Deciphering the Microstructure and Energy-Level Splitting of Tm3+-

Article Cite This: Inorg. Chem. XXXX, XXX, XXX−XXX

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Deciphering the Microstructure and Energy-Level Splitting of Tm3+-Doped Yttrium Aluminum Garnet Meng Ju,† MingMin Zhong,† Cheng Lu,*,‡,¶ and Yau-yuen Yeung*,§ †

School of Physical Science and Technology, Southwest University, Chongqing 400715, China Department of Physics, Nanyang Normal University, Nanyang 473061, China ¶ Department of Physics and High Pressure Science and Engineering Center, University of Nevada, Las Vegas, Nevada 89154, United States § Department of Science and Environmental Studies, The Education University of Hong Kong, Tai Po, NT, Hong Kong, China Downloaded via WASHINGTON UNIV on September 15, 2018 at 01:30:44 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.

‡

S Supporting Information *

ABSTRACT: Thulium-doped yttrium aluminum garnet (Tm:YAG) is an important solid-state laser crystal. The energy-level splitting within it is still an unresolved problem. Here, we perform a theoretical study on the microstructure of Tm3+-doped YAG using the CALYPSO structure search method in conjunction with first-principles calculations. The calculated results show that the 4.16% doping concentration of Tm3+ impurity causes an obvious structural distortion of YAG crystal, forming an orthorhombic phase in C222 symmetry. On the basis of our developed WEPMD method, we obtain a new and complete set of free-ion and crystal field parameters by a good fit (with proper irreducible representations) to 69 observed energy levels and determine the exact energy-level splitting of Tm3+ in YAG. The calculated Stark levels and electric dipole transitions are in excellent agreement with the measured data and similar theoretical calculations. Some promising emission lines between 3F3, 3F2, 1D2, and 1I6 states are presented. These findings offer fundamental insights and practical tools for further exploration of the structural and electronic properties of other transition-metal-doped YAG crystal. Since the first pulsed Tm:YAG laser system was realized by Kane et al.15 in 1990, the spectral characteristics of Tm:YAG have been extensively studied by many researchers. Stoneman et al.16 measured the laser emissions of Tm:YAG at room temperature and found that the Tm3+ 3F4 → 3H6 transition could be tuned continuously in the region from 1.87 to 2.16 μm. Detailed study of the spectroscopic properties for Tm:YAG was performed by Lupei et al.17 Their results identified the Stark levels of Tm3+ including 3F4, 3H4, 3F3, and 3F2 multiplets. Subsequently, Tiseanu et al.18 proposed an improved energylevel diagram for Tm:YAG by analyzing the experimental absorption spectra. Almost 70 of total 91 levels were determined by their experiments, while the others were still not clear. For the crystal structure of Tm:YAG, Seze et al.19 discussed the external magnetic field orientation in a site local frame and found that the Tm dopant ion would substitute for Y3+ of D2 site symmetry. To study the phase compositions of Tm:YAG, Zhang et al.20 reported the X-ray diffractions (XRD) with different doping concentration of Tm3+ (6%, 30%, 50%, 100%). Their results indicated that the maximum output

1. INTRODUCTION Rare-earth (RE)-doped host crystals play important roles as emitting sources in various laser systems.1−3 The extension of the use of RE-doped laser materials has been actively pursued, such as in remote sensing,4 medical surgery,5 fiber amplifiers,6 and energy-efficient lighting.7 A recent study reveals that the thulium-doped crystals may be excellent candidates for broadband quantum storages in a solid-state medium,8 thus bringing much attention to the thulium ions (Tm3+). Indeed, the Tm3+ ion (4f12 configuration) is widely recongnized as one of the most promising RE ions, because a large number of radiative transitions can be easily obtained within its 4f shell electrons. The well-known emission transition 3F4 → 3H6 at ∼2 μm of Tm3+ serves as a key component of solid-state laser technology.9 Y3Al5O12 (YAG) is one of the most important fluorescence laser materials, which possesses good optical, thermal, and mechanical properties.10 After being doped with appropriate ions (transition-metal or RE ions), YAG can be used as host material in white-light emitting diodes (WLEDs) and optical temperature sensors.11−13 Tm3+, as active laser ions, can be easily doped into YAG, yielding the Tm:YAG (Tm3+-doped YAG) lasers. According to the literature,14 Tm:YAG is also an active laser medium that operates between 1.89 and 2.18 μm. © XXXX American Chemical Society

