Theoretical study of local environment of Mn2+ in two different tetragonal sites in Cs2NaLaCl6 elpasolite

Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 115 (2013) 883–886

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Theoretical study of local environment of Mn2+ in two different tetragonal sites in Cs2NaLaCl6 elpasolite Mei-Ling Duan a, Jin-Hong Li b,⇑, Xiao-Feng Yang a a b

School of Science, North University of China, Taiyuan 030051, China School of Applied Science, Taiyuan University of Science and Technology, Taiyuan 030024, China

h i g h l i g h t s

g r a p h i c a l a b s t r a c t

 Establish the relation between

electronic structure and molecular structure.  Determine the local structure of the doped Cs2NaLaCl6:Mn2+ crystal.  Explain the experimental EPR parameters well.  Propose a method for researching the local properties of the doped system.

a r t i c l e

i n f o

Article history: Received 11 April 2013 Received in revised form 20 May 2013 Accepted 13 June 2013 Available online 26 June 2013 Keywords: Crystal structure and symmetry EPR parameters Complete energy matrix Cs2NaLaCl6:Mn2+ crystal

a b s t r a c t A theoretical method for investigating the inter-relation between the electronic and the molecular structures of a 3d5 ion in a tetragonal ligand-field has been established on the basis of a 252  252 complete energy matrix. By means of this method, the local lattice structures of Mn2+ in two different tetragonal sites in Cs2NaLaCl6 elpasolite are determined by the experimental EPR spectra. The Mn2+–Cl– distances have been obtained as: R1 = 3.2803 Å, R2 = 2.6495 Å for (MnCl6)La cluster, and R1 = 3.4558 Å, R2 = 2.5111 Å for (MnCl6)Na cluster in the Cs2NaLaCl6:Mn2+ system. And our results show R1 > R2 for each cluster, which exhibits an elongation distortion relative to the regular octahedron. And the elongation magnitude of a tetragonal (MnCl6)Na cluster is larger than that of a (MnCl6)La cluster in the Cs2NaLaCl6: Mn2+ system. Using this method, our calculation values of EPR parameters are well accordant with the experimental values. Crown Copyright Ó 2013 Published by Elsevier B.V. All rights reserved.

1. Introduction The elpasolite forms an interesting family of cubic symmetry compounds, their cubic prototype is Fm3m space group. The spectroscopic, magnetic, and electric properties of the cubic elpasolite system have been the subject of numerous studies reported over the past several decades [1–3]. Elpasolite has chemical formula ⇑ Corresponding author. Tel.: +86 3513925287. E-mail addresses: [email protected] (M.-L. Duan), [email protected] (J.-H. Li).

A2BRX6, in which A and B are monovalent alkaline cations, R is a trivalent ion from the lanthanide or actinide families, and X is one of the halide elements. Depending on the size of A, B and R cations, many elpasolites undergo different sequences of structural phase transitions leading to low temperature ferroelastic phases [4]. At present, the elpasolite, doped with transition metal ions such as Fe3+, Mn2+, Cr3+, has been studied by many workers [5– 10], this can be ascribed to the fact that it is useful for new tunable all-solid-state lasers [7–11]. Especially, Cs2NaLaCl6 crystal is a model system for the study of electronic energy levels [12], energy transfer [13] and magnetic [14] phenomena. So it is significant to

1386-1425/$ - see front matter Crown Copyright Ó 2013 Published by Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.saa.2013.06.059

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M.-L. Duan et al. / Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 115 (2013) 883–886

