Investigations of defect structure and EPR parameters for tetragonal Nd3+ centers in AWO4 (A=Ca, Sr, Pb) crystals by superposition model analysis

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Investigations of defect structure and EPR parameters for tetragonal Nd3 þ centers in AWO4 (AQCa, Sr, Pb) crystals by superposition model analysis Hui Li, Xiao-Yu Kuang, Ai-Jie Mao, Zhen-Hua Wang

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Received date: 13 February 2014 Revised date: 16 March 2014 Accepted date: 28 March 2014 Cite this article as: Hui Li, Xiao-Yu Kuang, Ai-Jie Mao, Zhen-Hua Wang, Investigations of defect structure and EPR parameters for tetragonal Nd3 þ centers in AWO4 (AQCa, Sr, Pb) crystals by superposition model analysis, Solid State Communications, http://dx.doi.org/10.1016/j.ssc.2014.03.020 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.

Investigations of defect structure and EPR parameters for tetragonal Nd3+ centers in AWO4 (A=Ca, Sr, Pb) crystals by superposition model analysis Hui Lia, Xiao-Yu Kuanga,*, Ai-Jie Maoa, Zhen-Hua Wanga a

Institute of Atomic and Molecular Physics, Sichuan University, Chengdu 610065, China

Abstract The characteristics of the local environment around the paramagnetic centers formed by the Nd3+ ions doped into three tungstate crystals (CaWO4, SrWO4 and PbWO4) are investigated by using superposition model analysis. The inter-relation between the electronic and molecular structures of Nd3+ ion in a tetragonal (S4 symmetry) ligand field has been established by a complete diagonalization (of energy matrix) method. The local lattice distortions in the vicinity of the impurity ion Nd3+ have been derived and the local distortion angles Δθ=-1.69°, Δθ=-1.13º, Δθ=-1.48º are obtained for Nd3+ in CaWO4, SrWO4 and PbWO4, respectively. The calculated EPR parameters are in good agreement with the experimental values. On the basis of this, the links between EPR g-factors and the local structure as well as crystal field parameters are studied. Keywords: A. Nd3+:AWO4 crystal; C. Point defects; D. Crystal and ligand fields; E. Electron paramaganetic resonance 1. Introduction 6 ) Scheelite-type structured tungstates AWO4 crystals crystallize in an I41/a ( C4h

space group with four molecules in each crystallographic cell [1-3]. The divalent Ca2+                                                                 ∗ 

 

Corresponding author at: Institute of Atomic and Molecular Physics, Sichuan University, Chengdu 610065, China. Fax: +86 2885405515. E-mail address: [email protected] (Xiao-Yu Kuang).  1 

(Sr2+ or Pb2+) ion occupy a distorted dodecahedral position and coordinate with eight O2- ions. Fig. 1 shows the nearest neighbor coordination environments of the Ca2+ (Sr2+ or Pb2+) ion. When doped with trivalent rare earth (RE3+) ions, CaWO4, SrWO4 and PbWO4 have received particular attention for wide potential industrial applications in scintillator, solid state lasers and luminescence devices [4-8]. So, it is important to investigate the ground multiplet and local lattice distortion structure of these compounds doped with RE3+ ions. To this end spectroscopic and electron paramagnetic resonance (EPR) serve as two powerful experimental methods [9, 10] have been applied for many years. Especially the EPR technology has been comprehensively regarded as an effective tool of investigating local structure around paramagnetic ions in crystal. In the past decades, the optical spectra for Nd3+ ion doped in CaWO4, SrWO4 and PbWO4 have been deduced from absorption and fluorescence experiments and analyzed  respectively [11-15] and the EPR parameters have also been measured by Kurkin [16, 17], Mims [18] and Rosa [19]. In order to interpret the EPR and optical spectra data from a theoretical point of view, Kumar [20] and Karayianis [21] have established 22×22 and 52×52 partial energy matrix. These partial matrices are constructed on the basis of determined ground states and neglected the admixture effects between the ground states and the high excited states. However, as is known, the contributions to the Zeeman interaction or the hyperfine interaction mainly arises from the states with ΔJ=0, ±1, and the admixture effects between the ground states and the high excited states by the coupling of crystal-field, spin-orbit and the magnetic interactions are usually difficult to expect. For making up 2   

