A Tb3+:YAB crystal was grown using a high-temperature solution growth on dipped seeds technique. Polarized ground state absorption and fluorescence spectra from the 5D4 level, as well as a fluorescence decay curves of 5D4 and 5D3 levels, were recorded at room temperature. Radiative properties such as emission probabilities, branching ratios, and radiative lifetime were investigated within the theory of 4f-4f transition intensity in the case of the intermediate configuration interaction.
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Nowadays trivalent terbium doped materials are used not only as Faraday rotators  and green emitting phosphors , but as successful gain media for visible solid-state lasers [3–5]. Up to this time efficient laser operation was obtained only in the family of Tb-doped fluorides. Fluoride crystals possess the large bandgap energy and the weak crystal field strength that make them favorable for the visible laser operation . But the low absorption and stimulated emission cross sections in the visible (∼10−22 cm2) is the main drawback of these crystals. To overcome this problem researches have been tried to find the suitable host among oxide crystals: aluminates , tungstates [7–8], phosphates . Several papers regarding the common luminescent and absorption properties, as well as the crystal field analysis of Tb:YAl3(BO3)4  and TbAl3(BO3)4 [11–12] were reported in the past. However, important properties regarding the applicability of Tb-doped borate crystals as laser materials have been not studied.
This work is devoted to the laser-related spectroscopic properties of Tb3+-doped YAl3(BO3)4 (Tb:YAB) for the visible optical application. The main advantage of oxyorthoborates is the low crystal field depression (CFD) of about 18000 ± 1000 cm-1  among oxide crystals.
Tb:YAB single crystals were grown by dipping seeded high-temperature solution growth method. Based on the earlier results, a complex flux of the K2Mo3O10 – Y2O3/Tb2O3 – B2O3 composition was used to grow such crystals . Growth of Tb:YAB bulk crystal was performed in a resistively heated furnace. The temperature was monitored using a Proterm-100 precision temperature controller with a set of Pt/Pt–Rh thermocouples (S - calibration). The temperature in the working zone of the furnace was maintained with stability of ± 0.1°C. The initial load was prepared by stoichiometric mixtures of the rare earth, aluminium and boron oxides of 99.9% purity. The terbium concentration in the mixture was 35 at.%. K2Mo3O10 was presynthesized by reacting potassium molybdate and molybdenum oxide at 650°C according to the scheme:
Starting chemicals were carefully mixed, grounded, and then the growth charge was loaded into 150-ml platinum crucibles and heated to 1130°C. The resulting melt was homogenized at this temperature within 24 h. Then, using the test seed method, the saturation temperature of the high temperature solution was determined, which was estimated to be 1058°C. Next, the melt was slowly cooled with rate from 1 to 1.5°/day. The growth process was completed at the temperature of 992°C. After that, the grown crystal was removed from the furnace and washed off from flux in a hydrochloric acid.
Identification of Tb:YAB crystal was carried out using ICCD database. Unit cell parameters were calculated from X-ray powder diffraction (XRPD) patterns using UnitCell software  for the hexagonal system (space group R32). XRPD set was collected using a computer-controlled ADP-3 powder diffractometer (Co K-α radiation cource, λ = 1.7903 Å; 2θ range – 6-80°). The composition and homogeneity of Tb:YAB crystal were studied using an analytical scanning electron microscope Leo 1420 VP with an INCA350 energy dispersive spectrometer. The analysis was performed on two adjacent well-developed as-grown faces of trigonal prisms and a polished cut plane perpendicular to the elongation of the crystal. The distribution coefficient of terbium (Kd) was defined as Kd = Ccryst / Cdiss, where Ccryst is the Tb content measured in the crystal and Cdiss is the nominal concentration, i.e. the concentration of Tb in the starting mixture.
For the spectroscopic measurements, the cut and polished sample with thickness of 3 mm and 1 mm were used. Polarized transmission spectra of the Tb:YAB were recorded in a Cary 5000 (VARIAN) spectrophotometer. In the visible and UV regions the spectral bandwidth (SBW) was set to 0.01-0.02 nm, and in the near infrared (NIR) region it was 0.1 nm. The fluorescence spectra were recorded under laser diode excitation at 488 nm. The fluorescence emission was collected on the input slit of MDR 23 monochromator with the SBW of 0.1 nm. The signal was detected with a C5460-01 APD module (Hamamatsu) associated with a SR830 Stanford lock-in amplifier. A gray body light source with a color temperature of 2900 K was used to correct the measured spectra with respect to the detector response, grating efficiency and other optical element`s influence.
