Investigations on the local structures and the EPR parameters for Er3+ in PbMoO4 and SrMoO4

Journal of Alloys and Compounds 375 (2004) 39–43

Investigations on the local structures and the EPR parameters for Er3+ in PbMoO4 and SrMoO4 Shao-Yi Wu a,b,∗ , Hui-Ning Dong b,c , Wang-He Wei a a

c

Department of Applied Physics, University of Electronic Science & Technology of China, Chengdu 610054, PR China b International Centre for Materials Physics, Chinese Academy of Sciences, Shenyang 110016, PR China College of Electronic Engineering, Chongqing University of Posts and Telecommunications, Chongqing 400065, PR China Received 29 September 2003; received in revised form 20 November 2003; accepted 20 November 2003

Abstract The local structures and the electron paramagnetic resonance (EPR) parameters g factors g , g⊥ and the hyperfine structure constants A and A⊥ for Er3+ in PbMoO4 and SrMoO4 are theoretically investigated by using the perturbation formulas of the EPR parameters for a 4f11 ion in tetragonal symmetry. In these formulas, the contributions to the EPR parameters from the second-order perturbation terms and admixtures of different energy levels are considered. Based on the studies, we find that the impurity-ligand bonding angles related to the four-fold axis in the impurity Er3+ centers are reduced by about 1.26 and 1.04◦ compared with those in host PbMoO4 and SrMoO4 crystals, respectively. The calculated EPR parameters are consistent with the observed values. The validity of the results is discussed. © 2003 Elsevier B.V. All rights reserved. Keywords: Defect structure; Electron paramagnetic resonance (EPR); Crystal-field theory; Er3+ ; PbMoO4 ; SrMoO4

1. Introduction PbMoO4 has received attention because of applications as acousto-optical modulators, deflectors, ion conductors and great potential to act as an effective low-temperature scintillator for nuclear instrumental application [1–4]. In addition, useful elastic properties of PbMoO4 and SrMoO4 and X-ray excited luminescence of SrMoO4 have also attracted interest of workers [5–8]. Moreover, these materials doped with rare-earth ions exhibit good fluorescence, which along with the high velocity of sound and hence large relaxation time qualifies their role as laser hosts [9]. These interesting properties may be related to electronic states and local structures (e.g. metal–ligand bonding lengths and angles) of doped impurity ions. It is well known that electron paramagnetic resonance (EPR) is a useful method to analyze the electronic properties and the local structures of paramagnetic impurity centers in crystals. Some experiments have been carried out on Er3+ ion-doped PbMoO4 and SrMoO4 with the EPR technique, and the EPR parameters g factors g , g⊥ and the hyperfine structure constants A and A⊥ were measured [10,11]. These EPR parameters were attributed to ∗

Corresponding author. E-mail address: [email protected] (S.-Y. Wu).

0925-8388/$ – see front matter © 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2003.11.137

the impurity Er3+ occupying the host divalent cation sites with tetragonal symmetry in both crystals [10,11]. Up to now, however, the above experimental results have not been satisfactorily explained, and the local structures of the impurity Er3+ centers in both crystals have not been determined either. Since information about electronic states and local structures for Er3+ in PbMoO4 and SrMoO4 may be helpful to understanding of the properties of these crystals (or other Mo-based materials), theoretical studies on the local structures as well as the EPR parameters for the above Er3+ centers is of significance. In this paper, we investigate theoretically the local structures and the EPR parameters for Er3+ in PbMoO4 and SrMoO4 by using the perturbation formulas of the EPR parameters for a 4f11 ion in tetragonal symmetry. In these formulas, the contributions to the EPR parameters from the second-order perturbation terms and admixtures of different energy levels are taken into account. The validity of the results is discussed.

2. Calculations Similar to scheelite CaWO4 , PbMoO4 and SrMoO4 belong to the tetragonal crystal structure of space group I41 /a 6 ). The Pb2+ (or Sr2+ ) site has eight nearest-neighbour (C4h

40

S.-Y. Wu et al. / Journal of Alloys and Compounds 375 (2004) 39–43 (1)

(2)

A⊥ = A⊥ + A⊥ , (2)

(1)

ˆ + |Γγ  >, A⊥ = P NJ < Γγ|N

A⊥ = 0.

