8	663	38.323	124.165	2971.481	1574.485	92.568

.

The fluorescence lifetime of ⁵F₅ level were fitting to be 92.568 μs. Then, the quantum efficiency (η) obtained by Equation (16):

$$\eta ={\tau }_f/{\tau }_{rad}$$

(16)

The obtained quantum efficiency η = 66%. Bigger quantum efficiency means more excited ions will deexcitation through laser transition emitting laser. It indicates that PMN-32PT:Ho³⁺/Yb³⁺ crystal is a promising luminescence material.

4. Conclusions

The new multifunctional crystal Ho³⁺/Yb³⁺ co-doped PMN-32PT is successfully grown using the flux method. Judd–Ofelt treatment has been performed on it for the first time. The obtained J–O intensity parameters are Ω₂ = 0.531 × 10⁻²⁰ cm², Ω₄ = 1.738 × 10⁻²⁰ cm², and Ω₆ = 0.530 × 10⁻²⁰ cm². The radiative lifetime of ⁵I₇ is 5.45 ms. The measured fluorescence lifetime of is ⁵F₅→⁵I₈ is 92.568 μs at 980 nm excitation, the obtained quantum efficiency η of which is 66%. In addition, up-conversion luminescence emission bands, including an intense green emission band at 553 nm, a red band at 663 nm, and a weak infra-red band at 755 nm, are generated at the 980 nm excitation. The coercive field Ec of the as grown crystals PMN-32PT:Ho³⁺/Yb³⁺ is 11.86 kV/cm, which is nearly three times higher than that of PMN-32PT. These investigations show that the new multifunctional crystal PMN-32PT:Ho³⁺/Yb³⁺ possesses excellent ferroelectric and luminescence properties. It is a promising laser crystal and it has a potential application in innovative multifunctional devices.