New Theoretical Insights into the Crystal-Field Splitting and Transition

Feb 21, 2019 - There has been considerable research interest paid to rare-earth transition-metal-doped Y3Al5O12, which has great potential for applica...
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Functional Inorganic Materials and Devices

New Theoretical Insights into the Crystal-Field Splitting and Transition Mechanism for Nd Doped YAlO 3+

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Meng Ju, Yang Xiao, MingMin Zhong, Weiguo Sun, Xinxin Xia, Yau-yuen Yeung, and Cheng Lu ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.9b00973 • Publication Date (Web): 21 Feb 2019 Downloaded from http://pubs.acs.org on February 22, 2019

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ACS Applied Materials & Interfaces

New Theoretical Insights into the Crystal-Field Splitting and Transition Mechanism for Nd3+ Doped Y3 Al5 O12 Meng Ju,† Yang Xiao,‡,¶ MingMin Zhong,† Weiguo Sun,¶ Xinxin Xia,¶ Yau-yuen Yeung,∗,§ and Cheng Lu∗,‡,∥ †

School of Physical Science and Technology, Southwest University, Chongqing 400715, China Department of Physics, Nanyang Normal University, Nanyang 473061, China ¶ Institute of Atomic and Molecular Physics, Sichuan University, Chengdu 610065, China § Department of Science and Environmental Studies, The Education University of Hong Kong, Tai Po, NT, Hong Kong, China ∥ School of Science, Northwestern Polytechnic University, Xi’an 710072, China ‡

Supporting Information ABSTRACT: There has been considerable research interest paid to rare-earth transition metals doped Y3 Al5 O12 which have great potential for application as laser crystals of new-type laser devices because of their unique optoelectronic or photophysical properties. Here, we present a new research conducted on the structural evolution and crystal field characteristics of rare earth Nd doped Y3 Al5 O12 laser crystal by using the CALYPSO structure search method and our newly developed WEPMD method. A novel cage-like structure with Nd3+ concentration of 4.16% is uncovered, which belongs to the standardized C 222 space group. Our results indicate that the impurity Nd3+ ions are likely to substitute the Y3+ at the central site of the host Y3 Al5 O12 crystal lattice. The laser emission 4 F3/2 → 4

I11/2 occuring at 1077 nm is in accord with that of the experimental data. By introducing the proper correlation crystal field, three

transitions 4 G5/2 → 4 I9/2 , 4 F7/2 → 4 I9/2 and 4 S3/2 → 4 I9/2 are predicted to be good candidates for laser action. These findings can provide powerful guidelines for further experiments of rare-earth doped laser crystals. KEYWORDS: Nd3+ doped Y3 Al5 O12 , electronic structure, crystal field splitting, Stark energy levels, transition mechanism

∎ INTRODUCTION ear-Infrared radiation (NIR) generated by rare-earth (RE) doped crystals can be widely used in a diversity of fields, including industrial, scientific, military and medical applications. 1–4 It is interesting that some night-vision devices using active NIR illumination enable the observation/detection of the living bodies without alerting them. 5 People consider those RE doped crystals, which demonstrate luminescence in the region of NIR, as promising laser materials owing to their narrow band transition, long lifetime and good stability. Recently, Ren et al. 6 have concluded from their study that the RE Neodymium (Nd3+ ) doped nanocrystals can properly serve as the laser emitting sources in the spectrum of NIR. The Nd-doped laser materials are also commonly used in solid-state lasers because of the large number of f-shell transitions within the active Nd3+ ions. Among these laser crystals, Nd-doped Yttrium aluminum garnet (YAG) is the most important laser crystal for generating the 1.06 µm NIR laser emission. Nd-doped YAG (Nd:YAG) possesses the desirable optical, chemical and mechanical properties for use as the standard material in engineering applications. Although many kinds of laser crystals are studied in recent years, 7,8 Nd:YAG crystal is better than other laser materials because of having higher efficiency and being easier to realize many applications. It is worthy noting that Nd:YAG is the best host crystal for the high output, Q-switch and mode-locked ultra short pulse laser systems. 9,10 The laser operation of Nd:YAG crystal was firstly demonstrated by Geusic et al. 11 in 1964. The experimental results indicated that the most intense line in Nd:YAG at room temperature was accurately located at 1.06 µm. Subsequently, Krupke et al. 12 measured the radiative transition intensities of Nd3+ ions doped in YAG crystal within their f-shell configuration. Their results revealed that the