this deficiency to some extent and account for the EPR spectra of Nd3+ in scheelites-type ABO4 compounds, Wu and Dong established second-order perturbation formulae of EPR parameters [22], however, still in the scheme of the operator equivalence. Besides, all these works are performed within the approximate D2d point symmetry. To date, two theoretical methods have been employed to investigate the EPR parameters of the lanthanide ions (Ln3+) doped systems, one is the ab initio calculation and the other is the crystal field model. Since the accuracy of ab initio calculation is inferior, the crystal field model is at present the only practicable model to analyze and simulate the energy level data sets of Ln3+ in crystal hosts [23, 24]. Besides, the complete diagonalization (of energy matrix) method has been made for rare earth ions in many crystals [25-27]. In the present work, the complete diagonalization (of energy matrix) method and superposition model (SPM) [28, 29] within S4 symmetry are employed in deriving local structure of Nd3+ doped in CaWO4, SrWO4 and PbWO4. By a quantitative modeling and theoretical simulation of the experimental ground state Stark levels and EPR spectra, the intrinsic parameters and the local distortion angles can be determined. The obtained Stark levels and EPR parameters ( g // , g⊥ , A// , A⊥ ) are also compared with the ones by the approximate D2d site symmetry model. The link between EPR g-factors ( g // , g⊥ ) and local structure of doped RE3+ ions in crystals is shown and the results have been discussed. 2. Calculation and results For a free Nd3+ ion, the electronic configuration is 4f3 with 4I9/2 ground state. 3   

When the Nd3+ ion incorporates into tungstates CaWO4, SrWO4 and PbWO4 crystals, it will occupy the Ca2+ (Sr2+ or Pb2+) site. Since the size, charge and nature of the impurity ion are unlike those of the replaced host ion, a local structural distortion is expected.  To calculate the EPR parameters (or optical spectra) for doped RE3+ (or transition metal) ion in crystal, we should first determine its site symmetry in the studied system. Strictly speaking, the local lattice structure of Nd3+ ion doped CaWO4 (SrWO4 or PbWO4) crystal will display tetragonal distortion and the space group belongs to the S4 symmetry. So, the effective perturbation Hamiltonian for Nd3+ ion with tetragonal S4 symmetry plus an external magnetic field required by EPR experiment can be written as [30-32]: H = H f + H CF + H Z + H hf

(1)

 

in which Hf is the free-ion Hamiltonian defined to include all spherically symmetric interactions and can be expressed as [33-35]:

H f = ∑ F k f k + ζ 4 f ASO + α L ( L + 1) + β G ( G2 ) + γ ( R7 ) k

(2)

+ ∑ T i ti + ∑ M j m j + ∑ P k pk i

j

k

                          

where k=2, 4, 6; i=2,3,4,6,7,8; j=0,2,4. All parameters and operators are defined according to standard practice.  Hf involves 15 free ion parameters controlling interaction between term multiplets, Fk is the Racah parameter, α, β and γ are the configuration-interaction parameters, Ti is the three-body parameter, and Mj and Pk are the magnetic interactions parameters representing the magnetically correlated corrections such as spin-spin and spin-other-orbit interactions and the electrostatically correlated spin-orbit interactions, respectively.  The remaining free-ion parameter ζ4f is 4   

the spin-orbit coupling constant which controls the interaction between SLJ levels. The HCF is the crystal field interaction which accounts for the breakdown of the degeneracy of the multiplet into the Stark levels and the optical properties of the RE3+ ion in the crystal. In the framework of the Racah algebra, the crystal-field Hamiltonian for the S4 symmetry can be described (in Wybourne notation) as follows [25, 33]:

H CF = B20C02 + B40C04 + B60C06 + B44 (C−44 + C44 ) + B64 (C−64 + C46 ) +i Im B44 (C−44 − C44 ) + i Im B64 (C−64 − C46 ) where Cqk are

the

normalized

spherical-tensor

                    

(3)

operators and Bkq are the

crystal-field parameters (CFPs). The Zeeman interaction term HZ in Eq. (1) can be expressed as [36]

H Z = μ B (kL + g s S ) H M                                                                                                               (4) where μB is the Bohr magneton. gs (≈2.0023) is the g value of free electron. k is the orbit reduction factor which is introduced because of the covalence of RE3+ ion clusters in crystals (note: k<1, if k= 1, the orbit reduction effect is neglected)[37, 38]. HM denotes the external magnetic field. For the magnetic hyperfine interaction, Hhf, we have [39] H hf