investigate the local lattice structure of Mn2+ ion doped in Cs2NaLaCl6 crystal for researching the phenomena of the transition metal ions doped in the elpasolite. In order to describe the various characteristics of transition metal cluster, it is important to establish the inter-relation between the electronic and the molecular structures. In the present work, a theoretical method for investigating such an inter-relation of a 3d5 configuration ion in a tetragonal ligand-field is proposed, by diagonalizing a 252  252 complete energy matrix and simulating simultaneously the sec0 0 4 ond-order and fourth-order EPR parameters b2 , b4 and b4 . As for A2BMF6 elpasolite, Flerov et al. [15] indicated that there exist two kinds of non-equivalent octahedral groups (BF6) and (MF6) alternating along the fourfold axes. Because both fluorine and chlorine are halide element, we think that the Cs2NaLaCl6 crystal also hosts (NaCl6) and (LaCl6) metal clusters. When Mn2+ ions doped into Cs2NaLaCl6 crystal, the first Mn2+ ion substitutes for a La3+ ion forming a (MnCl6)La cluster; while the second Mn2+ ion replaces one of the six Na+ ions nearest neighbors of the lanthanum ion, forming a (MnCl6)Na cluster. So (MnCl6)La and (MnCl6)Na octahedral groups are two different h1 0 0i tetragonal symmetry sites [6]. In order to study the local structure of (MnCl6)La and (MnCl6)2+ ion doped Na clusters, an EPR measurement on the impurity Mn in Cs2NaLaCl6 crystal has been made by Gleason et al. [6] and Quintanar et al. [16]. In the present paper, based on the 252  252 complete energy matrix for 3d5 configuration ion in a tetragonal ligand-field, we will investigate the local structures of (MnCl6)La and (MnCl6)Na clusters, respectively, in the Cs2NaLaCl6: 0 0 4 Mn2+ system by taking the EPR parameters b2 , b4 and b4 . into account simultaneously. We will directly obtains the Mn2+–Cl distances for (MnCl6)La and (MnCl6)Na clusters in the Cs2NaLaCl6:Mn2+ system. It is show that the value of R1 is larger than that of R2 for each cluster, which exhibits an elongation distortion relative to the regular octahedron. And the different distortion magnitudes of the two clusters are verified that the EPR spectrum is very sensitive to the local distortion. 2. Theoretical method It is well known that the EPR spectrum of a 3d5 configuration ion Mn2+ in a tetragonal ligand-field can be described in terms of the following spin Hamiltonian [17,18]:

b S ¼ g bHZ SZ þ g bðHX SX þ HY SY Þ þ 1 b0 O0 H == ? 3 2 2  1  0 0 0 þ b O þ b4 O04 60 4 4

ð1Þ

where the first two terms on the right of equation refer to the Zeeman interaction, the total spin S = 5/2 and b is Bohr magneton, and b equals to zero; they will be omitted when the magnetic field H Oqk ðSx ; Sy ; Sz Þ are the standard Stevens spin operators and the Z axis q is taken to be along C4 axis; bk are EPR zero-field splitting parameq 4 ters. Among bk , b4 corresponds to a fourth-order spin operator 0 standing for a cubic component of the tetragonal ligand-field, b2 0 and b4 are respectively the second- and fourth-order spin operators, denoting a component of the crystalline electronic field that is axially symmetric about the C4 axis. From the spin Hamiltonian, the expressions of the energy in the ground state 6A1 for a zero magnetic field can be given as follows:

  1 8 0 0 ¼  b2 þ 2b4 ; E  2 3    2 1  2 12 3 4 0 0 0 0 4 E  ¼ b2  b4  2b2 þ 2b4 þ b ; 2 3 5 4    2 1  2 12 5 4 0 0 0 0 4 E  ¼ b2  b4  2b2 þ 2b4 þ b : 2 3 5 4

Then, the zero-field-splitting energies, DE1 and DE2 in the ground state 6A1 can be explicitly expressed as a function of the 0 0 4 EPR parameters b2 , b4 and b4 : 0