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strong emission line at 1.06 µm was ascribed to the electric dipole (ED) transition 4 F3/2 → 4 I11/2 . In order to explicate the intensities of the emission lines, Hua et al. 13 studied the absorption spectra of Nd:YAG and reported the 95 Stark levels. On the theoretical side, Gruber et al. 14 were able to predict some Stark energy levels which match fairly well with the experimental data. The root mean square (r.m.s.) deviation between theoretical and experimental levels was reporetd to be 18 cm−1 . Further inclusion of the restricted crystal field corrections showed no special effects with any manifolds. Concerning the structure of Nd:YAG crystal, Shoji et al. 15 found from the study of the optical properties of Nd:YAG that the laser characteristics were closely related to the Nd concentrations. By using the popular Czochralski method, Kosti´c et al. 16 obtained good quality Nd:YAG crystals and reported the X-ray diffractions (XRD) at 0.8 wt% of Nd3+ . The recent study for the influence of Nd concentrations on the optical features for Nd:YAG was carried out by Bonnet et al. 17 Although it is concluded that the microstructure of Nd:YAG crystal plays an important role in its crystal field characteristics and optical behaviors, as far as we can see, these have not been investigated in the literatures. Here, we have systematically studied the microstructure, crystal field properties and dipole transition intensities of Nd-doped YAG system. The structure of Nd:YAG crystal is extensively searched and successfully identified by CALYPSO (Crystal structure AnaLYsis by Particle Swarm Optimization) 18–20 method combined with the first-principles calculations. Based on the obtained structures, we have further investigated the crystal field characteristics of Nd3+ in YAG using our developed WEPMD (WellEstablished Parametrization Matrix Diagonalization) method. 21–25 The crystal field correlations chosen for inclusion in the fitting process enable a significantly improved description of the crystal field

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splittings. Finally, 22 Stark levels are predicted for further investigations, and the physical origin of the dipole transitions is analyzed in detail.

∎ COMPUTATIONAL METHODS We used the CALYPSO method 18–20 to search for the crystal structures of Nd:YAG system. CALYPSO can predict the truly lowestenergy structures for many kinds of systems. 26–30 Here, we perform the evolutionary structure predictions for Nd:YAG at one and two formula units per cell. The obtained lowest-energy candidate structures are used to conduct the further structural relaxations and electronic calculations by using the Vienna Ab Initio Simulation Package (VASP) 31–33 which is based on the density functional theory (DFT) with local density approximation (LDA). An onsite Coulomb repulsion U is adopted to describe the strong correlations of f-electrons in Nd atom. 34 As reported by Herbst et al., 35 we set U = 6.50 eV for Nd. The energy cutoff is 500 eV with fine Monkhorst-Pack k meshes to make sure that all the enthalpy calculations will converge to less than 1 meV per atom. The present calculation scheme is accurate enough to perform the full lattice relaxation. The electronic band structures are further checked by Wien2k program 36 with full-potential linearized augmented planewave approach. For [NdO8 ]13− ligand complex of the Nd:YAG crystal lattice, we have constructed the model Hamiltonians to parametrize the Coulomb, magnetic and the interconfiguration interactions for the 4f3 electronic configuration for Nd3+ ions as well as the crystalfield interactions at D2 site symmetry between Nd3+ and its nearbyligands. The atomic energy levels of Nd3+ ions are analyzed by using our developed WEPMD method. 21–25 The details of the method have been described in our previous study 22 thus we have just listed the equations in the Supporting Information with literatures. 37–39 The statevectors are calculated from eigensolution in Equation (A1) can be used to study the transition intensities based on Eqs. (A3-A7).