2μB β N μ N = I

JJG G N ⋅I (5) ∑i ri 3 i                                                     

where βN is the nuclear magneton, μN is the value of the nuclear magnetic moment in nuclear magnetons, and I represents the nuclear spin. The complete energy matrix of the Hamiltonian in Eq. (1) is 364 × 364 dimensions. It can be established by means of the irreducible tensor operator method. 5   

The values of the reduced matrix elements for the tensor operators in Eq. (1) are published in the book of Nielson and Koster [40]. The free-ion parameters of Nd3+ in PbMoO4 are accepted here in this work [41]. Thus, using the Wigner-Eckart theorem we developed our generalized model based on 364×364 complete energy matrix. In order to study the relationship between EPR g-factors of central ion and its local structure, the SPM, as a very useful empirical model, is utilized and the CFPs Bkq can be written as t

R 2 B20 = 4 A2 ( R0 ) ∑ ( 0 ) (3cos 2 θ j − 1) j =1,2 R j B40 = 4 A4 ( R0 ) ∑ ( j =1,2

t

R0 4 ) (35cos 4 θ j − 30 cos 2 θ j + 3) Rj

B44 = 2 70 A4 ( R0 ) ∑ ( j =1,2

B60 = 4 A6 ( R0 ) ∑ ( j =1,2

t

R0 4 ) sin 4 θ j cos 4ϕi Rj

t

R0 6 ) (231cos 6 θ j − 315cos 4 θ j + 105cos 2 θ j − 5) Rj t

R 6 B64 = 6 14 A6 ( R0 ) ∑ ( 0 ) (11cos 2 θ j − 1) sin 4 θ j cos 4ϕi j =1,2 R j t

Im B44 = 2 70 A4 ( R0 ) ∑ (

R0 4 ) sin 4 θ j sin 4ϕi Rj

Im B64 = 6 14 A6 ( R0 ) ∑ (

R0 6 ) (11cos 2 θ j − 1) sin 4 θ j sin 4ϕi Rj

j =1,2

j =1,2

t

(6)

in which Ak ( R0 ) (k=2, 4, 6), expressed in the extended Stevens operator (ESO)[42, 43], are the intrinsic parameters with the reference distance R0 and tk are the power-law exponents. In most cases, it is enough to consider                only           eight nearest-neighbor oxygen ligands in the SPM calculation for RE3+ ion at tetragonal S4 symmetry in tungstate crystals. For the CaWO4 (SrWO4 or PbWO4) host crystal, the local structural parameters (i.e. metal-ligand diatances  Rih and polar angles θ ih   and 6   

azimuthal angles  ϕih , i=1, 2) of the eight O2- in the first coordination shell around Ca2+ (Sr2+ or Pb2+) ion are derived from Ref.[44, 45] and listed in Table 1. The local lattice structure of doped systems will change undoubtedly due to the difference radius of doped Nd3+ and host Ca2+ (Sr2+ or Pb2+) ion. In the present calculation, the distances Ri can be determined approximately by the empirical formula [46]

Ri ≈ Rih +

rd − rh (7) 2                                                      

where rd and rh are the ionic radii of the doped and host ion, respectively. According to [47], when coordination number (CN) is eight, the ionic radii for Nd3+, Ca2+, Sr2+, Pb2+ ions are 1.12Å, 1.12Å, 1.26Å, 1.29Å, respectively. The distances Ri obtained from the Eq. (7) are also listed in Table 1.  In general, the tetragonal distortion of the studied systems is mainly related to the local structure parameter θi, which can be written as

θi = θ ih + Δθ                                                                                                                 (8) where Δθ denotes the local distortion angle in this center. The power-law exponents  

t2=5, t4=6, t6=10 are used [48]. Since the intrinsic parameters are dependent upon the central metal ion, the ligands and the nature of metal-ligand bond, they are taken as adjustable parameters in the SPM. The free-ion parameters F2=71735 cm-1, F4=49739 cm-1, F6=33959 cm-1, ζ4f=878 cm-1, α=29.64 cm-1, β=-863 cm-1, γ=2481 cm-1, T2=449 cm-1, T3=34.9 cm-1, T4=83.2 cm-1, T6=-217 cm-1, T7=314 cm-1, T8=284 cm-1, M0=0.19 cm-1, M2=0.11 cm-1, M4=0.07 cm-1, P2=182 cm-1, P4=-174 cm-1, P6=-1158 cm-1 from Ref. [41] are applied here. Then, by diagonalizing the 364×364 complete energy matrix and fitting the calculated Stark levels and EPR g-factors (g ∥, g ⊥ ) to the 7   