Fig. 1. The local structure of the tetragonal Er3+ center in PbMoO4 (or SrMoO4 ). The direction of the four-fold (or Z) axis is upward from the paper plane. The metal–ligand bonding angles related to the four-fold axis are reduced from θ j (j = 1 and 2, denoting the ligands 1–4 and 5–8, respectively) in the pure crystal to θj in the impurity center by the magnitude |θ|.

O2− ions which can be divided into two sets of distorted interpenetrating tetrahedra [9,12–14] (see Fig. 1). Trivalent rare-earth ions (e.g. Er3+ ) tend to locate on divalent Pb2+ (or Sr2+ ) site and conserve the tetragonal (S4 ) site symmetry, for charge compensation may be far from the impurity centers. For an Er3+ (4f11 ) ion in tetragonal (S4 ) site without inversion symmetry, its 4 I15/2 ground state may be separated into eight Kramers doublets. The lowest doublet would be (Γ5 + Γ6 ) or (Γ7 + Γ8 ), corresponding to the cubic (Td ) representation Γ 6 or Γ 7 , with the average value g¯ [= (g + 2g⊥ )/3] of about 6.8 or 6 [15], respectively (note: the above notation for Td [15] is an exchange of that for octahedral cubic Oh symmetry in refs. [16,17]). Judging from the observed (≈6) for Er3+ in PbMoO4 and SrMoO4 [10,11], we suggest that the lowest doublet should be (Γ7 + Γ8 ) in both crystals. Thus, the perturbation formulas of the EPR parameters for a 4f11 ion in tetragonal symmetry can be expressed as follows [18]: (1)

(2)

g = g + g , (2)

g = 2

(1)

g = 2gJ < Γγ|Jˆ Z |Γγ >,


 < Γγ|H ˆ CF |ΓX γX >< ΓX γX |L ˆ Z |Γγ > E(ΓX ) − E(Γ)

(1)

X

g⊥ = g⊥(1) + g⊥(2) , (2)

g⊥(1) = gJ < Γγ|Jˆ + |Γγ  >,

g⊥ = 0,

(2)

A = A(1) + A(2) ,   A(2) = 2P 

ˆ Z |Γγ|, A(1) = 2P NJ < Γγ|N 


 Γγ|HCF |ΓX γX >< ΓX γX |N ˆ Z |Γγ > , E(ΓX ) − E(Γ) X

(3)

(4)

In the above expressions, the parameters gJ and NJ for various 2S+1 LJ configurations are given in refs. [16,17]. It is noted that the nondiagonal elements gJ  and NJ  may occur in the expansions of Eqs. (1)–(4) for the interactions between different 2S+1 LJ configurations. P is the dipolar hyperfine structure parameter of the 4f11 ion in crystals. In Eqs. (1)–(4), besides the contributions to the EPR parameters due to the first-order perturbation terms, we also include the contributions due to the second-order perturbation terms, which result from the admixture of the lowest (Γ7 + Γ8 ) doublet with the other 14 irreducible representations Γ x [i.e. seven (Γ5 + Γ6 ) and seven (Γ7 + Γ8 )] due to the tetragonal splitting of the ground 4 I15/2 and the first excited 4 I13/2 ˆ CF and orbital angular momentum states via crystal-field H ˆ interactions J (or hyperfine structure equivalent operator N) [18,19]. In Eqs. (2) and (4), however, the second-order per(2) (2) turbation contribution g⊥ (or A⊥ ) vanishes because none of the 14 Γ x has non-zero matrix element with the lowest ˆ CF and the x or y component of (Γ7 + Γ8 ) doublet for both H ˆ operators. The basis function Γ γ (or γ  , where γ Jˆ (or N) and γ  denote the two components of the Γ irreducible representation) in the above formulas contains admixtures of different energy levels, i.e. the admixture between the ground 4I 4 ˆ CF interaction, the 15/2 and the excited I13/2 states via H admixture among 2 K15/2 , 2 L15/2 , and 4 I15/2 and that among 2K 2 4 13/2 , I13/2 and I13/2 via spin-orbit coupling interaction. So, the expression for Γ γ (or γ  ) can be written as [18,19]: |Γγ(or γ  ) >
= C(4 I15/2 ; Γγ(or γ  )MJ1 )N15/2 (|4 I15/2 MJ1 > MJ1

+λK |2 K15/2 MJ1 > +λL |2 L15/2 MJ1 >)
+ C(4 I13/2 ; Γγ(or γ  )MJ2 )N13/2 (|4 I13/2 MJ2 > MJ2