Received: July 17, 2018

A

DOI: 10.1021/acs.inorgchem.8b02009 Inorg. Chem. XXXX, XXX, XXX−XXX

Article

Inorganic Chemistry

where Bkq are the crystal-field parameters (CFPs) and can be determined by the least-squares fit to the experimental energy levels.46 The Ckq are the normalized spherical-tensor operators.

power could be obtained at the doping concentration of 6%. However, Stoppler et al.21 indicated that the doping concentration of Tm:YAG should be in the range of 2%−4%. To the best of our knowledge, there are no reports in the literature describing the electronic structure, crystal-field characterizations, and physical origin of the dipole transitions for Tm3+-doped YAG. In this paper, we performed a systematic study on the microstructure and Stark energy-level splitting of Tm:YAG. The extensive structure search is performed by using the Crystal structure AnaLYsis by Particle Swarm Optimization (CALYPSO)22−28 method combined with first-principles calculations. The Stark energy-level splittings as well as the dipole transition intensities are determined by our developed Well-Established Parametrization Matrix Diagonalization (WEPMD) method.29−34 The outline of the paper is as follows. In Section 2, we describe the details of the calculations and theoretical methodology. The results and discussions are presented in Section 3. Conclusions are summarized in Section 4.

3. RESULTS AND DISCUSSIONS 3.1. Electronic Structure. First, the ground-state structure of YAG is carefully examined via the CALYPSO method under ambient conditions. With the knowledge of its chemical composition (Y/Al/O = 3:5:12), the structure searches can quickly identify the well-known cubic garnet phase corresponding to the standardized Ia3̅d (No. 230) space group. Our calculation reveals equilibrium lattice constants (a = b = c = 12.107 Å), which differ from the measured ones by less than 0.7%.47 This result provides great support for the reliability of the present structure searches. Second, we perform evolutionary supercell structure searches up to 160 atoms to realize nominal concentration of Tm3+ ions in YAG.48 The input chemical composition ratio used in the calculation is Tm/Y/Al/O = 1:23:40:96. Finally, the lowest-energy structure of Tm:YAG with the impurity concentration of 4.16% is obtained and plotted in Figure 1. From Figure 1, we can clearly see that the

2. COMPUTATIONAL DETAILS The crystal structure prediction of Tm:YAG system is performed by using the CALYPSO structure searching method.22−28 CALYPSO is an unbiased global minimum structure search method that has been successfully applied to the prediction of various known systems.35,36 To obtain the most stable structure of Tm:YAG system, we conduct the evolutionary structure predictions with 160 atoms per simulation cell under ambient pressure. The details of the structure prediction have been described in refs 22−28. Subsequently, the further geometric optimization of lowest-energy candidate structures are performed by using the density functional theory (DFT), as implemented in the Vienna Ab Initio Simulation Package (VASP).37−39 For describing the 4f electrons of Tm atoms in this system, we adopt the local density approximation (LDA) with an onsite Coulomb repulsion U calculation scheme.40 The parameter value of U added on Tm is equal to 7.30 eV, which has been precisely measured by Herbst et al.41 The accuracy of the present DFT calculations is sufficient and wellsuited to perform the full lattice relaxation. To study the atomic energy levels of (TmO8)13− ligand complex in Tm:YAG, we constructed the parametric Hamiltonian based on our developed WEPMD method.29−34 Essential higher-order interactions are included to reproduce the energy-level schemes for the RE3+ ions. This approach has been benchmarked on many impurity lanthanide ions in various crystal lattices.29−33 For Tm3+ ion (a 4f12 configuration), the model Hamiltonian can be calculated by using the following equation:42−44 Hf = EAVE +

∑

F kfk + ζ4f A SO + αL(L + 1) + βG(G2)