experimental results simultaneously, the Ak ( R0 ) and Δθ can be determined. Using the same method, by substituting the hyperfine interaction for the Zeeman interaction the hyperfine parameters ( A// , A⊥ ) can be obtained. Also, for the approximation of D2d symmetry, the calculations have been performed. All the values obtained from our calculations and the experimental values are summarized in Tables 2 and 3. 3. Discussions

From Tables 2 and 3, one can see that for the S4 symmetry the calculated results of the Stark energy levels and EPR parameters show better agreement with the experimental values, which means that the present assumption of structural distortion is reasonable and our complete energy matrix calculations combined with the SPM are effective. Comparing the calculated results in S4 symmetry with the approximate D2d shows a clear distinction  which may be attributed to the effect of the  non-zero ImB44 and ImB64 for the S4 symmetry. The small disparities between calculated and experimental values in Table 2 may be due to the following. (i) The impurity ligand distances Ri obtained from the empirical formula. (ii) The free-ion parameters are not obtained by the fitting procedures but rather by citing values in Ref. [41]. However, based on our calculations, we find that these errors have only a slight influence on the energy

levels.

The

values

of

obtained

intrinsic

parameters

A2 ( R0 )=350 cm -1 , A4 ( R0 )=59 cm -1 , A6 ( R0 )=28 cm -1 for

Nd3+

Ak ( R0 ) are

in

CaWO4,

A2 ( R0 )=300 cm -1 , A4 ( R0 )=54 cm -1 , A6 ( R0 )=27 cm -1 for Nd3+ in SrWO4 and A2 ( R0 )=250 cm -1 , A4 ( R0 )=50 cm -1 , A6 ( R0 )=25 cm -1 for Nd3+ in PbWO4. It is

worthwhile to note that the obtained values of A4 ( R0 ) and  A6 ( R0 ) for the Nd3+ doped 8   

in three tungstate crystals are very close, whereas the values of the 2nd-rank parameters A2 ( R0 ) displayed striking differences for each other due to long-range effect. In table 3, it can be easily found out that the calculated EPR parameters based on angular distortions Δθ in S4 symmetry are in better agreement with experimental values than the approximate D2d. A suitable orbit reduction factor k is also considered in the EPR parameters calculations. Seeking to understand the general relationships between the EPR g-factors and the polar angular distortion Δθ as well as the intrinsic parameters Ak ( R0 ) , the calculated g-factors as functions of the Δθ and Ak ( R0 ) for CaWO4: Nd3+are depicted in Figs. 2 and 3. Fig. 2 clearly shows that there is an approximate linear relation between the g-factors and the local distortion angle Δθ. The line of g∥ is almost parallel to the Δθ axis, whereas the value of g⊥ decrease clearly with increasing Δθ. Looking at Fig. 3 it can be noted that the three crystal field terms characterized by the corresponding intrinsic parameters have the different contribution to the EPR g-factors and the effects of the intrinsic parameters on the g∥ are more obviously than the g⊥. Finally, in order to check the influence of the non-zero ImB44 and ImB64 on the EPR g-factors, we vary them from zero, which corresponds to the D2d symmetry. Fig. 4 plots the variation of the g-factors as functions of ImB44 and ImB64. From Fig. 4 we can find that the contribution of the ImB44 and ImB64 on the EPR g-factors should not be ignored and the real S4 symmetry instead of approximate D2d should be considered when we understand precisely about the EPR parameters for Nd3+ in tungstate 9   

crystals. 4.