+λK |2 K13/2 MJ2 > +λI |2 I13/2 MJ2 >),

(5)

where MJ 1 and MJ 2 are within the ranges of −15/2 to 15/2 and −13/2 to 13/2, respectively. The coefficients C(4 I15/2 ; Γγ(or γ  )MJ1 ) and C(4 I13/2 ; Γγ(or γ  )MJ2 ) can be obtained by diagonalizing the 30 × 30 energy matrix containing 4 I15/2 and 4 I13/2 states. Ni and λi are, respectively, the normalization factors and the mixing coefficients, which can be determined by using spin-orbit coupling matrix elements and perturbation method. In PbMoO4 (or SrMoO4 ) crystal, the Pb2+ (or Sr2+ ) site occupied by the impurity Er3+ has the S4 point symmetry. However, D2d symmetry turns out to be a good approximation due to the rather small distortion from D2d to S4 [9,20] (see Fig. 1), as suggested by many works on trivalent rare-earth ions in scheelite-type crystals [21,22]. Here, we still take the D2d approximation for simplicity. Therefore,

S.-Y. Wu et al. / Journal of Alloys and Compounds 375 (2004) 39–43

the crystal-field interaction for a 4f11 (Er3+ ) ion in tetragonal (D2d ) symmetry can be written in terms of the Stevens operator equivalents as follows ˆ CF = B20 O02 + B40 O04 + B60 O06 + B44 O44 + B64 O46 , H

Table 1 The EPR parameters for the tetragonal Er3+ centers in PbMoO4 and SrMoO4 g

g⊥

A A⊥ (10−4 cm−1 ) (10−4 cm−1 )

(6)

q

where Bk (k = 2, 4, 6; |q| ≤ k) are the crystal-field parameters. They can be obtained by using the superposition model [23], i.e.  tk 2
R0 q q ¯ Bk = Ak (R0 ) Kk (θj , φj ), (7) Rj j=1

PbMoO4

Cal.a Cal.b Expt. [10]

1.964 1.172 1.195

7.912 8.434 8.45

68.2 42.3 42 (1)

277.3 304.7 300 (5)

SrMoO4

Cal.a Cal.b Expt. [11]

1.806 1.042 1.019 (3)

8.023 8.401 8.43 (2)

63.9 38.2 35.3 (3)

280.3 302.9 295 (3)

Calculation based on the host metal–ligand bonding angles θ j . Calculation based on the local impurity-ligand bonding angles θj with the angular distortions θ. a

b

q

where Kk (θj , φj ) are the coordination factors determined from the structural data of the studied impurity centers ¯ k (R0 ) and tk are the intrinsic parameters (with [23,24]. A the reference distance R0 ) and the power-law exponents, respectively. In PbMoO4 (or SrMoO4 ), the host Pb2+ (or Sr2+ ) ion is coordinated to eight nearest O2− ions, with four of them at the distance RH 1 and angles θ 1 and φ1 , and the other four at the different distance RH 2 and angles θ 2 and φ2 , where θ j and φj (j = 1, 2) are, respectively, the polar angles and the azimuthal angles of the metal–ligand distances RH j related to Z (or four-fold) and X-axes of the crystal [9,25,26] (see Fig. 1). In general, the tetragonal distortions of the studied systems are mainly related to the above polar angles θ j . According to refs. [9,25,26], we ◦ have the structural parameters RH 1 ≈ 2.632 Å, θ1 ≈ 68.01 , H ◦ ◦ φ1 ≈ −36.08 , R2 ≈ 2.608 Å, θ2 ≈ 141.63 and φ2 ≈ −27.28◦ for Pb2+ site in PbMoO4 , and RH 1 ≈ 2.610 Å, H ◦ ◦ θ1 ≈ 68.13 , φ1 ≈ −35.78 , R2 ≈ 2.583 Å, θ2 ≈ 141.90◦ and φ2 ≈ −27.32◦ for Sr2+ site in SrMoO4 , respectively. Since the charge and ionic radius of the impurity Er3+ is different from that of the replaced host Pb2+ (or Sr2+ ), the impurity-ligand distances Rj in the doped crystals may be unlike the host values RH j . However, we can reasonably estimate Rj from the approximate formulas [27] Rj ≈ RH j +

41

ri − rh . 2

(8)

