Author’s Accepted Manuscript Ab-initio study on the structural and spectral properties of Ce3+ in strontium silicates phosphors Jun Cheng, Jiajia Cai, Jun Wen, Yonghu Chen, Min Yin, Changkui Duan www.elsevier.com/locate/jlumin
PII: DOI: Reference:
S0022-2313(16)30140-5 http://dx.doi.org/10.1016/j.jlumin.2016.05.021 LUMIN13992
To appear in: Journal of Luminescence Received date: 31 January 2016 Accepted date: 11 May 2016 Cite this article as: Jun Cheng, Jiajia Cai, Jun Wen, Yonghu Chen, Min Yin and Changkui Duan, Ab-initio study on the structural and spectral properties of Ce3+ in strontium silicates phosphors, Journal of Luminescence, http://dx.doi.org/10.1016/j.jlumin.2016.05.021 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Ab-initio study on the structural and spectral properties of Ce3+ in strontium silicates phosphors Jun Cheng a, Jiajia Cai a, Jun Wen b, Yonghu Chen a, Min Yin a, Changkui Duan a,* a
Key Laboratory of Strongly-Coupled Quantum Matter Physics, Chinese Academy of Sciences,
University of Science and Technology of China, Hefei 230026, China b
School of Physics and Electronic Engineering, Anqing Normal University, Anqing 246011, China
ABSTRACT The structural properties and the 4f→5d transitions of Ce3+ in strontium silicates (Sr3SiO5 and
Sr2SiO4) were investigated using the density functional theory (DFT) with the supercell models and the wavefunction-based CASSCF/CASPT2 embedded cluster methods. The calculated 4f→5d transition energies are associated with two types of Ce3+ sites and show good consistency with the experimental spectra available. Moreover, the crystal-field parameters and the anisotropic g-tensors as well as the signs of the product of the principal g-values (gxgygz) for Ce3+ sites were obtained based on the calculated energies and wavefunctions.
Keywords: Strontium silicates; Ab-initio calculations; Ce3+ ions; Spectral parameters.
1. Introduction Rare-earth doped strontium silicates (Sr3SiO5 and Sr2SiO4) phosphors are widely used as scintillators, white light-emitting diodes, long afterglow phosphors and field emission displays [1-5]. Recently, rare-earth doped crystals such as Y2SiO5 and Y3Al5O12 have received increasing attention and show strong prospects in quantum information applications [6-10] due to the outstandingly long spin coherence times and large inhomogeneous broadened optical transitions of rare-earth ions in crystals [11]. Among these materials, the Ce-doped strontium silicates may have potentially better coherent properties due to the zero nuclear spin of the primary isotopes of the
*
Corresponding author. Tel.: +86 551 63606287. E-mail address:
[email protected] (C.K. Duan).
hosts, which makes them become candidates in quantum information applications. There are two different crystallographic Sr2+ sites in both Sr3SiO5 and Sr2SiO4. In Sr3SiO5, the two sites are both six-coordinated, one with C2 symmetry (referred to as Sr1 hereafter) and the other with C4v symmetry (Sr2), as shown in Fig. 1 (a, b) [12]. There are two different crystallographic phases for Sr2SiO4, i.e., a low-temperature monoclinic β-form and a high-temperature orthorhombic α’-form (minor phase, stable above 85 ºC) [13]. We investigated only the major phase β-Sr2SiO4, which also contains two Sr2+ sites, one is six-coordinated (Sr1) and the other is eight-coordinated (Sr2), and both sites are of C1 symmetry (see Fig. 1 (c, d) ) [14].
(a)
(c)
(b)
(d)
Fig. 1. Schematic representations of the unit cell and local coordination structures of Sr1 and Sr2 sites of Sr3SiO5 (a, b) and Sr2SiO4 (c, d).
In this work, the geometry optimization and the ab-initio model potential (AIMP) embedded cluster calculations were performed to better understand the structural properties and 4f→5d transition energies of Ce-doped strontium silicates. Based on the combination of the parametric crystal-field (CF) model with the ab-initio calculations, the crystal-field parameters (CFPs) were extracted. With the CFPs and the empirical 4f and 5d spin-orbit coupling (SOC) parameters, the splittings of the Kramers doublets in an applied magnetic field were determined. Then the anisotropic
g-tensors of Ce3+ sites and the absolute principal g-values were extracted. Moreover, the signs of the product (gxgygz) were determined through the analyses of the consistency of wavefunctions.