Figure 1. Coordination structures of the optimized YAG and Tm:YAG. The red, blue, gray, and green spheres represent O, Al, Y, and Tm atoms, respectively.

k = 2,4,6

+ γG(R 7) +

∑ j = 0,2,4

M jmj +

∑

P kpk

k = 2,4,6

(1)

Tm3+ impurity ion causes a significant structural distortion to the structure of YAG. The doped Tm3+ tends to substitute the Y3+ sites in the host crystal, because the mentioned two ions have the similar radius and electronic configurations. This result is similar to that of Nd:YAG system.49 The calculated and experimental measured47 lattice constants for the pure and the Tm-doped YAG crystals are summarized in Table S1 (see Supporting Information). Interestingly, we find that the local configuration of [TmO8]13− is similar to that of [YO8]13−, while the structural distortion is distinctly observed. The Tm3+ ion possesses the site symmetry of D2 and is surrounded by the nearest eight O2− ligands. There are equivalent two groups of the bond lengths (2.285 and 2.445 Å), which is in good

The detailed information of these terms has been described in our previous studies.30,33 The state vectors obtained from the eigensolution of Eqn 1 will be used to calculate various physical properties of transition intensities using eqs A1−A5 in Supporting Information. Considering the ligand complex of Tm3+ in YAG crystal, the CF interaction operator HCF should be introduced. According to Wybourne normalization, the crystal field (CF) Hamiltonian having D2 symmetry is of the form:45 HCF = B20 C 20 + B22 (C 22 + C 2−2) + B40C40 + B42 (C42 + C4−2) + B44 (C44 + C4−4) + B60C60 + B62 (C62 + C6−2) + B64 (C64 + C6−4) + B66(C66 + C6−6)

(2) B


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Inorganic Chemistry

the reliable Wien2k program54 was used to perform the ab initio calculations of the electronic properties of YAG, we obtained Eg = 4.60 and 6.37 eV for the conventional Perdew−Burke− Ernzerhof (PBE) and the modified Becke and Johnson (BJ) methods,39,55 respectively. The latter (shown in Figure S2) is very close to the observed data. Furthermore, the sequence of high symmetry points (Γ, H, N, P, Γ, and N) is in excellent agreement with ref 52. For Tm:YAG crystal, the overall electronic band structure is obviously different from that of YAG. As shown in Figure 3b, there is a direct band gap at Γ point for Tm:YAG. The value of this gap is calculated to be 2.31 eV, owing to the presence of the central conduction band from 2.31 to 2.51 eV. The central conduction band is very flat and apart from the high conduction band above 4.65 eV. In Figure 3d, it can be seen from the total and partial DOS that the central occupied states are dominated by the f states. The valence band below Fermi level consists of p states. The high conduction band is mainly formed by d states, while the s states only show weak contributions. Thus, we can conclude that the presence of the central conduction band is caused by the impurity Tm3+ ions. 3.2. Energy-Level Splitting. It is well-known that the energy levels of rare-earth ions will split into many Stark levels after doping in the host crystals. For Tm3+ ions in YAG crystal, the energy-levels diagram and splitting process have been investigated by many previous studies.17,18,56,57 However, the rootmean-square (rms) deviation between the theoretical and experimental energy levels is relatively largem and the CFPs are also needed to be improved. Here, the total 91 Stark levels (including 13 different J-multiplets, namely, 3H6,5,4, 3F4,3,2, 1G4, 1 D2, 1I6, 3P0,1,2, and 1S0) are analyzed based on Eqns 1 and (2) through the fitting process of the CFPs. It is worth noting that all available experimentally observed energy levels18,56 are employed in the least-squares calculations. By using the Novák’s novel method58−60 in conjunction with the Wien2k program,54 we perform the ab initio calculation to obtain the initial values of CFPs Tm3+ ions in YAG. These CFPs are fixed during the fitting process, while the free-ion parameters are set for fitting (Fit 1). It can be seen from Table 1 that the results based on Fit 1 are subject to refinement as reflected by the large rms deviation 42.63 cm−1. There are two likely sources of uncertainties in the present ab initio results, namely, (1) inaccuracies in the ionic positions because of the local distortion induced by the doping of Tm3+ in the YAG host lattice and (2) crystal field induced configuration interaction.61 We can account for the latter effect by incorporating the correlation crystal field,62 but this will substantially increase the number of unknown parameters. To improve the accuracy of the simulation, we will first set all crystal field parameters as freely adjustable for the subsequent fitting process. The best-fitted parameters (named Fit 2) as well as the results in the literature18,56 are summarized in Table 1. From Table 1, we can see that the calculated and fitted values of CFPs are closely similar to those reported by Tiseanu et al.18 and fairly consistent with the results obtained by Gruber et al.56 For work in both refs 18 and 56 it is noted that there were 21 freely varying parameters (nine crystal field parameters and centroids of the 12 J-multiplets) used in their fits. Their free-ion parameters were not explicitly determined even though some initial values were taken from other sources. They employed two more free parameters than our Fit 2 in which the rms deviation (8.51 cm−1) is found to be lower than theirs and significantly reduced compared to that of Fit 1, demonstrating that the parameters