The decay curve of the upper 5D4 manifold was registered under pulsed excitation at 485 nm from an optical parametric oscillator LT-2214 (LOTIS TII). The fluorescence emission at 540 nm was imaged onto the entrance slit of a monochromator MDR-12. The signal was detected by a Hamamatsu photodetector C5460 connected to an oscilloscope Tektronix TDS-3052B.
3. Results and discussion
As a result, Tb:YAB single crystal with high optical quality with mass of 2.909 g and size of 15×8×8 mm has been grown. Observed morphology differs from that common for huntite-type borates. The grown crystal shown in Fig. 1 has been faceted by a combination of pinacoid (0001)$,$ two hexagonal prisms $(11\overline 2 0 )$ and $(2\overline 1 \overline 1 0)$, three rhombohedron faces $(10\overline 1 1)$, $(40\overline 4 1)$ and $(02\overline 2 1)$. XRPD studies of Tb-doped YAB crystal confirmed that it exhibits R32 space group (Fig. 2). Unit cell parameters of Tb:YAB single crystals obtained by least-squares refinement are as follows a = b = 9.3154(2) Å, c = 7.2814(5) Å, V = 547.202(3) Å3. The investigations of Tb:YAB composition reveal that the Tb/Y ratio in the crystal obtained almost fully corresponds to the ratio in the starting flux melt and does not change during the growth process. This indicates that the solubility of end-members of the examined solid solution is comparable. The distribution coefficient of terbium is closed to the unit and estimated as 0.95-0.97 for all crystallographic directions studied. The terbium concentration NTb was estimated to be 19.6×1020 cm−3 using the measured volumetric crystal density of 4 g/cm3. The concentration of Mo3+ ions, revealed in the absorption spectrum (Fig. 3) is below then the detection limits of energy dispersive spectrometer (∼0.3-0.5 wt.%).
3.1 Ground state absorption and f-f transition intensities
The polarization dependent ground state absorption spectra of the Tb:YAB were recorded in the 310-500 nm and 1500-2700 nm spectral ranges. The spectra were corrected for the Fresnel losses using the Sellmeier`s coefficients for the YAB crystal . The spectra of absorption cross section σGSA in the UV, visible and NIR spectral ranges are shown in Fig. 4.
The absorption spectra of the Tb:YAB exhibit pronounced polarization anisotropy. In the visible spectral range, the characteristic 7F6 → 5D4 transition has a peak value of 3.2×10−21 cm2 (for σ-polarization) at 484.7 nm that make this crystal suitable for frequency doubled optically pumped semiconductor laser or laser diode pumping in the cyan spectral region. The peak absorption coefficient of 6.8 cm-1 for Tb(35 at.%):YAB is larger than the absorption values of Tb-doped fluoride crystals . But the efficient absorption of pumping radiation requires the accurate tuning of pumping wavelength.
Efficient populating the 5D4 level is possible via the cross-relaxation process5D3 → 5D4 : 7F6 → 7F0 by laser diodes pumping in the region of 370-380 nm. Despite the higher quantum defect, this spectral region possesses broader spectral lines and cross-sections values up to 2×10−21 cm2.
It is well known that Tb3+ ion among the triply ionized rare-earth ions has the lowest energetic position of the excited configuration 4f75d1. The experimental 9D level energy position of about 37157 cm-1 (Fig. 3) is in good agreement with the theoretical value of 37381 cm-1 based on semi-empirical method of P. Dorenbos . The shortwave wing of this absorption band cannot be observed due to fundamental YAB matrix absorption with the cut-off wavelength of about 170 nm . The levels of this configuration can be terminal during excited state absorption (ESA) from the upper laser level 5D4. However, the interconfigurational ESA has the low probability due to the doubly spin-forbidden transitions . Since the band gap energy of YAB crystals is about 7.3 eV , only the f-f ESA transitions can be detrimental for laser action in the visible.
The transition intensities of Tb3+ ions in YAB crystal were determined according to the theory of 4f-4f transition intensities with taking into account the influence of 4fN-15d excited configuration. The case of intermediate configuration interaction (ICI approximation)  gives the best agreement between the calculated results and experimental data. The line strength S of the electric-dipole (ED) transition from initial J manifold to some terminal J′ manifold, in this case, can be evaluated by the formula:
The experimental oscillator strengths fexp were calculated from the measured absorption spectra:
The intensity parameters Ωt as well as the Rt parameters were evaluated by the least-square fitting procedure and are presented in Table 3. The root mean square deviation was 0.06×106.
