Investigation of optical spectra and local structure for (CrF6)3− cluster in Cs2NaAlF6:Cr3+ and Cs2NaGaF6:Cr3+ systems

Chemical Physics Letters 458 (2008) 227–230

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Investigation of optical spectra and local structure for (CrF6)3 cluster in Cs2NaAlF6:Cr3+ and Cs2NaGaF6:Cr3+ systems Huang Jin-Ling a, Kuang Xiao-Yu a,b,*, Li Ying a a b

Institute of Atomic and Molecular Physics, Sichuan University, Chengdu 610065, PR China International Centre for Materials Physics, Academia Sinica, Shenyang 110016, PR China

a r t i c l e

i n f o

Article history: Received 11 December 2007 In final form 17 April 2008 Available online 22 April 2008

a b s t r a c t To investigate the local structure of the (CrF6)3 cluster for Cr3+ in Cs2NaAlF6 and Cs2NaGaF6, the unified calculations of the whole EPR, optical spectra are made based on the 120  120 complete energy matrices which are constructed on the basis of the complete set of the basis jJ, MJi. The results demonstrate that Cr3+ substitute for the two inequivalent M3+ sites rather than the Na+ or Cs+, which accord with the conclusion of several experiments. Simultaneously, the local structure parameters are determined and the relationship between the structure and the temperature has been discussed. Ó 2008 Elsevier B.V. All rights reserved.

1. Introduction

2. Theory model

Impurities in solid materials have been a subject of wide interest in recent years as doped materials can display new properties which are absent in pure compounds [1,2]. Undoubtedly, among the impurities, the trivalent Cr3+ is the major investigated impurity ion in the development of solid-state laser materials, due to its specific energetic structure [3,4]. For example, elpasolite Cs2NaAlF6 and Cs2NaGaF6 doped with Cr3+ are of significant interest due to their simplified [4], potentially portable [5], highly efficient laser source properties [6], which make success in developing compact diode-pumped femtosecond solid-state lasers [7,8]. A better insight into the detailed physical and chemical properties of the Cs2NaAlF6:Cr3+ and Cs2NaGaF6:Cr3+ systems due to Cr3+ in an insulating center requires the knowledge of the actual structure of impurity cluster [9]. Many experiments, such as optical and EPR spectroscopy [10,11], X-ray and neutron diffraction [12,13], Raman spectroscopy [14], have been performed to study the local structures of Cr3+ centers in the two systems, respectively. These experiments show that there are two inequivalent Cr3+ centers in the two systems. However, the local structure distortions of (CrF6)3 cluster are not determined at the present time. And there is no quantitative and unified explanation for the EPR, optical spectra, g factors and the local structure of Cr3+ in Cs2NaAlF6 and Cs2NaGaF6 systems. In this work, the relationship between the optical spectra, EPR parametersD, g and the local structure distortion has been established based on the complete energy matrices for d3 configuration in trigonal ligand–field.

The complete energy matrices for d3 configuration have been constructed by employing the Slater’s method. Firstly, to construct the complete energy matrix, the jJ,MJi basic functions need to be expanded into jL,S,ML,MSi functions by the Clebsch–Gordon coefficients which are associated with the coupling of two angular moments. According to the jL,S,ML,MSi functions and considering the magnetic field effect simultaneously, the perturbation Hamiltonian can be expressed as:

* Corresponding author. Fax: +86 028 85405515. E-mail address: [email protected] (K. Xiao-Yu). 0009-2614/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2008.04.072

b ¼H b ee þ H b SO þ H b LF þ H b Zeeman H P 2 P P P ~ ¼ e =r i;j þ f li  sj þ V i þ lB ðk~li þ g e~ si Þ  H i
j

i

ð1Þ

i

b ee , H b SO , H b LF and H b Zeeman are, respectively, the electron–elecwhere H tron repulsion interaction, the spin–orbit coupling interaction, the ligand–field interaction and the Zeeman interaction, and k is the orbital reduction factor. Usually, the Zeeman interaction is treated as a perturbation term in the explanation of the g factors. For d3 configuration in trigonal ligand–field, the 120  120 complete energy matrices including the parallel or perpendicular component of Zeeman term have been constructed. The matrix elements are the functions of the Racah parameters B and C, the spin–orbit coupling coefficient f, and the ligand–field parameters. For Cr3+ ion replaced the M3+ (M = Al, Ga) ion at the octahedral site in Cs2NaAlF6 and Cs2NaGaF6 systems, the local symmetry belongs to D3d[4,11,15]. If the coordinate system is chosen as in Fig. 1a, the forms of the ligand–field parameters can be described as:

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H. Jin-Ling et al. / Chemical Physics Letters 458 (2008) 227–230

C3

The EPR spectra of Cr3+ in trigonal ligand–field can be described by the following spin Hamiltonian [23]:

z

F− F

−

θ R M

x

F

3+

b S ¼ g bHz Sz þ g bðHx Sx þ Hy Sy Þ þ D½S2  ð1=3ÞSðS þ 1Þ H == ? z

−

where D is zero-field splitting parameter. From Eq. (6) the energy levels in the ground state 4A2 for zero magnetic field may be written as:

Cr3+

y θ0

F−

Eð1=2Þ ¼ D; Eð3=2Þ ¼ D:

R0

DE ¼ Eð3=2Þ  Eð1=2Þ ¼ 2D:

Cs+

F- M3+(Al3+, Ga3+)

a

Na+

b

Fig. 1. (a) is the local structure of (CrF6)3 cluster in Cs2NaAlF6 and Cs2NaGaF6 crystals, R is the Cr–F bond length, h is the angle between Cr–F bond and C3 axis. R0 and h0 are the structure parameters of host crystals. (x, y, z) is the coordinate system, (b) is the crystal structure drawing of Cs2NaAlF6 and Cs2NaGaF6 Refs. [4,30].

1X G2 ðsÞð3 cos2 hs  1Þ; 2 s 1X ¼ G4 ðsÞð35 cos4 hs  30 cos2 hs þ 3Þ; 8 s pffiffiffiffiffiffi 35 X 3 ¼ G4 ðsÞ sin hs cos hs 4 s

B20 ¼

Bc43

ð2Þ

with G2 ðsÞ ¼

A2 R3s

;

ð7Þ

The corresponding ground-state zero-field splitting energy level DE can be expressed as:

F−

F−

B40

G4 ðsÞ ¼

ð6Þ

A4 R5s

ð3Þ

where A2 =  eqshr2i, A4 =  eqsh r4i, and A2/A4 = hr2i/h r4i. The ratio of hr2i/h r4i = 0.151227 for Cr3+ ion is obtained from the parametric radial wave function [16]. A4 is almost a constant for octahedral (CrF6)3 cluster and its value can be determined from the optical spectra and the Cr–F bond length of the CrF3 crystal [17,18]. By this way, we derive A4 = 26.525 a.u. and A2 = 4.011 a.u. for octahedral (CrF6)3 cluster and we will take them in the following calculation. The advantage of confirming the value of A4 is to reduce the number of adjustable parameter and make the choosing of parameter more reasonable, once the value of A4 is determined, there are only the Racah parameters B, C and the spin orbit coefficient f as adjustable parameters. A general relationship between the ligand–field parameters Bkq and the AOM parameters has been given by the equation [19,20]: X Bkq ¼ W lkq el l¼0;1;2

ð8Þ

With above theoretical formulas and the complete energy matrices, the local structure of (CrF6)3 cluster, the optical and EPR parameters D, g for the Cr3+ in Cs2NaAlF6 and Cs2NaGaF6 will be respectively determined in detail. 3. Calculations of the local structure distortion and EPR, optical spectra of (CrF6)3 cluster The crystallographic properties of hexagonal elpasolite are well studied [3,4,15,24–30]. Perfect elpasolite Cs2NaAlF6 and Cs2NaGaF6 possess two inequivalent M3+ (Al3+, Ga3+) sites labeled M1 and M2, two inequivalent Cs+ sites and one Na+ site, respectively, as displayed in Fig. 1b. Both sites of (MF6)3 have a sixfold nearly regular octahedral fluorine coordination, slightly distorted to the D3d symmetry along the C3 axis of the crystal. The optical and EPR spectroscopy show that there exist two inequivalent Cr3+ centers, when doped with Cr3+ in elpasolite. Furthermore, some experimenters presume that Cr3+ will substitute at the two inquivalent M3+ sites, considering the most important factors the ionic radius (rCr > rGa> rAl) as well as electron–photon coupling strength for substitution [11] and X-ray diffraction [3,4,31]. The Cr3+ is octahedral coordinated to six nearest-neighbor F anions. We use R0, h0 to represent the M–F (M = Al or Ga) bond length and the angle between M–F bond and C3 axis of the host crystals, respectively, then the local structure parameters R and h for (CrF6)3 cluster can be expressed as: R ¼ R0 þ DR; h ¼ h0 þ Dh