agreement with the experimental data reported by Hayes et al.50 To clarify the global minimum structure of the Tm:YAG, we simulated the X-ray diffraction (XRD) patterns and compared the results to the experimental data, as illustrated qualitatively in Figure 2. In the region of 2θ from 20° to

Figure 2. Simulated XRD pattern of (a) YAG and (b) Tm:YAG compared with experimental data.

70°, the agreement between the simulated spectra and the observed ones is reasonably good,20,51 which demonstrates the true structure of Tm:YAG and the accuracy of the present simulation. Table S2 lists the structural parameters of the optimized YAG and Tm:YAG. The gound-state structure of Tm:YAG is characterized by orthorhombic phase (C222) with lattice constants a = b = 12.102 Å and c = 12.097 Å. Tm atom can occupy the local dodecahedral (D2) sites in the crystal lattice and take the Wyckoff 1a position (0, 0, 0.5). Moreover, we are also able to identify a large number of metastable structures for Tm:YAG. According to the energies from low to high, the first four isomers are schematically shown in Figure S1 (see Supporting Information). Table S2 summarizes the lattice constants, unit-cell volume, and the relative energies of these metastable structures. Although the isomer (a) possesses the same C222 space group as the ground-state Tm:YAG, an obvious structural distortion can be evidenced due to the different substitution sites of Tm3+ impurity ions. It is found that the isomers (b) and (c) exhibit the P1 space group and possess relatively large lattice constants. When the Tm3+ ions occupy the point sites of the crystal lattice, we obtained the isomer (d) which is 0.32 eV higher than the lowest-energy structure of Tm:YAG. To gain more insight into the electronic properties of the pure YAG and Tm:YAG crystals, we computed their electronic band structures and densities of states (DOS). The results are shown in Figure 3. Our calculation indicates that the band gap Eg of YAG, directly at Γ point, is equal to 4.20 eV. The value of band gap is similar to the result (4.71 eV) obtained by Xu et al.,52 which is almost two-thirds of the experimentally measured values (6.73 eV).53 This can be ascribed to the fact that the standardized LDA calculations generally underestimated the values of electronic band gaps. However, when C


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Inorganic Chemistry

Figure 3. Calculated band structures and total and partial DOS of YAG and Tm:YAG. The Fermi level is indicated by the dotted line.

Table 1. Free-Ion and Crystal-Field Parameters for Tm3+ in YAGa paramb

fit 1

error

fit 2

error

EAVE F2 F4 F6 ζ α β γ M0 P2 B02 B22 B04 B24 B44 B06 B26 B46 B66 Nexpe Npf rms

18 092 101 724 73 116 53 911 2627 13.1 −546 [993] 4.79 724 [726] [−46] [−185] [−1060] [−479] [−968] [−415] [335] [−295] 69 9 42.63

2 26 89 185 1.0 0.3 13

18 094 101 538 72 735 53 354 2626 13.4 −530 1168 4.5 762 615 37 5.2 −1438 −703 −1224 −304 432 −374 69 19 8.51