2. Methodology Considering both the size of unit cell and computational cost, two 2×2×1 supercells containing 144 atoms for Sr3SiO5 and 112 atoms for Sr2SiO4 were constructed to model the Ce-doped Sr3SiO5 and Sr2SiO4. Then the DFT calculations within the generalized gradient approximation (GGA) were carried out to optimize the supercells, using the Vienna ab-initio Simulation Package (VASP) [15,16]. One of Sr2+ ions was substituted by a Ce3+ ion. Another Sr2+ ion far away from the doping Ce3+ ion was replaced by a Li+ ion for charge compensation [1]. The configurations of Ce 5s25p64f15d16s2, Sr 4s4p5s, Si 3s23p2, O 2s22p4, and Li 2s1 were treated as valence electrons. Their interactions with the cores were described by the projected augmented wave (PAW) method [17]. The Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional was adopted [18]. The geometry optimizations were performed using the conjugate gradient technique, until the energy change was less than 10−5 eV and the Hellmann-Feynman forces on atoms were less than 10−2 eV/Å. Besides, only one k-point Γ was used to sample the Brillouin zone, and the plane-wave cutoff energy was set to 550 eV. Based on the optimized supercell structures, the Ce-centered clusters containing the nearest-neighboring O2− and Si4+ ions, (CeSr1O6Si4)7+ and (CeSr2O6Si4)7+ for Sr3SiO5, (CeSr1O6Si4)7+ and (CeSr2O8Si4)3+ for Sr2SiO4, were constructed for two types Ce3+ sites. All of the ions within a sphere of radius 10 Å surrounding these clusters were modeled by the AIMP embedding potentials [19]. The remainders of the surroundings within a sphere of radius 30 Å were treated as point charges at the lattice sites. For these embedded clusters, the wavefunction-based CASSCF/CASPT2 calculations [20-28] with the spin-orbit effect [29] were performed to obtain the 4f1 and 5d1 energy levels of Ce3+ by using the program MOLCAS [30]. In the CASSCF calculations, a [4f, 5d, 6s] complete active space was adopted, where the single
unpaired electron occupies one of the 13 molecular orbitals of main characters Ce 4f, 5d, and 6s. In the CASPT2 calculations, the dynamic correlation effects of Ce3+ 5s, 5p, 4f and 5d, and O2− 2s and 2p electrons were considered. In these calculations, a relativistic effective core potential ([Kr] core) with a (14s10p10d8f3g)/[6s5p6d4f1g] Gaussian valence basis set from Ref. [31] was used for Ce, a [He] core effective core potential with a (5s6p1d)/[2s4p1d] Gaussian valence basis set from Ref. [32] was used for O, and a [Ne] core effective core potential with a (7s6p1d)/[2s3p1d] Gaussian valence basis set from Ref. [32] was used for Si. These basis sets were further augmented by the respective auxiliary spin-orbit basis sets for a proper description of the inner core region in the spin-orbit calculations. Based on the combination of the parametric CF model with the ab-initio calculations, the CFPs of Ce3+ can be derived. The details for the extraction of CFPs can be found in Refs. [33-35]. In order to investigate the magnetic properties of Ce3+ in strontium silicates, an effective Hamiltonian was constructed. In the presence of a magnetic field B (ignoring the hyperfine interaction), the Hamiltonian can be written as [36, 37] 𝐻eff = ∑𝑘,𝑞 𝐵𝑞𝑘 𝐶𝑞𝑘 + 𝜁𝒔 ∙ 𝒍 + 𝜇B (𝑔𝑠 𝒔 + 𝒍) ∙ 𝑩,
(1)
where Bkq are the CFPs, Ckq are the spherical tensor operators, ζ is the SOC parameter, μB is the Bohr magneton, gs = 2.00232 is the electron spin g-factor, s is the spin angular momentum, l is the orbital angular momentum. By using the calculated CFPs and empirical 4f and 5d SOC parameters (ζ4f = 614.9 cm-1, and ζ5d = 1082 cm-1 from Ref. [38] were used), the energy levels and wavefunctions were calculated by diagonalizing the matrix of the effective Hamiltonian, using the f-shell program package [39]. In the absence of a magnetic field, the energy levels of Ce3+ are Kramers degenerate. In a magnetic field B, the doublets split into two energy levels and the Zeeman term can be described as μBBT·g·S using an anisotropic g-tensor [40]. Based on the calculated energy levels, the factor g(n) = ∆E/(μBB) was extracted. With the g(n)’s relative to some certain directions of the magnetic field, the matrix g∙gT of a Ce3+ site was determined. The
detailed method of the determination of the matrix g∙gT from g(n)’s was given in Ref. [41]. Then the absolute principal values of g∙gT were derived as well as the principal axes with respect to the chosen coordinate axes. Although the signs of individual principal g-value are arbitrary, the sign of the product of the three principal g-values (gxgygz) can be determined unambiguously [42]. Here we provided a simple method to determine the sign of the product (gxgygz) for a given Kramers doublet as follow. In the magnetic field along three principal axes of a g-tensor, the energy levels and wavefunctions are calculated. By setting gz and gx positive, the eigenfunctions of the effective spin operator 𝑆̃𝑥 and 𝑆̃𝑦 can be expressed as linear combinations of the 𝑆̃𝑧 eigenfunctions, and the coefficients of the expressions are compared to those of the spin S = 1/2 eigenfunctions. The consistency of wavefunctions can then uniquely determine the sign of the product (gxgygz).