With obtained data, the radiative lifetime τrad of the 5D4 and the branching ratios β can be evaluated . The radiative lifetime of the 5D0 state is calculated to be 1.83 ms and the calculated transitions probabilities A∑ = AED + AMD, as well as branching ratios, are listed Table 4.
3.2 Radiative properties
Polarized fluorescence spectra of Tb:YAB in the range of 475-700 nm were recorded under excitation at 488 nm and corrected to the spectral response of the luminescence set-up. The observed emission bands are related to the radiative transitions from 5D4 manifold to the lower lying levels. Manifold to manifold branching ratios βJ′J for the transitions from the upper state 5D4 to the lower lying states are found from βJ′J = ∫λIJ′J(λ)dλ ∕ ∑J∫ λIJ′J(λ)dλ, where IJ′J(λ) is the spectral density fluorescence power in arbitrary units. The experimental averaged values of βJ′J over two polarizations with respect to calculated ones are presented in Table 4. It is evident that almost 60% of emitted energy is distributed in the green spectral range.
The fluorescence lifetime of the 5D4 manifold was measured at a wavelength of 545 nm under excitation at 488 nm. The obtained curve (Fig. 6(a)) is single exponential with the lifetime of 1.7 ms which is close to the radiative lifetime of the 5D4 manifold (1.83 ms) calculated from the Judd-Ofelt theory. Comparison of the experimental fluorescence lifetime to the calculated radiative lifetime yields the quantum efficiency of about 93%. Figure 3 shows also the decay curve of TbAl3(BO3)4 (TbAB). The lifetime of 5D4 level is decreased up to 0.9 ms for this crystal and corresponding fluorescence quantum yield η of 49%. The fluorescence quenching is observed with increasing Tb ions concentration due to the energy transfer from Tb3+ ions to Mo3+ ions. For these cases, the decay curves are single exponential. It means, that the energy migration among Tb ions prevails over the Tb3+ → Mo3+ energy transfer. It necessary to utilize other solvents, for example BaO-B2O3 or Li2B4O7 [22,23], during the crystal growth in order to avoid this detrimental process.
Under 355 nm pumping the fluorescence lifetime of the emitting 5D3 level of Tb:YAB was measured at a wavelength of ∼434 nm and the obtained decays curves with the fluorescence lifetimes are presented in Fig. 6(b). The curves have non-exponential character due to cross-relaxation process and the fluorescence lifetime was obtained from τf = ∫tI(t)dt / ∫I(t)dt. The short 5D3 level fluorescence lifetime and decreasing in value from 2.3µs for Tb(35% at.)YAB to 0.3µs for TbAB indicate the efficient cross-relaxation and consequently the population of 5D4 level.
The obtained spectroscopic results allow to conclude, that Tb:YAB crystals are suitable candidates for laser operation in the visible spectral range. In Table 5 we compare obtained in this study spectroscopic parameters of Tb:YAB crystal with ones of other Tb-doped materials.
A high quality single crystal of Tb3+-doped YAl3(BO3)4 was grown by dipping seeded high-temperature solution growth method. The most suitable pumping transition 7F6 → 5D4 has a peak absorption cross section of 3.2×10−21 cm2 (for σ-polarization) at a wavelength of 487.7 nm. However, the spectral region of 370-380 nm with absorption cross section values up to 2×10−21 cm2 can be used for laser diode pumping. The highest stimulated emission cross sections of 3.4×10−21 cm2 (for σ- polarization) was found in the green spectral region at 541 nm. The 4f-4f transition intensities were calculated by applying the theory for a system with intermediate configuration interaction and the radiative lifetime of the upper state 5D4 was derived to be about 1.95 ms. The fluorescence lifetime and quantum efficiency of this level were found to be 1.7 ms and 87%, respectively for terbium ion concentration of 35 at. %. High values of cross-section in the absorption and luminescence with the low value of the crystal field depression make Tb3+-doped YAB crystals suitable for visible laser operation in the green spectral range.
Russian Foundation for Basic Research (18-29-12091mk).
M. Demesh appreciates BRFFR (F20MB-10) for the partial support of this research.
The authors declare no conflicts of interest.
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