1 36 89 127 0.2 0.1 4 32 0.1 15 3 3 7 5 6 11 7 6 5

0.4 44

otherc

otherd

603 39 −59 −1441 −707 −1181 −302 448 −360 69 21 9.00

[103 886] [77 024] [57 448] [2628] [14.7] [−632] [0] [0] [0] 474 47 −213 −1571 −824 −984 −310 591 −193 66 21 11.00

a All parameter values are expressed in units of inverse centimeters. Values in brackets are fixed in the fitting, and their values for the crystal field parameters were obtained from the present ab initio calculations. bRemark: there are fixed ratios between Mj and Pk parameters: M2 = 0.56M0; M4 = 0.38M0; P4 = 0.75P2; P6 = 0.5P2. cReference 18, in which nine crystal field parameters and the centroids of the 12 J-multiplets were set to vary freely. d Reference 56, in which nine crystal field parameters and the centroids of the 12 J-multiplets were set to vary freely, and so they implicitly modified the values of those free-ion parameters. eNexp refers to the numbers of experimental energy levels used in the fit. fNp refers to the total number of freely varying parameters.

need to incorporate the correlation crystal field, as it can yield rather little improvement of the fit. Of course, Gruber et al.’s experimental results should be more reliable, as they have

of Fit 2 are well-suited to describe the Stark energy-level splitting for Tm3+ ions in YAG. Besides, the irreducible representations of all levels are determined. Hence, there is no D


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Inorganic Chemistry Table 2. Calculated Stark Energy Levelsa of Tm3+ in YAGb present work 2S+1 3

H6

3

F4

3

H5

3

H4

3

F3

LJ state

Γn

Eobs18

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

2 1 4 3 2 1 4 1 3 2 4 3 1 1 3 2 4 1 2 1 3 4 4 3 1 3 2 4 2 3 1 2 4 1 2 2 4 3 1 4 1 3 2 4 2 4

0 27 216 240 247 300 450 588 610 650 690

5555 5764 5832 5901 6042 6111 6170 6199 8340 8345 8516 8530 8556 8700 8750 8773

12607 12644 12732 12747 12824 13036 13112 13152 14599 14659 14666 14679

present work

Ecalc

ΔE

other56

other18

−6 15 235 240 247 310 462 589 619 646 691 795 811 5545 5762 5830 5901 6049 6111 6166 6179 6184 8342 8343 8504 8520 8551 8573 8683 8751 8760 8902 8903 12597 12655 12732 12748 12840 12975 13043 13119 13162 14609 14659 14664 14683

−6 −12 19 0 0 10 12 1 9 −4 1

−3 24 215 225 262 253 518 610 650 684 698 751 765 5536 5757 5810 5912 6040 6111 6164 6228 6243 8343 8353 8507 8517 8524 8558 8712 8774 8804 8873 8885 12614 12677 12749 12818 12832 12954 13070 13127 13159 14643 14649 14661 14683

−10 12 235 237 250 304 461 589 614 647 688 781 798 5545 5763 5827 5906 6048 6119 6175 6175 6190 8345 8347 8510 8525 8552 8577 8687 8761 8766 8900 8901 12591 12652 12733 12751 12833 12973 13038 13113 13149 14613 14658 14663 14687

−10 −2 −2 0 7 0 −4 −15 2 −2 −12 −10 −5 −17 1 −13

−10 11 0 1 16 7 7 10 10 0 −2 4

2S+1

3

F2

1

G4

1

D2

1

I6

3

P0 I6

1

3

P1

3

P2

1

S0

LJ state

Γn

Eobs18

Ecalc

ΔE

other56

other18

47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91

3 1 3 3 1 4 2 1 1 2 3 4 1 2 4 3 1 1 3 2 4 1 1 4 3 4 4 3 1 1 2 1 2 1 3 1 3 4 2 3 4 1 1 2 1

14706 14720

14690 14713 14751 15204 15248 15262 15408 15416 20819 21205 21231 21372 21526 21677 21746 21761 21773 27868 27898 28001 28040 28063 34356 34367 34418 34471 34530 34728 34741 34934 34935 35234 35239 35372 35386 35408 36228 36398 36420 37937 38064 38085 38404 38438 76089