3. Results and discussion The structures of the undoped strontium silicates were first optimized using the DFT-PBE methods, as shown in Table 1. The results show that the optimized lattice parameters are slightly larger than the experimental data by 0.65-2.7%. The discrepancy may be traced to the inherent imperfection of the DFT-PBE functional. Then the Ce-doped strontium silicates were modeled by an appropriate supercell. Table 2 presents the optimized bond lengths of Ce3+-O2− and Sr2+-O2−. As can be seen, the substitution of Ce3+ at Sr2+ sites decreases the distances to the nearest O2− ions, which is qualitatively consistent with the smaller ionic radius of Ce3+ than Sr2+ in the same coordination number [43]. The decreases of bond lengths can be approximately described by a scalar factor η:
d Sr 2+ -O2- d Ce3+ -O2- r Sr 2 r Ce3
,
(2)
where d(Sr2+-O2−) (or d(Ce3+-O2−)) are the average bond lengths of Sr2+ (or Ce3+) and neighboring O2− ions, r(X) is the Shannon’s ionic radius of X ion corresponding to the coordination number and valence state. The scalar factor η for two types of CeSr sites
are 0.57 and 0.76 in Sr3SiO5, and 0.70 and 0.76 in Sr2SiO4, indicating that the decrements of bond lengths are not so large as the difference of ionic radii between Ce3+ and Sr2+. According to the DFT total energies of the Ce-doped supercells, the dopant Ce3+ prefers to occupy the Sr1 site by 239 meV in Sr3SiO5 and tend to occupy the Sr2 site by 292 meV in Sr2SiO4.
Table 1 Optimized and experimental lattice parameters for strontium silicates. Hosts Sr3SiO5 Sr2SiO4
Method
a (Å)
b (Å)
c (Å)
β (deg) a
DFT-PBE
7.141
7.141
10.83
-
6.952
6.952
10.76
-
5.755
7.16
9.854
93.35
5.663
7.084
9.767
92.67
Expt.
b
DFT-PBE Expt.
b
a
β is the angle between the basis vector na and nc of the unit cell.
b
The experimental data are from Refs. [12] and [14].