ð9Þ

where R0 = 1.820 A, h0 = 55.0° for M1 site and R0 = 1.813 A, h0 = 53.3° for M2 site in Cs2NaAlF6 [3,4], and R0 = 1.901 A, h0 = 55.2° for M1 site and R0 = 1.902 A, h0 = 53.2° for M2 site in Cs2NaGaF6 [4,11]. As for Racah parameters B, C, and spin–orbit coupling coefficient f can be obtained from their optical spectra derived from time-resolved meansurement [10,14], the value are estimated as: B ¼ 667 cm1 ; C ¼ 3164 cm1 ; f ¼ kf0 ¼ 233:6 cm1 1

1

1

B ¼ 740 cm ; C ¼ 3308 cm ; f ¼ kf0 ¼ 242:2 cm

for M1 site; for M2 site

with W lkq

 1 3 k 3 2k þ 1 ¼ ð1Þl ð2  dl0 Þ 7 0 0 0    al 3 k 3 X R  C kq ðhs ; /s Þ : R l 0 l s s

for Cr3+ doped in Cs2NaAlF6 crystal;

ð4Þ

In Eq. (4), el(l = 0, 1, 2 corresponding to r, p, d, respectively) are the AOM parameters, al are the power exponents. The relations between er, ep, ed and G0, G2, G4 can expressed as[21,22]: 2 2 er ¼ G0 þ G2 þ G4 ; 7 7 1 4 G4 ; ep ¼ G0 þ G2  7 21 2 1 G4 : ed ¼ G0  G2 þ 7 21

ð5Þ

B ¼ 730 cm1 ; C ¼ 3295 cm1 ; f ¼ kf0 ¼ 241:2 cm1

for M1 site;

B ¼ 695 cm1 ; C ¼ 3180 cm1 ; f ¼ kf0 ¼ 236:2 cm1

for M2 site;

pffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffi for Cr3+ doped in Cs2NaGaF6 crystal. Here k  ð B=B0 þ C=C 0 Þ=2, where B0, C0 and f0 are the free-ion parameters and their values have been reported [32,33]. Thus, the ligand–field parameters B20 ; B40 ; Bc43 are only the functions of DR andDh. The EPR and optical spectra are simulated with use of DR and Dh, due to their high sensitivity to the local structure of chromium center. Synchronously, the DR and Dh for Cr3+ in the two crystals are determined and listed in Table 1. From the results, we can see that the local structures of Cr3+ replacing M3+ in the two systems exhibit expansion distortions as shown in Fig. 1a. This tendency is mainly due to the fact that the

229

H. Jin-Ling et al. / Chemical Physics Letters 458 (2008) 227–230 Table 1 The local structure parameters R, h of (CrF6)3, and the EPR parameters D, g factors, where D is in units of cm1 Cs2NaAlF6:Cr3+

Cs2NaGaF6:Cr3+

M1 T(K) DR(A) R(A) Dh(deg) h(deg) g// g\ Dg 2D

M2

20 0.082 1.902 0.455 55.455 1.9672 1.9735 1.9696 1.9738 0.0024 0.5105 0.5106

Calc. Ref. [4] Calc. Ref. [4] Calc. Ref. [4]

300 0.087 1.907 0.460 55.460 1.9667 1.9731 1.9692 1.9737 0.0025 0.5181 0.5181

20 0.089 1.902 0.398 53.698 1.9690 1.9730 1.9650 1.9748 0.0040 0.7822 0.7823

M1 300 0.091 1.904 0.396 53.696 1.9688 1.9743 1.9648 1.9744 0.0040 0.7863 0.7863

20 0.001 1.902 0.111 55.311 1.9652 1.9740 1.9673 1.9736 0.0021 0.4183 0.4181

M2 300 0.001 1.902 0.130 55.330 1.9652 1.9722 1.9673 1.9728 0.0021 0.4319 0.4318

20 0.018 1.920 0.602 53.802 1.9688 1.9728 1.9652 1.9751 0.0036 0.7127 0.7127

300 0.020 1.922 0.589 53.789 1.9687 1.9719 1.9650 1.9747 0.0037 0.7252 0.7252

Table 2 The observed and calculated optical spectra for Cr3+ ions in two crystals at both sites M1 and M2 with f = 0, the units in cm1 A2(4A2g)?