0

0



DE2 ¼ 4b2  3b4 

0

0

2

0

0

2

2b2 þ 2b4

2b2 þ 2b4

þ

1 1  4 2 2 b4 ; 5

þ

1 1  4 2 2 b4 : 5

ð3Þ

Herein, the up sign and the down sign in ‘‘±’’ and ‘‘’’ in Eqs. (2) and 0 0 (3) is corresponding to b2 > 0 and b2 < 0, respectively. With the calculated splitting values DE1 and DE2, we can study the relationship 0 0 between the low-symmetry EPR parameters b2 , b4 and the cubic 4 EPR parameter b4 , and our calculation has been listed in Table 1. Besides, we also perform a theoretical calculation by diagonalizing the complete energy matrix for the spin-Hamiltonian of a 3d5 configuration with C4 symmetry, and the corresponding spin-Hamiltonian matrix is presented in Table 2. From Tables 1 and 2, we see that 0 0 the splitting parameters b2 and b4 are insensitive to a change of 4 0 the parameter b4 . Therefore, the low-symmetry EPR parameters b2 0 and b4 can be determined from DE1 and DE2 by diagonalizing the 4 complete energy matrix and fixing the cubic parameter b4 in generm ally. It should be noticed that, bn are related to the zero field splitting parameters D, a and F (conventionally used in some literature), by the following relations [17,18]: 0

b2 ¼ D;

0

b4 ¼

a F þ ; 2 3

4

b4 ¼

5 a: 2

ð4Þ

The Hamiltonian for a 3d5 configuration ion in tetragonal ligand-field can be written as:

b ¼H b ee þ H b so þ H b lf ¼ H

X e2 i
r ij

þf

X X li  si þ V i; i

ð5Þ

i

b ee denotes the electrostatic repulsion energy, H b so denotes where H b lf denotes the ligand-field enthe spin–orbit coupling energy and H ergy. Z is the spin–orbit coupling coefficient, and Vi is the ligandfield potential:

V i ¼ c00 Z 00 þ c20 r2i Z 20 ðhi ; ui Þ þ c40 r 4i Z 40 ðhi ; ui Þ þ cc44 r 4i Z c44 ðhi ; ui Þ þ cs44 r 4i Z s44 ðhi ; ui Þ:

ð6Þ

where ri, hi and ui are spherical coordinates of the ith electron. Zlm, Z clm and Z slm are defined as:

Z l0 ¼ Y l0 ;  pffiffiffi Z clm ¼ 1= 2 ½Y l;m þ ð1Þm Y l;m ;  pffiffiffi Z slm ¼ i= 2 ½Y l;m  ð1Þm Y l;m :

ð7Þ

The Yl,m in Eq. (7) is the spherical harmonics. cl0, cclm and cslm are associated with the local lattice structure of the 3d5 configuration ion by the relations:

Table 1 The influence of parameter 104DE2 = 2227.3 cm1. 4

ð2Þ

0

DE1 ¼ 4b2  3b4 

4

b4

on

0

b2

0

and

0

b4

for

104DE1 = 6587.1 cm1, 0

104 b4 ðcm1 Þ

104 b2 ðcm1 Þ

104 b4 ðcm1 Þ

0 25 49.5 75 100

1096.72 1096.72 1096.70 1096.67 1096.62

6.77 6.78 6.80 6.85 6.90

885

M.-L. Duan et al. / Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 115 (2013) 883–886 Table 2 The spin-Hamiltonian matrix. 5 5

;

S, MS 5 5

; 2 2 5

;5 2 2 5 3

; 2 2 5

;3 2 2 5 1

; 2 2 5

;1 2 2

cl0 ¼ 

2 2

10 0 3 b2

5

;5

5 3

;

0

0 pffiffi

2

0

þ b4

0 0 pffiffi

2

10 0 3 b2 þ pffiffi 5 4 5 b4

5

;3

2 2

0

b4

5 4 5 b4 0  23 b2

0

0

0

0

0

0

0

0

0

0

0

0

0

0

n 4p X eqs c Z lm ðhs ; us Þ; 2l þ 1 s¼1 Rlþ1 s

ð8Þ

n X

4p eqs s Z lm ðhs ; us Þ; 2l þ 1 s¼1 Rlþ1 s

1=2 5 c20 hr2 i; 4p  1=2 9 ¼ c40 hr4 i; 4p  1=2 9 ¼ cc44 hr4 i; 8p  1=2 9 ¼i cs44 hr4 i: 8p

2 2



2

0

0 3b4

2

0 0

0

0

 83 b2 þ 2b4 0

0

0

 83 b2 þ 2b4

Table 3 The observed and calculated optical spectrum for Mn2+ in MnCl2, N = 0.96933, A4 = 68.255 a.u., all values in units of cm1.