Table 2 Optimized bond lengths of Sr2+-O2− and Ce3+-O2− in strontium silicates (in Å). Sr3SiO5 Bond M-O1 M-O2 M-O3 M-O4 M-O5 M-O6 M-O7 M-O8
Site 1
Sr2SiO4 Site 2
Site 1
Site 2
M=Sr1
M=CeSr1
M=Sr2
M=CeSr2
M=Sr1
M=CeSr1
M=Sr2
M=CeSr2
2.5244 2.5244 2.6017 2.6017 2.6231 2.6231
2.4243 2.4243 2.4876 2.4876 2.5464 2.5464
2.4499 2.5880 2.5880 2.5880 2.5880 2.9640
2.2884 2.4663 2.4663 2.4702 2.4702 2.8890
2.4109 2.5517 2.6355 2.7292 2.7814 2.8585
2.3634 2.4317 2.4748 2.5421 2.6430 2.7302
2.5580 2.5625 2.5831 2.6187 2.6609 2.6722 2.7520 2.7949
2.5022 2.5061 2.5099 2.5269 2.5461 2.5987 2.6239 2.6705
The CASSCF/CASPT2 calculations were performed on the Ce-centered embedded clusters to obtain the 4f1 and 5d1 energy levels of Ce3+ in strontium silicates. The results are presented in Tables 3 and 4 as well as the experimental data available. The splittings of 4f1 energy levels with the SOC effect are obviously larger than the practical situation, due to the overestimate of the SOC effect in the ab-initio calculations. However, the 5d1 energy levels with the SOC effect are uniformly raised by about 1000 cm−1. By comparing the calculated 4f→5d transition energies with the
experimental excitation spectra, the excitation bands at 415 nm (~24100 cm−1) and 327 nm (~30600 cm−1) are assigned to the 4f1→5d1,2 transitions of CeSr1 sites in Sr3SiO5 [44]. The excitation bands at 354 nm (~28200 cm−1), 282 nm (~35500 cm−1), 250 nm (~ 40000 cm−1) and 230 nm (~43500 cm−1) are ascribed to the 4f1→5d1-4 transitions of CeSr2 sites in Sr2SiO4 [13]. According to the good consistency of the 4f→5d transition energies with the experimental spectra, we may conclude that Ce3+ ions prefer to occupy Sr1 sites in Sr3SiO5 and Sr2 sites in Sr2SiO4, which is in agreement with the analyses of the total energies of supercells.
Table 3 Calculated energies of the 4f1 and 5d1 levels for Ce3+ in Sr3SiO5 (in cm−1). CeSr1 (CeO6Si4)7+
Energy levels
Without SOC b
With SOC b
4f1 4f2 4f3 4f4 4f5 4f6 4f7 5d1 5d2 5d3 5d4 5d5
0 78 116 179 815 1551 2329 23713 29757 32254 42524 50564
0 280 1336 2224 2366 3160 4151 24804 30888 33511 43812 51827
35762 26851
E5d
a
∆E5d a
a
CeSr2 (CeO6Si4)7+ Expt.c
Without SOC
With SOC
0 87 90 161 186 221 1258 25127 32675 32753 41923 47874
0 79 468 2238 2262 2353 3092 26227 33399 34402 43237 49141
36968
36070
37281
27023
22747
22914
~24100 ~30600
1 3+ E5d and ∆E5d denote the centroid and splitting of 5d energy levels of Ce .
b
The energy levels are calculated at CASPT2 level without and with the SOC effect.
c
The experimental data are from Ref. [44]. They correspond to the peak values of broad bands in
the excitation spectra (monitoring 5d→4f emissions). The uncertainties are at least the order of 100 cm−1.
Table 4 Calculated energies of 4f1 and 5d1 levels for Ce3+ in Sr2SiO4 (in cm−1). CeSr1 (CeO6Si4)7+
CeSr2 (CeO8Si4)3+
Energy levels
Without SOC
With SOC
Without SOC
With SOC
4f1 4f2 4f3 4f4 4f5 4f6 4f7 5d1 5d2 5d3 5d4 5d5
0 370 413 446 759 832 1554 32613 34467 35494 42267 50168
0 305 759 2229 2464 2756 3286 33442 35194 36921 43421 51331
0 156 359 376 667 1020 1136 29458 34605 41839 43401 47777
0 274 694 2240 2488 2686 3127 30455 35582 42883 44645 49072
E5d
39002
40062
39416
40527
∆E5d
17555
17889
18319
18617
a
Expt. a
~28200 ~35500 ~40000 ~43500
The analyses of the assignments of 5d→4f emissions are similar to Table 3 except for the
experimental data from Ref. [13].
Based on the calculated energies and wavefunctions, the 4f and 5d CFPs for Ce3+ were extracted. The complex values of CFPs are available on request. Tables 5 lists the scalar CF strength parameters [45, 46] at CASPT2 level for the 4f and 5d electrons of Ce3+, which reflect the overall CF interaction. It is shown that the S4f of the CeSr1 sites are larger than those of the CeSr2 sites in both Sr3SiO5 and Sr2SiO4, while the S5d of CeSr1 sites are slightly larger in Sr3SiO5 and slightly smaller in Sr2SiO4 than those of CeSr2 sites, consistent with the 4f and 5d CF splittings. The CFPs of Ce3+ obtained from our calculations are very useful in the analyses of other rare-earth ions in the same hosts, where the computational cost of ab-initio calculations on the rare-earth ions with more than one 4f electron is formidable.