4

Cs2NaAlF6: Cr3+

Cs2NaGaF6: Cr3+

M1

2

E(2Eg) A2(2T1g) 2 2 E( T1g) 4 A1(4T2g) 4 4 E( T2g) 2 2 E( T2g) 2 A1(2T2g) 4 2 E( T1g(F)) 4 A2(4T1g(F)) 2 A1(2A1g) 4 A2(4T1g(P)) 4 4 E( T1g(P)) 2

b

M2

M1

M2

Calc.

Obsd.a

Calc.

Obsd.a

Calc.

Obsd.b

Calc.

Obsd.b

14389 14873 15056 15980 16271 21444 21821 22696 23009 28329 34937 36157

14265

15270 16166 15891 16495 16009 22988 22348 23489 22984 29044 37602 35712

14903

15196 15765 15920 16017 16253 22516 22839 23145 23437 28977 35565 36585

14782 15649

14578 15395 15157 15712 15286 21916 21366 22315 21887 27739 35674 34030

14144 15152

16000

22599

16129

23256

16051

23070

15350

22100

a Sosman et al., Ref. [10]. Fonseca et al., Ref. [14].

radius of Cr3+ (r = 0.63 A) is larger than that of Al3+ (r = 0.50 A) or Ga3+ (r = 0.62 A) [34], and Cr3+ will push the F anion outwards. The similar effect of extending has been reported for Mn5+ in tetra–oxo coordination using the AOM in Ref. [35]. The distortion parameters show that at the same site but different temperatures the distortions are almost similar, which indicates that the crystals are independent of temperature. The local structure parameters R and h listed in Table 1 have been deduced by Eq. (8) and the results indicate that the local structures of the both sites in the two crystals close to that of Cs2NaCrF6 (R = 1.906 A at M1, R = 1.913 A at M2) [30]. From Tables 1, 2, we can see that the EPR and optical spectra are in the experimental range. Based on our calculated results, we may conclude that Cr3+ may occupy the M3+ sites in the two systems rather than the Cs+ or Na+ sites. The results are consistent with other theoretical consequence and X-ray diffraction experiment. 4. g Factors The orbital reduction factor k is employed in the calculated program. Using above parameters again and fixing the local structure parameters, g factors have been calculated by diagonalizing the 120  120 complete energy matrices. The theoretical g factors are in fair agreement with the experimental values as shown in Table 1. From Table 1, one can see that the sign of Dg(D g = g//  g\) is consistent with that of D, which accords with the conclusion given by using perturbation theory.

5. Conclusions The relationship between the EPR, optical spectra, g factors and the local structure is established by a theoretical method. According to the analysis, we can conclude that the calculated EPR and optical spectra are in good agreement with the experimental findings. The distortion parameters DR, Dh of (CrF6)3 cluster in the different sites at 20 and 300 K in Cs2NaAlF6 and Cs2NaGaF6 crystals are respectively determined, which indicate that the local structures of (CrF6)3 have the expansion distortions. We find that the distortion tendency is very similar at the inequivalent sites and the different temperatures in isomorphic crystals and the local structures in the two systems are close to that of the Cs2NaCrF6. The sign of D and Dg are confirmed to be uniform. Acknowledgements This project was supported by National Natural Science Foundation of China (No.10774103) and the Doctoral Education fund of Education Ministry of China (No.20050610011). References [1] E. Zhecheva, R. Stoyanova, R. Alcántara, J.L. Tirado, J. Phys. Chem. B 107 (2003) 4290. [2] S.K. Misra, S.I. Androenko, J. Phys. Chem. B 108 (2004) 9397. [3] H.N. Bordallo, et al., J. Chem. Phys. 115 (2001) 4300. [4] H. Vrielinck, F. Loncke, F. Callens, P. Matthys, Phys. Rev. B 70 (2004) 144111.

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