Bs44

0

0  23 b2

Energy levels

4

4

4

Observed [21] Calculated

18,500 18,500

22,000 22,202

23,700 23,700

B40

ð9Þ

For the octahedral (MnCl6)La and (MnCl6)Na clusters, their local structures symmetry belong to C4 group in the Cs2NaLaCl6:Mn2+ system. Taking the superposition model, the ligand-field parameter Bs44 will vanish, (the coordinates is chosen as shown in Fig. 1), and the rest can be written as

T1g(G)

T2g(G)

A1g(G)

! 1  R31 R32 ! A4 4 3 ¼ þ 2 R51 R52  1=2 35 A4 ¼ ; 8 R52

B20 ¼ 2A2

Bc44

B20 ¼

Bc44

0

0

where (Rs, hs, us) are the spherical coordinates of the sth ligand, qs is its effective charge. The matrix elements of Hamiltonian (5) are functions of the Racah parameters B and C, the spin–orbit coupling coefficient f, and the ligand-field parameters which are generally expressed as following [19]

B40

0

 3b4

n 4p X eqs Z l0 ðhs ; us Þ; 2l þ 1 s¼1 Rlþ1 s

cslm ¼ 

5

;1

0

5 4 5 b4

cclm ¼ 

5 1

;

2 2 pffiffi 5 4 b 5 4

4

4

26,900 27,101

28,300 28,570

T2g(D)

E(D)

1

ð10Þ

where R1 and R2 are, respectively, the Mn2+–Cl distances in the vertical plane and in the horizontal plane as shown in Fig. 1. A2 and A4 can be expressed as

A2 ¼ eqs hr2 i;

A4 ¼ eqs hr 4 i;

A2 hr 2 i ¼ : A4 hr 4 i

ð11Þ

With regard to the optical spectrum of Cs2NaLaCl6:Mn2+ crystal, it has not been reported, but strength A4 and covalent factor N (this concept is proposed by Curie et al. [20]) are respectively, almost a constant for the (MnCl6) octahedron in different complexes. So A4 and N can be reasonably estimated by simulating optical spectra and Mn2+–Cl bond length of the MnCl2 [20,21] on the basis of the complete energy matrix. By this method, we can determine the average covalent factor N = 0.96933 and strength A4 = 68.255 a.u. (see Table 3). In addition, from the radical wave function of Mn2+ ion in complexes [22], we get the ratio hr2i/ hr4i = 0.119328, so A2 = 8.1447 a.u. is also determined. Using Eqs. (8) and (10), the inter-relation between the local lattice structure parameters R1 and R2 of (MnCl6)La and (MnCl6)Na clusters in the 0 0 4 Cs2NaLaCl6:Mn2+ system and the EPR parameters b2 , b4 and b4 can be established by the complete energy matrix.

3. Calculation and analysis

Fig. 1. The local structure of tetragonal (MnCl6)Na or (MnCl6)La cluster in the Cs2NaLaCl6:Mn2+ system, and R1 > R2 corresponds to an elongation distortion.

When Mn2+ ions doped into Cs2NaLaCl6 crystal, the first Mn2+ ion substitutes for a La3+ ion, while the second Mn2+ ion replaces one of the six Na+ ions nearest neighbors of the lanthanum ion. The two different sites form two different clusters (MnCl6)La and (MnCl6)Na, and their local structures belong to C4 symmetry, as shown in Fig. 1. The experimental EPR data for Mn2+ in two different tetragonal sites in Cs2NaLaCl6 elpasolite have been reported [16]. From the experimental EPR spectra, we can study the local geometric structure by diagonalizing the complete energy matrix. According to Curie et al.’s covalence theory [20], the Racah parameters B and C, Racah–Trees correction a, Seniority correction b, and