Table 5 Calculated CF strength parameters at CASPT2 level for Ce3+ in strontium silicates (in cm−1). Sr3SiO5
CF strength
4f1
1
5d
Sr2SiO4
CeSr1
CeSr2
CeSr1
CeSr2
S2
1180
424
632
481
S4
1194
535
628
851
S6
530
516
831
499
S4f
1017
494
703
634
S2 S4 S5d
7828 16111 12666
6054 13582 10515
5936 14140 10844
4931 15027 11183
Due to the potential applications in quantum information, the anisotropic g-tensors of Ce3+ sites in strontium silicates were investigated. The matrices g∙gT for the two types of Ce3+ sites in Sr3SiO5 and Sr2SiO4 were obtained by using the calculated CFPs and empirical SOC parameters. The results were presented as follows: For the 4f1 energy level of Ce3+ in Sr3SiO5, (𝐠 ∙ 𝐠
T)
CeSr1
3.595 −0.087 0 = (−0.087 1.077 0 ), 0 0 1.144
3.286 0 0 (𝐠 ∙ 𝐠 T )CeSr2 = ( 0 3.286 0 ). 0 0 3.461
(3)
(4)
For the 5d1 energy level of Ce3+ in Sr3SiO5, 1.702 0.375 0 (𝐠 ∙ 𝐠 T )CeSr1 = (0.375 3.176 0 ), 0 0 2.838 (𝐠 ∙ 𝐠
T)
CeSr2
2.918 0 0 =( 0 2.918 0 ). 0 0 1.977
(5)
(6)
For the 4f1 energy level of Ce3+ in Sr2SiO4, 2.390 5.228 −1.176 (𝐠 ∙ 𝐠 T )CeSr1 = ( 5.228 12.624 −3.200), −1.176 −3.200 1.002
(7)
2.047 −0.563 1.491 (𝐠 ∙ 𝐠 T )CeSr2 = (−0.563 2.125 1.270). 1.491 1.270 7.268
(8)
For the 5d1 energy level of Ce3+ in Sr2SiO4, 0.540 −0.808 −0.119 (𝐠 ∙ 𝐠 T )CeSr1 = (−0.808 2.538 0.159 ), −0.119 0.159 0.963
(9)
3.121 0.277 −0.596 (𝐠 ∙ 𝐠 T )CeSr2 = ( 0.277 2.690 −0.428). −0.596 −0.428 2.300
(10)
The sign of the product (gxgygz) defines the sign of the Berry phase of a (pseudo) spin and determines the direction of the precession of the magnetic moment in a magnetic field [47], which makes it have a physical meaning. Here we investigated the principal g-values of the 4f1 and 5d1 energy levels and the signs of the product (gxgygz) for two types of Ce3+ sites in strontium silicates. The results are presented in Table 6. In Sr3SiO5, the g-tensors of CeSr1 sites have a symmetry axis while the g tensors of CeSr2 sites tend to isotropy. In Sr2SiO4, the g-tensors for two types of Ce3+ sites show high anisotropy. Moreover, the signs of the product (gxgygz) of the 4f1 and 5d1 energy levels for two types of Ce3+ sites in Sr2SiO4 are opposite, which can be easily distinguished from EPR spectra.