−16 −7

14710 14730 14737 15246 15260 15302 15433 15440 20815 21191 21225 21387 21513 21681 21767 21824 21864 27914 27940 28027 28048 28067 34380 34424 34446 34449 34522 34679 34726 35034 35034 35204 35227 35372 35387 35399 36254 36381 36408 37935 38000 38088 38402 38409 79064

14690 14716 14748 15202 15245 15252 15397 15408 20818 21199 21230 21373 21516 21680 21748 21764 21764 27876 27896 28010 28034 28061 34363 34371 34418 34464 34524 34717 34735 34938 34939 35220 35226 35372 35385 36402 36229 36395 36419 37943 38063 38090 38408 38430

15190 15246 15263

20806 21212 21228 21381 21530 21680 21735 21775 27868 27877 28016 28042 28070 34370 34420 34520 34746

35372 35388 36231 36390 37933 38065 38097 38400

14 2 −1

13 −7 3 −9 −4 −3 11 −2 0 21 −15 −2 −7 −3 −2 10 −5

0 2 −3 8 4 −1 −12 4

All in inverse centimeters. bΓn = irreducible representation.

a

previously reported in the literature.18,56 It can be clearly seen from Table 2 that the ground-state energy levels are included in 3H6 multiplets. The assignment of ground-state levels is calculated to be −6, 15, 235, 240, 247, 310, 462, 589, 619, 646, 691, 795, and 811 cm−1. These results are in good agreement with the observed values, especially for 3H6(4) and 3H6(5). The sequence of the excited states in the present calculation also follows the same scheme as the results reported by previous studies. Furthermore, the irreducible representations (Γn) of the corresponding Stark energy levels are also calculated.

properly taken into account the irreducible representation labels of every observed crystal field level, avoding the pitfall for more fits of being trapped in the local minima due to the lowsymmetry site with six equivalent coordinate frames. Although the energy levels of Tm3+ ions in YAG were measured by means of stimulated emissions and optical absorption spectra, the complete Stark energy-level schemes still require elucidation. Table 2 shows our theoretical results of the total 91 Stark energy levels associated with 13 J-multiplets. For comparison, we also list the relative results that have been E


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Inorganic Chemistry

Table 3. Calculated Wavelengths (λ), ED (AED) and MD (AMD) Radiative Decay Rates, Branching Ratios (β), and Radiative Lifetimes (τ) for Spontaneous Emission Transitions between J-Multiplets in Tm:YAGa Atotal (s−1) transition 1

I6

3

H6 F4 3 H5 3 H4 3 F3 3 F2 1 G4 1 D2 3 H6 3 F4 3 H5 3 H4 3 F3 3 F2 1 G4 3 H6 3 F4 3 H5 3 H4 3 F3 3 F2 3 H6 3 F4 3 H5 3 H4 3 F3 3 H6 3 F4 3 H5 3 H4 3 H6 3 F4 3 H5 3 H6 3 F4 3 H6 3

1

D2

1

G4

3

F2

3

F3

3

H4

3

H5

3

F4

−1

−1

λ (nm)

AED (s )

AMD (s )

present

291 347 382 456 496 511 748 1461 364 455 517 663 751 787 1533 477 647 780 1170 1474 1617 677 1079 1509 4228 16773 705 1153 1658 5652 805 1448 2346 1226 3784 1815

2062 17294 101 4223 57 1758 4053 164 19908 10897 208 1840 950 1783 185 1355.6 316.6 1053.5 270.0 111.8 33.0 1225.5 472.1 469.0 12.4 0.1 4177.7 118.0 264.6 5.6 1530.2 149.2 53.2 411.7 15.3 271.2

65.8 0 21.0 0 0 0 0 0 0 0 0 0 95.4 58.9 0 0 11.0 133.1 33.5 3.7 0 0 0 0 0 0 0 64.3 0 0.2 0 22.6 9.0 85.4 0.2 0

2130.8 17294 122 4223 57 1758 4053 164 19908 10897 208 1840 1045.4 1841.9 185 1355.6 327.6 1186.6 303.5 115.4 33.0 1225.5 472.1 469.0 12.4 0.1 4177.7 182.3 264.6 5.8 1530.2 171.8 62.2 497.1 15.5 271.2