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Table 4 0 0 The ground-state splittings DE1 and DE2 and the EPR parameters b2 and b4 for two different tetragonal sites in Cs2NaLaCl6:Mn2+ system as a function of R1 and R2, where 104DE1, 0 0 4 104DE2, 104 b2 , 104 b4 and 104 b4 are in units of cm1. R1 (Å)

R2 (Å)

104DE1

104DE2

104 b2

0

104 b4

104 b4

site

3.3418 3.2999 3.2803 3.2557 3.2003 Expt.[16]

2.6425 2.6475 2.6495 2.6515 2.6545

4481.7 4487.1 4488.2 4491.5 4496.0

1503.1 1503.4 1503.1 1503.4 1503.1

746.6 747.6 747.8 748.4 749.2 747.8

1.98 1.66 1.52 1.35 0.96 1.5

23.1 23.1 23.1 23.1 23.1 23.1

Na+ site

3.4737 3.4558 3.4371 Expt.[16]

2.506 2.5111 2.516

6580.6 6587.2 6594.0

2227.2 2227.2 2227.3

1095.5 1096.7 1097.9 1096.7

7.25 6.77 6.31 6.8

49.5 49.5 49.5 49.5

La

3+

the spin–orbit coupling coefficient f are dependent on the free-ion parameters B0, C0, a0, b0 and f0, and the relations are given as

B ¼ N4 B0 ;

C ¼ N4 C 0 ; 2+

a ¼ N4 a0 ; b ¼ N4 b0 ; f ¼ N2 f0

ð12Þ

1

where the free Mn ion parameters B0 = 918 cm , C0 = 3273 cm1, f0 = 347 cm1, [23] a0 = 65 cm1 [24] and b0 = 131 cm1 [25] had already been given, and the covalent factor N = 0.96933 can be derived too by means of the method mentioned above. Using these 0 0 4 parameters, the EPR parameters b2 , b4 and b4 can be calculated by diagonalizing the complete energy matrix. Meanwhile, we also per0 0 4 form a theoretical calculation of EPR parameters b2 , b4 and b4 for the 5 spin Hamiltonian of 3d configurations with C4 symmetry by diagonalizing the complete energy matrix. From the results listed in 0 0 Tables 1 and 2, we can see that b2 and b4 are almost independent 4 0 of b4 , so we can calculate the low-symmetry EPR parameters b2 0 and b4 by describing them as the functions of R1 and R2. The theoretical results are tabulated in Table 4. As listed in Table 4, we can see that there are different local structure parameters R1 and R2 for the two clusters: R1 = 3.2803 Å, R2 = 2.6495 Å for (MnCl6)La cluster, and R1 = 3.4558 Å, R2 = 2.5111 Å for (MnCl6)Na cluster in the Cs2NaLaCl6:Mn2+ system. So we can get the difference of distances DR (DR = R1  R2) are respectively, 0.6308 Å for (MnCl6)La cluster and 0.9447 Å for (MnCl6)Na cluster, which exhibits an elongation distortion relative to the regular octahedron, and the elongation magnitude of a tetragonal (MnCl6)Na cluster is larger than that of a (MnCl6)La cluster. This may be attributed to the fact that the EPR spectrum is sensitive to the local structure distortion. For the calculated structure 0 0 parameters, both the EPR parameters b2 and b4 can be satisfactorily explained. This means that an elongation model for (MnCl6)La and (MnCl6)Na clusters relative to a regular octahedron is a reasonable one for describing the local distortion. Furthermore, the theoretical EPR parameters agree with the experimental data. Certainly, in order to clarify the local structures of (MnCl6)La and (MnCl6)Na clusters in the Cs2NaLaCl6:Mn2+ system in detail, more careful experiments especially ENDOR experiment are required to perform. 4. Conclusions A theoretical method for studying the inter-relation between the molecular and the electronic structures of a 3d5 (C4) systems has been proposed on the basis of a 252  252 complete energy matrix. With this method, the local-micro-structures can be determined by experimental EPR spectra and optical absorption spectra. As an application, we calculate the lattice structures for (MnCl6)La and (MnCl6)Na clusters in the Cs2NaLaCl6:Mn2+ system. And our results show that the value of R1 is larger than that of R2 for each