Table 6 The absolute principal g-values (|gx|, |gy|, |gz|) and corresponding principal axes of the 4f1 and 5d1 energy levels, and the signs of the product (gxgygz) for Ce3+ sites in strontium silicates. Hosts
Sites
Energy levels 4f1
CeSr1 5d1 Sr3SiO5 4f1 CeSr2 5d1
4f1 CeSr1
Principal g-values
Principal axes with respect to a axis
b axis
c axis
3.598 1.074 1.144 1.270 1.807 1.685 1.813 1.813 1.860 1.708 1.708 1.708
−0.999 −0.035 0 −0.973 0.233 0 1 0 0 1 0 0
0.035 −0.999 0 0.233 0.973 0 0 1 0 0 1 0
0 0 1 0 0 1 0 0 1 0 0 1
0.594 3.952 0.217 0.500
−0.698 −0.375 −0.610 −0.942
0.113 −0.899 0.424 −0.327
−0.707 0.227 0.669 −0.084
Sign(gxgygz)
+
−
+
+
+
5d1 Sr2SiO4 4f1 CeSr2 5d1
1.686 0.974 0.958 1.628 2.806 1.910 1.603 1.376
0.334 −0.046 −0.709 −0.668 0.226 −0.765 −0.544 0.345
−0.937 −0.123 −0.641 0.744 0.189 −0.434 0.831 0.349
−0.101 0.991 0.295 0.011 0.956 0.476 −0.118 0.872
+
−
−
4. Conclusion We have investigated the structural properties using the DFT calculations with supercell models and the 4f→5d transition energies by the CASSCF/CASPT2 embedded cluster calculations for two types of Ce3+ in strontium silicates. The results indicate that Ce3+ favorably occupies the Sr2+ site of C2 symmetry in Sr3SiO5 and the Sr2+ site with six-coordinated O2− in Sr2SiO4. The calculated 4f→5d transition energies were associated with two types of Ce3+ sites and are in agreement with the experimental spectra available. Based on the calculated energy levels and wavefunctions, the CFPs of Ce3+ were extracted, which may be very useful to predict the complicated energy-level structures of other rare-earth ions in the same crystal. Moreover, the anisotropic g-tensors and the signs of the product (gxgygz) of the lowest 4f and 5d energy levels for Ce3+ sites were predicted. The present study demonstrates an effective way to investigate the structural and spectral properties of Ce-doped optical materials.
Acknowledgments This work was supported by the National Key Basic Research Program of China (No. 2013CB921800), National Natural Science Foundation of China (Nos. 11274299, 11374291, 11574298, 11204292, 11404321), and Anhui Provincial Natural Science Foundation (Nos. 1308085QE75, 1508085QA09). We thank the Supercomputing Center of USTC for support in performing parallel computations.
References [1] H.S. Jang, D.Y. Jeon, Appl. Phys. Lett. 90 (2007) 041906.
[2] H.D. Luo, J. Liu, X. Zheng, L.X. Han, K.X. Ren, X.B Yu, J. Mater. Chem. 22 (2012) 15887. [3] M.G. Ha, J.S. Jeong, K.R. Han, Y. Kim, Y.S. Yang, E.K. Jeong, K.S. Hong, Ceram. Int. 38 (2012) 5521. [4] K. Dong, J.J. Liao, S.G. Xiao, X.L. Yang, J.W. Ding, J. Mater. Res. 27 (2012) 2535. [5] M.A. Tshabalala, F.B. Dejene, S.S. Pitale, H.C. Swart, O.M. Ntwaeaborwa, Physica B 439 (2014) 126. [6] T. Utikal, E. Eichhammer, L. Petersen, A. Renn, S. Götzinger, V. Sandoghdar, Nat. Commun. 5 (2014) 3627. [7] Y. Yan, J. Karlsson, L. Ripple, A. Walther, D. Serrano, D. Lindgren, M. Pistol, S. Kröll, P. Goldner, L. Zheng, J. Xu, Phys. Rev. B 87 (2013) 184205. [8] B. Lauritzen, N. Timoney, N. Gisin, M. Afzelius, H. de Riedmatten, Y. Sun, R.M. Macfarlane, R.L. Cone, Phys. Rev. B 85 (2012) 115111. [9] R. Kolesov, K. Xia, R. Reuter, R. Stöhr, A. Zappe, J. Meijer, P.R. Hemmer, J. Wrachtrup, Nat. Commun. 3 (2012) 1029. [10] R. Kolesov, K.W. Xia, R. Reuter, M. Jamali, R. Stöhr, T. Inal, P. Siyushev, J. Wrachtrup, Phys. Rev. Lett. 111 (2013) 120502. [11] W. Tittel, M. Afzelius, T. Chanelière, R.L. Cone, S. Kröll, S.A. Moiseev, M. Sellars, Laser Photon. Rev. 4 (2010) 244. [12] L.S.D. Glasser, F.P. Glasser, Acta Crystallogr. 18 (1965) 453. [13] N. Lakshminarasimhan, U.V. Varadaraju, J. Electrochem. Soc. 152 (2005) H152. [14] M. Catti, G. Gazzoni, G. Ivaldi, Acta Crystallogr. C 39 (1983) 29. [15] G. Kresse, J. Furthmüller, Phys. Rev. B 54 (1996) 11169. [16] G. Kresse, D. Joubert, Phys. Rev. B 59 (1999) 1758. [17] P.E. Blöchl, Phys. Rev. B 50 (1994) 17953. [18] P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865. [19] Z. Barandiarán, L. Seijo, J. Chem. Phys. 89 (1988) 5739. [20] B.O. Roos, P.R. Taylor, P.E.M. Siegbahn, Chem. Phys. 48 (1980) 157. [21] P.E.M. Siegbahn, A. Heiberg, J. Almlöf, B.O. Roos, J. Chem. Phys. 74 (1981) 2384. [22] K. Andersson, P.-Å. Malmqvist, B.O. Roos, A.J. Sadlej, K. Wolinski, J. Phys. Chem. 94 (1990) 5483.