∎ RESULTS AND DISCUSSION To obtain the ground state structure with nominal concentration of Nd:YAG crystal, we have carried out the structure search of Nd:YAG with chemical stoichiometric ratio of Nd : Y : Al : O = 1 : 23 : 40 : 96 under ambient conditions. The lowest-energy structure is successfully identified and plotted in Fig. 1. The impurity concentration of Nd3+ is approximately 4.16% which is almost comparable to the previous results reported by Ikesue et al. 40 The ground state structure of Nd:YAG is a cage-like structure and belongs to the standardized C 222 space group with an orthorhombic phase. The lattice constants a = b = c = 12.1145 Å are in reasonable agreement with the published data 41 but slightly larger than those of pure YAG crystal. As shown in Fig. 1, the impurity Nd3+ substitutes the Y3+ at the central site and takes the 1a Wyckoff position at (0.5, 0.5, 0.5). This result can be ascribed to the fact that the doped Nd3+ (0.98 Å) possess similar electronic configurations and radius with Y3+ (0.90 Å). The site symmetry of the local structure [NdO8 ]13− is calculated to be D2 . Although there are many O2− surrounding the central Nd3+ , they are found to be locared at two kinds of distances from the Nd3+ ion with the Nd-O bond lengths of 2.397 Åand 2.512 Å. This finding is highly consistent with the results measured by Kosti´c et al. 16 The coordinates of all atoms for the ground state Nd:YAG are listed in the Supporting Information together with a great many metastable structures obtained. According to the relative energies, the first four isomers are shown in Fig. S1 (See Supporting Information) and the corresponding structural

parameters are summarized in Table S1. It should be noted that the space groups of isomers (a) and (d) are both P1 , which differ from the other structures. Although the lattice constants of these structures are very close, the volumes of unit-cell for the isomers are almost 0.1% larger than that of ground state Nd:YAG.

Figure 1. Structure of the optimized cage-like Nd:YAG. The green, blue, yellow and red spheres represent Nd, Y, Al and O atoms, there are two kinds of Nd-O bond lengths 2.397 and 2.512 Å, respectively.

The X-ray diffraction (XRD) analysis is a widely accepted way to investigate the atomic and molecular structures of crystals. For Nd:YAG crystal, many XRD measurements have been published in the literatures 16,40,41 but there are inconsistencies concerning both the locations of the peaks and the corresponding intensities. Therefore, we simulate the XRD patterns of Nd:YAG based on the obtained ground state structure. The theoretical results together with avaliable experimental data are shown in Fig. 2. As clearly shwon in Fig. 2 the overall distribution of the simulated peaks agrees very well with those reported in Ref. 16 This result demonstrates the validity of the Nd:YAG structure as well as the high accuracy of the calculation. Moreover, the simulated relative intensities of these peaks can also be comparable to the results measured by Zhang et al. 41 excepting a peak at 2θ of 65.8○ (See Fig. S2). This discrepancy may result from the low concentrations of Nd3+ ions in YAG. In Fig. 3, we have presented the electronic band structure of the ground state Nd:YAG using the modified Becke and Johnson (BJ) method 42 as implemented in the reliable Wien2k program. 36 The Fermi level is represented by the horizontal dotted line. The Fig. 3 clearly reveals that the Nd:YAG possesses a direct band gap of Eg = 6.51 eV. This value is slightly smaller than the experimentally measured band gap of pure YAG (6.73 eV). 43 However, the overall

Figure 2. Simulated X-ray diffraction pattern of Nd:YAG compared with experimental data.