0

4

cluster, which exhibits an expansion distortion relative to the regular octahedron; and the expansion magnitude of a tetragonal (MnCl6)Na cluster is larger than that of a (MnCl6)La cluster in the Cs2NaLaCl6:Mn2+ system. Moreover, we draw a conclusion that 0 0 the EPR low-symmetry parameters b2 and b4 are almost indepen4 dent of the cubic parameter b4 . Acknowledgements The authors are grateful to the National Natural Science Foundation of China (Grant Nos. 11247278 and 61178067), the Natural Science Foundation for Young Scientists of Shanxi Province (Grant Nos. 2013021010-4 and 2012021016) and the High Level Talented Person Scientific Research Starting Foundation of North University of China. References [1] P.A. Tanner, Chem. Phys. Lett. 388 (2004) 488–493. [2] F. Ruiperez, Z. Barandiaran, L. Seijo, J. Chem. Phys. 123 (2005) 244703–244711. [3] M.E. Villafuerte, M.R. Estrada, J. Gomez, J. Duque, R. Pome, J. Solid State Chem. 132 (1997) 1–5. [4] M.A. Bunuel, L. Lozano, J.P. Chaminade, B. Moine, B. Jacquier, Optic. Mater. 13 (1999) 211–223. [5] M.G. Brik, K. Ogasawara, Phys. Rev. B 74 (2006) 045105–045113. [6] R.J. Gleason, J.L. Boldu, E. Cabrera, C. Quintanar, E. Manozp, J. Phys. Chem. Solid 58 (1997) 1507–1512. [7] A. Al-Abdalla, L. Seijo, Z. BarandiaraAn, J. Mole. Struct. 451 (1998) 135–142. [8] H. Vrielinck, F. Loncke, F. Callens, P. Matthys, Phys. Rev. B 70 (2004) 144111(1)–144111(111). [9] R.J.M. daFonseca, A.D. TavaresJr, P.S. Silva, T. Abritta, N.M. Khaidukov, Solid State Commun. 110 (1999) 519–524. [10] H.N. Bordalloa, R.W. Henningb, J. Chem. Phys. 115 (2001) 4300–4305. [11] M. Laroche, M. Bettinelli, S. Girard, R. Moncorge, Chem. Phys. Lett. 311 (1999) 167–172. [12] P.A. Tanner, C.S.K. Mak, M.D. Faucher, J. Chem. Phys. 114 (2001) 10860–10871. [13] P.A. Tanner, M. Chua, M.F. Reid, J. Alloys. Compd. 225 (1995) 20–23. [14] M.R. Roser, J. Xu, S.J. White, L.R. Corruccini, Phys. Rev. B 45 (1992) 12337– 12342. [15] I.N. Flerov, M.V. Gorev, J. Grannec, A. Tressaud, J. Fluo. Chem. 116 (2001) 9–14. [16] C. Quintanar, R.J. Gleason, J.L. Boldu, E. Manozp, J. Chem. Phys. 100 (1994) 6979–6980. [17] C. Rudowicz, Magn. Res. Rev. 13 (1987) 1–89. [18] A. Abragam, B. Bleaney, Electron Paramagnetic Resonance of Transition Ions, Oxford University Press, Oxford, 1986. [19] D.J. Newman, W. Urban, Adv. Phys. 24 (1975) 793–843. [20] D. Curie, C. Barthon, B. Canny, J. Chem. Phys. 61 (1974) 3048–3062. [21] J.S. Griffith, The Theory of Transition-Metal Ions, Cambridge University Press, Cambridge, 1964. [22] M.G. Zhao, The Theory of Crystal Field and Electron Paramagnetic Resonance, Science Press, China, 1991. [23] X.Y. Kuang, W. Zhang, I. Morgenstern-Badarau, Phys. Rev. B 45 (1992) 8104– 8107. [24] R.E. Trees, Phys. Rev. 83 (1951) 756–760. [25] G. Racah, Phys. Rev. 85 (1952) 381–382.