Here ri (≈0.881 Å [28] ) is the ionic radius of the impurity Er3+ ion. rh ≈ 1.20 Å (or 1.12 Å) is the ionic radius of the host Pb2+ (or Sr2+ ) ion [28]. Thus, the distances Rj can be obtained for Er3+ in PbMoO4 and SrMoO4 . The power-law exponents t2 ≈ 3.5, t4 ≈ t6 ≈ 6 and the intrin¯ 2 (R0 ) ≈ 400 cm−1 , A ¯ 4 (R0 ) ≈ 50 cm−1 sic parameters A −1 ¯ and A6 (R0 ) ≈ 17 cm (with the reference bonding length R0 ≈ 2.466 Å) were given for Er3+ -doped scheelite in refs. [9,29]. They can also be adopted for the Er3+ centers in this work. The free-ion parameters of the Coulombic repulsion (F 2 ≈ 97504, F 4 ≈ 70746 and F 6 ≈ 48042 cm−1 ), the two-body interaction parameters (α ≈ 20.95, β ≈ −689 and γ ≈ 1839 cm−1 ) and the spin-orbit coupling coefficient (ζ4f ≈ 2339 cm−1 ) in the energy matrix were obtained for Er3+ -doped scheelite in ref. [30]. In view of the covalency between the 4f orbitals of the Er3+ ion and the 2p orbitals

of O2− for the Er3+ –O2− bonds in both crystals, the orbital reduction factor k ≈ 0.979 for the similar Er3+ –O2− bond in MgO: Er3+ [16,18,19] and that (≈0.979) for Yb3+ in scheelite-type crystals [31] can also be applied in this work. Thus, the dipolar hyperfine structure parameter can be written as P ≈ k P0 , where P0 (≈ −54.6 × 10−4 cm−1 ) is the corresponding free-ion value [16]. Substituting these parameters into Eqs. (1)–(4), the EPR parameters for the Er3+ centers in both crystals are calculated and compared with experiment in Table 1. From Table 1, one can find that the calculated g or A factors for the Er3+ centers in both systems are not in agreement with the observed values, particularly, the theoretical anisotropies g(= g − g⊥ ) or A(= A − A⊥ ) for g or A factors are smaller in magnitude than the observed values. Since g or A depends upon the tetragonal distortion and hence upon the polar angles θ j , the local lattice (angular) distortion may be expected to increase the tetragonal distortion and hence the calculated g or A of the studied systems. So, the above host metal–ligand bonding angles θ j may be reasonably replaced by the local impurity-ligand bonding angles θ j  as θj ≈ θj + ∆θ, where θ stand for the local angular distortions of the impurity centers. By fitting the calculated g or A to the experimental results for both crystals, we obtain the angular distortions θ ≈ −1.26◦

(9)

for PbMoO4 and θ ≈ −1.04◦

(10)

for SrMoO4 . Obviously, the negative sign means that the metal–ligand bonding angles in the host crystals are reduced by the amounts |θ| in the impurity centers (see Fig. 1). The corresponding theoretical g and A factors are also shown in Table 1.

3. Discussions One can see from Table 1 that the calculated EPR parameters based on the local impurity-ligand bonding angles θ j 