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ACS Applied Materials & Interfaces band structure and sequence of high symmetry points of Nd:YAG are quite different with those of YAG. To further investigate the contributions of electronic energy bands, we display the partial density of states (DOS) for each atom of Nd:YAG in Figure S3. The DOS show that the low valence bands are mainly consisted of the occupied O p and Al p states. The dominant contributors of the high conduction bands above 8 eV are Al s and Y d state, while the contributions of the Nd d states dominate the bands at 7.81 eV. It shoud be noted that the energy bands at 6.51 eV mostly come from Nd d states, indicating that the slight drop of the energy gap is resulted from the doping of Nd3+ ions.

Figure 3. The calculated band structure of Nd:YAG.

Although crystal field Stark levels for Nd3+ in YAG crystal have already been examined quite thoroughly in some previous studies, 10,13,14 yet the energy levels of some multiplet manifolds are not clearly observed and the theoretical predictions of the crystal field splittings are still unsatisfactory. Therefore, we have carried out atomic energy calculations of the Nd3+ ions by using our developed WEPMD method. All observed 149 Stark levels are analyzed and used to perform the least-squares fit process. The initial values of the CFPs (Crystal Field Parameters) are obtained through the ab initio calculations by using the Novák’s novel method 44,45 and the Wien2k program. 36 Firstly, the free-ion parameters are fitted with values of CFPs fixed at those of the ab initio calculations and the results are reported in Table 1 (Fit 1). The root mean square (r.m.s.) deviation between theoretical and experimental levels of Fit 1 is calculated to be 24.00 cm−1 , suggesting that the first-principles calculations of CFPs is fairly satisfactory but the CFPs may still not be very accurate for describing the crystal field splittings of Nd3+ ions in YAG. Subsequently, we set the CFPs freely fitting during the least-squares fit process. The fit of the CFPs leads to an r.m.s. deviation of 18.38 cm−1 , as summarized in Table 1 (Fit 2). This result is in reasonable agreement with the previous study (18.40 cm−1 ) reported by Gruber et al. 14 However, our present set of CFPs is very different from theirs due to the use of a very different set of staring values and it cannot be transformed to theirs through one of the six equivalent coordinates frames asociated the D2 site symmetry. Besides, they had not included the notorious level 2 G(2)9/2 (169) at 47200 cm−1 in their spectroscopic studies, probably due to the relatively large discrepancy of the Stark levels above 40000 cm−1 . In order to further improve the r.m.s. deviation between observed and calculated levels, Gruber et al. 14 introduced the SCCF (Spin Correlated Crystal Field) interactions in their model. The result with the inclusion of SCCF terms was reported to be 18.30 cm−1 , which was very close to those obtained with no SCCF. It is evidenced that the contribution of SCCF are not suitable for an improved description of the crystal field interactions of Nd3+ ion in YAG. To deal