β

prev68

present

τ (μs) prev68

−0.07

1246 310 1116 294 144

1382 169 58.0 472 5 255

present

prev68

expt68

34 0.58 0 0.14 0 0.06 0.14 0.01 0.55 0.30 0.01 0.05 0.03 0.05 0.01 0.40 0.10 0.36 0.09 0.04 0.01 0.56 0.22 0.21 0.01 0 0.90 0.04 0.06 0 0.86 0.10 0.04 0.97 0.03 1

28

0.40 0.09 0.36 0.09 0.05

301

322

459

216

0.86 0.10 0.04 0.99 0.01 1

567

621

1951

2100

3687

3930

560

10000

a

Available theoretical and experimental results are also listed for comparison.

theory in terms of three J-O intensity parameters. Fortunately, the values of J-O intensity parameters (Ω2 = 1.58 × 10−20 cm2, Ω4 = 3.12 × 10−20 cm2, and Ω6 = 1.82 × 10−20 cm2) for Tm:YAG have been carefully measured by Thomas et al.68 through the least-squares fitting of absorption spectra. The refractive index (n = 1.81)69 for YAG crystal is also employed in the present calculation to obtain the actual transition intensities. The detailed information for calculating these ED transitions can be found in the Appendix section of the Supporting Information. For references, the calculated eigenvectors of each state for Tm3+ ions in YAG are specifically reported in Table S3. Table 3 summarizes the transitions between the first eight excited states as well as the corresponding wavelengths (λ), radiative decay rates (AED, AMD; MD = magnetic dipole), branching ratios (β), and radiative lifetimes (τ). The first emission transition at 1815 nm corresponds to 3F4 → 3H6, which is the most widely used in solid-state laser technology around 1.9 μm. For the radiative lifetime of the 3H4 state,

All the irreducible representations are in good agreement with those reported by Tiseanu et al.18 except for the 1I6(78) state. More detailed studies should be performed to determine its irreducible representation. For the excited states that have not been determinated by experiments (22 Stark levels), we predict the reasonable values as well as the corresponding multiplets. Noticeablely, the 1I6(81) and 1I6(82) are highly excited and located above the 3P0 state, indicating that the discrepancy of 1 I6 multiplets is relatively large. 3.3. Electric and Magnetic Dipole Transitions. Judd− Ofelt (J-O) theory, introduced by B. R. Judd63 and G. S. Ofelt64 in 1962, is widely used for probing the transition properties within the 4f shell of trivalent RE ions in host crystals. In recent years, it has been successfully applied to evaluating the transition intensities for many RE-doped laser materials.65−67 In this work, the electric dipole (ED) transitions of Tm3+ ions in YAG are calculated based on the Judd−Ofelt F


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Inorganic Chemistry evidently our theoretically calculated result (567 μm) reproduces consistently the experimental data (560 μm), demonstrating the reliability of the present calculation. According to the result reported by Thomas et al.,68 the absorption transition 3H6 → 1G4 was exactly located at 460 nm. However, Mares et al.70 indicated the transition occurring at 481 nm. Our calculated wavelength of the transition from 1G4 → 3H6 is equal to 477 nm, which suggests a slightly better agreement with Mares et al.70 The transitions at 364, 455, and 511 nm are assigned to 1D2 → 3H6, 1D2 → 3F4, and 1I6 → 3F2, respectively. This result is also in perfect agreement with the observed data in the literature.56,70 In fact, the transitions 1D2 → 3F2 and 3 H4 → 3H6 are observed in the region from 783 to 825 nm, but the locations of the peaks in the excitation spectra are indistinguishable.70 Our result suggests that the transition 1D2 → 3 F2 may occur at 787 nm, while 3H4 → 3H6 is located at 805 nm. Furthermore, some promising ED transitions between 3 F3, 3F2, 1D2, and 1I6 states are predicted in Table 3. Most noticeably, the calculated branching ratios of emission transitions 3F3 → 3H6, 3F2 → 3H6, and 1I6 → 3H4 are relatively large, indicating that these transitions may be good candidates for laser action. Meanwhile, the radiative decay rates of MD transition are calculated. The AMD of transition 1G4 → 3H5 is calculated to be 133.1 cm−1, which is almost 12% of AED. This implies that the transition intensities of the MD transition are relatively weak. The magnetic dipole transitions between Stark energy levels are considered to be important medium for studing the magnetic properties of the light−matter interaction. Thus, we calculate the MD absorption lines for the lowest levels of each state in Tm:YAG. Figure 4 shows the predicted oscillator