[23] K. Andersson, P.-Å. Malmqvist, B.O. Roos, J. Chem. Phys. 96 (1992) 1218. [24] A. Zaitsevskii, J.P. Malrieu, Chem. Phys. Lett. 233 (1995) 597. [25] J. Finley, P.-Å. Malmqvist, B.O. Roos, L. Serrano-Andrés, Chem. Phys. Lett. 288 (1998) 299. [26] A.B. Muñoz-García, L. Seijo, Phys. Rev. B 82 (2010) 184118. [27] L.X. Ning, L.H. Lin, L.L. Li, C.B. Wu, C.K. Duan, Y.F. Zhang, L. Seijo, J. Mater. Chem. 22 (2012) 13723. [28] L.X. Ning, X.X. Huang, J.C. Sun, S.Z. Huang, M.Y. Chen, Z.G. Xia, Y.C. Huang, J. Phys. Chem. C 120 (2016) 3999. [29] P.Å. Malmqvist, B.O. Roos, B. Schimmelpfennig, Chem. Phys. Lett. 357 (2002) 230. [30] G. Karlström, R. Lindh, P. Malmqvist, B.O. Roos, U. Ryde, V. Veryazov, P. Widmark, M. Cossi, B. Schimmelpfennig, P. Neogrady, L. Seijo, Comput. Mater. Sci. 28 (2003) 222. [31] L. Seijo, Z. Barandiaran, B. Ordejon, Mol. Phys. 101 (2003) 73. [32] Z. Barandiaran, L. Seijo, Can. J. Chem. 70 (1992) 409. [33] M.F. Reid, C.K. Duan, H.W. Zhou, J. Alloys Compd. 488 (2009) 591. [34] L.S. Hu, M.F. Reid, C.K. Duan, S.D. Xia, M.Yin, J. Phys.: Condens. Matter 23 (2011) 045501. [35] J. Wen, L.X. Ning, C.K. Duan, Y.H. Chen, Y.F. Zhang, M. Yin, J. Phys. Chem. C 116 (2012) 20513. [36] G.K. Liu, in: G.K. Liu, B. Jacquier (Eds.), Spectroscopic Properties of Rare Earth in Optical Materials, Springer, Berlin, 2005, p. 1-94. [37] A. Abragam, B. Bleaney, Electron Paramagnetic Resonance of Transition Ions, Dover Publications, New York, 1986, p. 584-599. [38] L. van Pieterson, M.F. Reid, R.T. Wegh, S. Soverna, A. Meijerink, Phys. Rev. B 65 (2002) 045113. [39] M.F. Reid, F-Shell Empirical Programs, University of Canterbury, Christchurch, New Zealand. [40] J.A. Weil, J.R. Bolton, Electron Paramagnetic Resonance: Elementary Theory and Practical Applications, second ed., John Wiley & Sons, New Jersey, 2007, p. 85-111. [41] J. Wen, C.K. Duan, L.X. Ning, Y.C. Huang, S.B. Zhan, J. Zhang, M. Yin, J. Phys. Chem. A 118 (2014) 4988.
[42] M.H.L. Pryce, Phys. Rev. Lett. 3 (1959) 375. [43] R.D. Shannon, Acta Crystallogr. A32 (1976) 751. [44] Y. Li, J. Wang, W.L. Zhou, G.G. Zhang, Y. Chen, Q. Su, Appl. Phys. Express 6 (2013) 082301. [45] N.C. Chang, J.B. Gruber, R.P. Leavitt, C.A. Morrison, J. Chem. Phys. 76 (1982) 3877. [46] D.J. Newman, B. Ng, Crystal Field Handbook, Cambridge University Press, Cambridge, 2000. [47] L.F. Chibotaru, L. Ungur, Phys. Rev. Lett. 109 (2012) 246403.