with this problem, we introduced the OCCF (orthogonal correlation crystal field) operators within the corresponding CF Hamiltonian in our theoretical model. The OCCF operators can be represented by: 46,47 HOCCF = ΣGki,q gki,q . Here, gki,q represent the operators of type i, component q and rank k while Gki,q are the corresponding parameters. It should be pointed out that the types i = 2, 10A and 10B are widely acknowledged and well suited to describe the crystalfield splittings of Nd3+ ions in many host crystals. 22,46,47 Finally, a new set of CFPs together with OCCF parameters are determined and the results are listed in Table 1 (Fit 3). It is worth noting that the fitted values of parameters in Fit 3 lead to an r.m.s. deviation of 14.00 cm−1 , which is much smaller than the previous results. Table S2 shows the calculated 171 Stark levels with 38 different J-multiplets, including 4 I J , 4 F J , 2 H(2) J , 4 S J , 4 G J , 2 G J , 2 G(1) J , 2 K J , 2 D(1) J , 2 P J , 4 D J , 2 I J , 2 L J , 2 H(1) J , 2 D(2) J , 2 G(2) J . Previous results available in the literature 10,13,14 are also listed for comparison. From Table S2, we can see that the Stark levels of the ground 4 I9/2 are calculated to be -12, 130, 197, 311 and 850 cm−1 . This agree fairly well with the measured values reported by Kaminskii et al. 10 and Hua et al. 13 but different from those calculated by Gruber et al. 14 For the excited states, we note the anomalous splitting of 4 F5/2 and 2 H(2)9/2 multiplets, as reflected by the large deviation reported by Gruber et al. 14 In our simulation, the corresponding Stark levels are 12354, 12437, 12500, 12590, 12640, 12646, 12827 and 12844 cm−1 . Hence, our calculated values of these Stark levels are in reasonable agreement with the measured data, demonstrating the validity of the OCCF correlation as well as the reliability of the present calculations. Furthermore, we also predict 22 Stark levels with detailed values that have not been observed by experiments previously. It is expected that our predicted results could provide useful information to assist further experimental investigation. It is well-known that the Nd:YAG laser operating at 1.06 µm is widely used in many different applications. Under diode pumping at 885 nm, 48 this laser is characterized by the emission from 4 F3/2 → 4 I11/2 . While a number of studies are reported on the practical applications of Nd:YAG, we are motived to exploit its luminescence properties in the visible spectral and near infrared regions. In the present work, we employ the Judd-Ofelt (J-O) theory to calculate the ED transition intensities for Nd:YAG. The J-O theory is independently proposed by B. R. Judd 49 and G. S. Ofelt 50 in 1962, which has been successful in describing the transition intensities for the f-shells of rare-earth ions. From Ref., 12 three J-O intensity parameters for Nd:YAG crystal have been experimentally determined as Ω2 = 0.2×10−20 cm2 , Ω4 = 2.7×10−20 cm2 and Ω6 = 5.0×10−20 cm2 . For the calculation of transition intensities, we use the refractive index of 1.81 which has been reported by Buryy et al. 51 Detailed information of the ED calculations and equations are given in the Supporting Information. The transition channels within the first 11 excited states and the transition properties are summarized in Table S3 which also enlists the related experimental dataas available in the literature. For references, the detailed statevectors of the first 11 excited states are also listed in Table S4. The Table S3 reveals that the wavelength of the most extensively used laser emission 4 F3/2 → 4 I11/2 is calculated to be 1077 nm, which is very close to the value (1073 nm) observed by Deserno et al. 52 The transition 4 F3/2 → 4 I13/2 occurring at 1367 nm was also previously studied by many researchers. 12,48 The simulated radiative lifetime of 4 F3/2 level is 274 µs. This is in excellent agreement with the measured fluorescence lifetimes (259 and 250 ± 25 µs). 12,53 Moreover, some promising ED transitions are predicted in our calculations. The first 3 excited states 4 I11/2 , 4 I13/2 and 4 I15/2 possess much larger radiative lifetimes than those of other states. This result suggests that the favorable population inversions may be easily