Figure 5. MD emission lines and corresponding emission rates for Tm3+ in YAG between 300 and 2500 nm.

P2 (86) →1D2 (64) exhibits the strongest emission rates of 17.0 s−1. Interestingly, the strong emission line at 777 nm is assigned to 1G4 (56) →3H5 (23), which possesses the rate of 15.5 s−1. In the visible spectrum, two similar transitions from 3 P2 (86) and 3P2 (88) to 3F3 (43) are obtained. The emission rates of these transitions are 12.5 and 11.5 s−1, respectively. However, there are no available experimental data for the transition properties of MD transitions. We hope that our predicted results can provide more insights for further experimental studies. 3

4. CONCLUSIONS In summary, we have performed a comprehensive computational study on the microstructure and Stark energy-level splitting of Tm:YAG by an unbiased CALYPSO structure searching method combined with first-principles calculations. We have determined the ground state of Tm:YAG, which is an orthorhombic structure with C222 space group symmetry. For the local (TmO8)13− ligand complex in Tm:YAG, we have obtained a complete set of free-ion and crystal field parameters by a good fitting to 69 observed energy levels and then predicted the total 91 Stark levels and electric dipole transitions between the first nine multiplets of Tm3+ ions. The transition from 1G4 to 3H6 occurring at 477 nm is in good agreement with the experimental data. We have indicated two significant transitions of 1D2 → 3F2 and 3H4 → 3H6, locating at 787 nm and 805 mn, respectively. It is hoped that the two new transitions of Tm:YAG can be confirmed by further experimental studies.

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ASSOCIATED CONTENT

S Supporting Information *

Figure 4. Plot of the MD absorption lines and corresponding MD oscillator strengths for each state of Tm3+ in YAG between 300 and 2500 nm.

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.8b02009. Structures of the optimized metastable Tm:YAG, the calculated total and partial DOS of YAG by modified BJ method, the calculated spontaneous emission rates and MD oscillator strengths of transitions for Tm3+ in YAG (PDF)

strengths (PMD) and the corresponding wavelengths in the region from 300 to 2500 nm. It is worth noting that the MD absorption lines are extremely multitudinous, while most of them are relatively weak. There are two strong absorption lines with oscillator strengths larger than 20 × 10−8. The strongest absorption line is ascribed to the transition 1D2 (64) →3P2 (86) at 993 nm. Another strong absorption line occurs at 1197 nm from the ground state 3H6 (1) to 3H5 (23). In addition, the MD emission lines from the excited states to the lowest levels of each state are also calculated, and the results are plotted in Figure 5. The detailed values of the emission rates (A′MD) as well as the corresponding wavelengths are provided in Table S4. In Figure 5, we can clearly see that the transition

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. (C.L.) *E-mail: [email protected]. (Y.-Y.Y.) ORCID

Meng Ju: 0000-0002-2822-3383 Cheng Lu: 0000-0003-1746-7697 G


Article

Inorganic Chemistry Notes

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The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China (Nos. 11504301 and 11304167), Fundamental Research Funds for the Central Universities (SWU118055), the 973 Program of China (2014CB660804), the Special Program for Applied Research on Super Computation of the NSFC-Guangdong Joint Fund (the second phase; Grant No. U1501501), and the Program for Science & Technology Innovation Talents in Universities of Henan Province (No. 15HASTIT020). Funding support from the Committee on Research and Development and Dean’s Research Grants of the Faculty of Liberal Arts and Social Sciences, EdUHK, is gratefully acknowledged.

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Deciphering the Microstructure and Energy-Level Splitting of Tm3+-

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