Conclusion

A theoretical method for studying the inter-relation between the molecular and the electronic structures of a 4f3 (S4) system has been proposed on the basis of complete energy matrix approach. With this method, the local-micro-structures can be determined by experimental EPR spectra. As an application, the local (or defect) structure for Nd3+ ion in CaWO4, SrWO4 and PbWO4 has been calculated. To get reasonable explanations to both the ground multiplet and EPR parameters for Nd3+ in the three tungstate crystals, the S4 symmetry has been considered in the SPM and compared with approximate D2d symmetry. According to comparison, the local (or defect) structure obtained by the S4 symmetry can be regarded as acceptable and the present results indicate that the S4 symmetry for the local structure rather than the approximate D2d should be utilized in the investigation of EPR parameters for Nd3+ in tungstate crystals. Acknowledgement

This work was supported by the National Natural Science Foundation of China (No.11104190 and No.11274235) and the Doctoral Education Fund of Education Ministry of China (No. 20111223070653). References

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10   

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Figure captions Fig.1. Local coordination geometry environment of A2+ (A=Ca, Sr or Pb), S4 axis is marked. Fig.2. The dependence of EPR g-factors on the angular distortion Δθ for CaWO4:Nd3+. Fig.3.The influence of the intrinsic parameters Ak ( R0 ) on the EPR g-factors for the CaWO4:Nd3+. Fig.4. Variation of g-factors as a function of ImB44 and ImB64.

14   

Ca, Sr or Pb), S4 axis is marrked. Fig.1. Local coordinnation geomettry environmeent of A2+ (A=C

15   

Fig.2. The dependence of EPR g-factors on the angular distortion Δθ for CaWO4:Nd3+.

16   

Fig.3.The influence of the intrinsic parameters Ak ( R0 ) on the EPR g-factors for the CaWO4:Nd3+.

17   

Fig.4. Variation of g-factors as a function of ImB44 and ImB64.

18   

Table 1. Structural data of Nd3+ in AWO4 (A=Ca, Sr, Pb) crystals. Host

CaWO4[44]

SrWO4[44]

PbWO4[45]

R1h (Å)

2.479

2.610

2.637

R2h (Å)

2.438

2.579

2.580

R1 (Å)

2.479

2.540

2.552

R2 (Å) 

2.438

2.509

2.495

θ1h (deg.) 

66.73

68.00

68.02

θ 2h (deg.) 

139.88

141.10

141.48

ϕ1h (deg.) 

-36.55

-36.20

-36.50

ϕ 2h (deg.) 

-30.30

-27.87

-27.80

19   

Table 2. Calculated and experimental ground multiplets of Nd3+ ion in tungstates. Stark level positions of 4I9/2(cm-1) CaWO4:Nd3+

SrWO4:Nd3+

PbWO4:Nd3+

Cala

Calb

Exp[11]

Cala

Calb

Exp.[12]

Exp[13]

Cala

Calb

Exp[14]

Γ7

0

0

0

0

0

0

0

0

0

0

Γ7

120

114

114

108

92

91

88

102

97

99

Γ5

135

158

161

152

158

155

157

140

172

185

Γ5

238

232

230

224

218

218

216

216

213

213

Γ7

486

471

471

415

396

396

390

392

371

370

Level

a

 Calculations on the approximate D2d symmetry model. 

b

Calculations on the S4 symmetry.

                              20   

          Table 3. EPR parameters g factors ( g // , g⊥ ) and hyperfine structure constant ( A// , A⊥ ) for Nd3+ in tungstates.

g av

A// (10-4cm-1)

A⊥ (10-4cm-1)

2.529

2.394

204

247

2.034

2.537

2.369

194

248

Exp. [16,17]

2.035

2.537

2.370

203

260

Cal.a

1.681

2.574

2.276

156

254

1.542

2.571

2.228

142

254

Exp. [18]

1.541

2.571

2.228

151

269

Cal.a

1.5254

2.6199

2.2551

139

259

1.3614

2.5941

2.1832

123

257

1.3614

2.5941

2.1832

129

264

Compounds CaWO4

∆θ Cal.a Cal.b

SrWO4

Cal.b

PbWO4

Cal.b Exp. [19]

-1.690

-1.130

-1.480

g //

g⊥

2.125

a

Calculations on the approximate D2d symmetry model.

b

Calculations on the S4 symmetry (the orbital reduction factor k=0.992, 0.990 or 0.993).

21   

Highlights z

EPR parameters for Nd3+ in three tungstate crystals are explained reasonably.

z

The feasible values of the structural distortions due to Nd3+ ion are determined.

z

The theoretical results agree with the experimental ones.

z

Dependence of EPR g-factors on Δθ and Ak ( R0 )   was analyzed.

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