42

S.-Y. Wu et al. / Journal of Alloys and Compounds 375 (2004) 39–43

are in better agreement than those based on the host bonding angles θ j with the observed values, suggesting that the related parameters and the perturbation formulas adopted in this work are reasonable in physics. Therefore, the EPR parameters for the tetragonal Er3+ centers in PbMoO4 and SrMoO4 are satisfactorily interpreted and the local structures of the impurity centers in both crystals are also determined. (1) Since the ionic radius (≈0.881 Å [28]) of the impurity Er3+ is much smaller than that (≈1.20 or 1.12 Å [28]) of the host Pb2+ or Sr2+ , considerable local relaxation can be induced due to size mismatching substitution of Er3+ for Pb2+ or Sr2+ . Thus, it is understandable that the local bonding angles θ j  in the impurity centers are different from those in the pure crystals. Interestingly, similar angular distortion (e.g. θ ≈ −1.1◦ ) for the [ErO8 ]13− cluster in garnets [e.g. YGG:Er3+ , where the size of the impurity Er3+ is smaller than that (≈0.893 Å [28]) of the replaced trivalent Y3+ ] was also obtained on the basis of the superposition model studies [32]. Further, the larger angular distortion θ for PbMoO4 than that for SrMoO4 is attributed to the bigger size of the replaced host cation and hence to the larger local relaxation around the impurity of the former. So, the local angles θ j  of the impurity centers obtained in this work can be regarded as reasonable. In passing, for Er3+ in CaMoO4 , where the size (≈0.99 Å [28]) of the host Ca2+ is only slightly larger than that of the impurity Er3+ , the local relaxation may be largely counteracted by the extra positive charge of Er3+ and hence stronger electrostatic attraction between Er3+ and the ligand. As a result, the [ErO8 ]13− cluster should be relatively stable and then the angular distortion θ can be regarded as negligible in CaMoO4 . Considering that the physical mechanism for CaMoO4 :Er3+ may be different from that for PbMoO4 (or SrMoO4 ):Er3+ in this work, we do not study the former here for simplicity. (2) The observed anisotropic EPR parameters reveal the axial (tetragonal) symmetry of the Er3+ centers in both crystals. Noteworthily, there are two possible cases which would lower the local symmetry of the impurity centers, i.e. neighbouring charge compensation and off-center displacement of the impurity ion. On one hand, charge compensation may be so distant from the impurity centers that its influence on their local symmetry can be regarded as negligible [33]. On the other hand, Kiel and Mims [20] found on the basis of Born-Mayer theory of ionic bonding that impurity ions smaller than 0.8 Å would be unstable on the ideal Ba2+ site in BaWO4 and then undergo an off-center displacement away from the regular cation site. However, for the studied Er3+ -doped PbMoO4 and SrMoO4 crystals in this work, the impurity Er3+ (where ri ≈ 0.881 Å [28]) is not sufficiently small to be unstable. Consequently, both the possible cases leading to lower symmetry can be excluded and the local tetragonal symmetry of the

Pb2+ or Sr2+ site is therefore conserved in the studied impurity centers. (3) Based on the calculations, we find that the contributions to g and A from the second-order perturbation terms are about 8–10% from those of the first-order perturbation terms. So, in order to explain the EPR parameters for Er3+ centers in crystals to a better extent, the second-order perturbation contributions should be taken into account. According to the above studies, importance of the contributions due to the second-order perturbation terms is related to the tetragonal crystal fields, i.e. both the numerators and the denominators in Eqs. (1) and (2) increase with increasing the strength of the crystal-fields. Meanwhile, the contributions arising from some irreducible representation Γ x are very small or cancel each other. On the whole, the total contributions to g or A from the second-order perturbation terms are approximately 10% from those of the corresponding first-order perturbation terms. On the other hand, the contributions to the EPR parameters from the admixtures between different energy levels are about 5%, which is much smaller than those from the second-order perturbation terms. Obviously, higher excited states 4 I11/2 , 4 I9/2 , etc. would have even smaller influence. Therefore, significant improvement of the calculated EPR parameters can hardly be achieved by merely expanding the size of the energy matrix within the limit of the first-order perturbation treatments, as pointed out in our previous work [19]. (4) It is noted that the hyperfine constants A ≈ 42(1) × 10−4 cm−1 and A⊥ ≈ 300(5) × 10−4 cm−1 (and also the g factors g ≈ 1.195 and g⊥ ≈ 8.45) for Er3+ in PbMoO4 were attributed to an (unspecified) excited state by Zverev et. al. in ref. [34]. However, since (i) the theoretical EPR parameters based on the ground-state calculations in this work show good agreement with the experimental results and (ii) the average g value for an excited state is usually smaller (e.g. ≤4.8 for the excited state 4 I13/2 ), the above experimental values for PbMoO4 :Er3+ in ref. [34] should be undoubtedly attributed to the ground state. There may be some errors in the estimated angular distortions θ for both systems due to approximation of the theoretical model and the related parameters adopted in this work. In addition, errors also arise from adoption of single θ for quite different polar angles θ 1 and θ 2 in each impurity center. Even though two angular distortions θ j (j = 1, 2) are introduced and adjusted respectively for the corresponding θ j , the deviations of the θ j from the above θ in Eqs. (9) and (10) are expected to be no more than 4%. For the sake of reducing the number of adjustable parameters, the effective or average angular distortion θ is reasonably applied in this work. So, our results and conclusions can still be regarded as valid. It seems that useful information about the local structures of Er3+ (or other 4f11

S.-Y. Wu et al. / Journal of Alloys and Compounds 375 (2004) 39–43

ions) in scheelite-type crystals (or other tetragonal ABO4 compounds) can be obtained by analyzing their EPR data.

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