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ACS Applied Materials & Interfaces Table 1. The free-ion and CFPs for Nd3+ in YAG (cm−1 ). Values in brackets are fixed during the fitting process.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Parameters Fit 1 Error Fit 2 Error Fit 3 Error Other 14 Error Other 14 E AV E 24125 1 24120 1 24121 1 24117 40 F2 71193 18 71187 18 71197 17 71090 45 F4 51316 60 50992 54 51032 56 50917 65 F6 34147 32 34204 18 34254 28 34173 45 ζ 875 0.8 872 0.6 872 0.6 875 7.0 α 21.2 0.1 21.0 0.1 21.0 0.1 20.8 2.1 β -661 4 -647 3 -643 3 -651 16 γ 1801 13 1823 7 1811 10 1868 24 T2 183 6 206 6.5 208 5.8 231 27 T3 46 0.6 47 0.6 47 0.7 46 9.0 T4 30 1.8 43 1.2 41 1.4 39 11 T6 -251 4.5 -247 4.3 -238 4.2 -236 14 T7 232 4.9 252 4.8 239 4.5 237 20 T8 174 4.8 172 6.0 185 5.5 174 23 M0 3.14 0.1 2.62 0.1 2.80 0.1 2.58 1.3 P2 347 18 354 15 389 14 275 35 B02 [-410] -398 5 -394 5 -690 23 -702 B22 [161] 260 4 251 4 -158 21 -176 B04 [-2956] -2832 12 -2730 11 -343 39 -409 2 B4 [241] 554 12 515 15 -2401 29 -2262 B44 [1178] 1112 9 1116 9 -1097 33 -1072 B06 [1190] 943 11 1008 12 2315 44 2174 B26 [-373] -352 12 -313 11 922 36 974 B46 [1695] 1630 7 1618 5 -1124 35 -1069 B66 [-167] -166 10 -147 6 836 38 917 G02 -206 33 G04 932 28 G06 61 27 N exp 149 149 149 148 41 Np 16 25 28 25 r.m.s. 24.00 18.38 14.00 18.4 N exp refers to the numbers of experimental energy levels used in the fit. N p refers to the total number of freely-varying parameters. Remark: there are fixed ratios between M j and Pk parameters:M2 = 0.56M0 ; M4 = 0.38M0 ; P4 = 0.75P2 ; P6 = 0.5P2 .

achieved in these states. We note that the transition 4 F5/2 → 4 I9/2 is exactly located at 822 nm, which is comparable to the experimental measurements. 48,54 The radiative decay rate of this transition is the largest among the transitions from 4 F5/2 . In the visible spectral region, the strong emission lines are ascribed to the transitions 4 G5/2 → 4 I9/2 and 4 G5/2 → 4 I11/2 . The wavelengths of the two transitions are equal to 597 and 672 nm, respectively. It should be pointed out that the three transitions 4 G5/2 → 4 I9/2 , 4 F7/2 → 4 I9/2 and 4 S3/2 → 4 I9/2 may be good candidates for laser action due to their large branching ratios. Meanshile, the magnetic dipole (MD) contributions of the corresponding transitions are also calculated. Our result suggests that the intensities of magnetic dipole emission lines are overall much weaker than those of ED transitions. The transition 2 H(2)9/2 → 4 I9/2 occurring at 811 nm possesses the A MD of 6.9 s−1 . This transition may be used for probing the magnetic properties of light-matter interactions.

∎ CONCLUSION

C 222 space group symmetry is identified. Calculations show the impurity Nd3+ ion substitutes the Y3+ at the central site of the host crystal lattice. We obtain an entirely new set of CFPs with OCCF parameters that could povide a much enhanced description of the crystal field splittings of Nd3+ ions in YAG. 149 Stark levels are confirmed and compared with the previous results, and 22 new Stark levels are reported with detailed values. Three promising transitions 4 G5/2 → 4 I9/2 , 4 F7/2 → 4 I9/2 and 4 S3/2 → 4 I9/2 are found to be good candidates for laser action. These results will open a new route to develop and design the next-generation laser devices.

∎ ASSOCIATED CONTENT Supporting Information Metastable structures, lattice parameters and relative energies of Nd:YAG, experimental and calculated Stark energy levels and transition properties of Nd:YAG.

In summary, we demonstrate the structural evolutions and energy level transitions of Nd:YAG laser crystal by CALYPSO and WEPMD methods. A novel cage-like structure of Nd:YAG with

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ACS Applied Materials & Interfaces

∎ AUTHOR INFORMATION Corresponding Authors

*E-mail: [email protected] (Y.Y.Y) *E-mail: [email protected] (C.L) Notes The authors declare no competing financial interest.

∎ ACKNOWLEDGMENTS The authors acknowledge the funding supported by Fundamental Research Funds for the Central Universities (SWU118055), National Natural Science Foundation of China (Nos. U1804121 and 11504301), and Grants of the Faculty of Liberal Arts and Social Sciences, EdUHK.

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