Defect structure of Co2+ center in rhombohedral BaTiO3

Optical Materials 29 (2007) 714–717 www.elsevier.com/locate/optmat

Defect structure of Co2+ center in rhombohedral BaTiO3 Zheng Wen-Chen a

a,c,*

, Mei Yang a, Wu Xiao-Xuan

a,b,c

, Zhou Qing

a

Department of Material Science, Sichuan University, No. 29, Wangjiang Road, Chengdu City 610064, Sichuan Province, PR China b Department of Physics, Civil Aviation Flying Institute of China, Guanghan 618307, PR China c International Center for Materials Physics, Chinese Academy of Sciences, Shenyang 110016, PR China Received 6 December 2004; accepted 15 September 2005 Available online 10 January 2006

Abstract The spin-Hamiltonian parameters (g factor gk, g? and hyperfine structure constants Ak, A?) of Co2+ ion in rhombohedral BaTiO3 crystal are calculated from the perturbation formulas based on the cluster approach for the spin-Hamiltonian parameters of 3d7 ion in trigonal octahedral site. The calculations are related to the trigonal field parameters and hence to the defect structure of Co2+ center. From the calculations, it is found that in order to reach a good fit between calculations and experiments, the off-center displacement of Co2+ ion in oxygen octahedron of BaTiO3 is much smaller than that of the host Ti4+ ion it replaces. This point is similar to the case of Fe3+ ion in BaTiO3 obtained in the previous studies by analyzing EPR zero-field splitting from the superposition model.  2005 Elsevier B.V. All rights reserved. PACS: 76.30.Fc; 71.70.Ch; 61.16.Hn Keywords: Defect structure; Electron paramagnetic resonance; Crystal and ligand field; Photorefractive material; Co2+; BaTiO3

1. Introduction BaTiO3 is a famous displacetive ferroelectric system with perovskite structure and exhibits three phase transitions [1]. It is also regarded as a promising photorefractive material for technological applications in optical computing and metrology due to its large electrooptic coefficients and dielectric constants [2–4]. As is known, the transition-metal ions doped into BaTiO3 play a central role for photorefractivity to occur [5–9]. So, the optical and EPR spectra for BaTiO3 doped with 3dn ions were extensively studied [9– 13]. In the low-temperature rhombohedral phase of BaTiO3, the oxygen octahedron surrounding Ti4+ ion is slightly elongated along h1 1 1i axis. The point symmetry of Ti4+ site is C3v and the trigonal distortion of (TiO6)8 octahedron is *

Corresponding author. Address: Department of Material Science, Sichuan University, No. 29, Wangjiang Road, Chengdu City 610064, Sichuan Province, PR China. Tel.: +86 28 8541 2371; fax: +86 28 8541 6050. E-mail address: [email protected] (W.-C. Zheng). 0925-3467/$ - see front matter  2005 Elsevier B.V. All rights reserved. doi:10.1016/j.optmat.2005.12.001

due mainly to the off-center displacement S of Ti4+ along h1 1 1i axis (i.e., C3) axis [1,13] (see Fig. 1). By analyzing the EPR zero-field splitting of the isolated Fe3+ center with trigonal symmetry in the rhombohedral phase of BaTiO3 from the superposition model, Siegel and Muller [13] found that Fe3+ replaces Ti4+ in BaTiO3, but it does not occupy the same lattice site as the Ti4+, i.e., the off-center displacement S of Fe3+ ion in oxygen octahedron along C3 axis is much smaller than that of the replaced Ti4+ ion and so Fe3+ ion remains at the approximate center of this octahedron. Thus, the trigonal distortion of (FeO6)9 octahedron is much smaller than that of (TiO6)8 octahedron in BaTiO3. The spin-Hamiltonian parameters (g factors gk, g? and hyperfine structure constants Ak, A?) for the isolated Co2+ center with trigonal symmetry in rhombohedral BaTiO3 were also found from EPR experiment [9] (note: although the Co2+–V0 pair defect with tetragonal symmetry along h0 0 1i axis caused by charge compensation for Co2+ in a similar compound KNbO3 [9] and similar Mn+–V0 pair defects for other 3dn ions in perovskites [9,14,15] were found from EPR experiments, the Co2+–V0 pair has not been

W.-C. Zheng et al. / Optical Materials 29 (2007) 714–717

[111]

4ðka þ 2Þ gk ¼ 2 þ

S

O2-

Co2+ (or Ti4+)

Ba2+

Fig. 1. Co2+ in the rhombohedral phase of BaTiO3.

h

715

h i i  a h3 4 4 þ 2 x92  ðxþ2Þ v3  ðxþ2Þ 2 v1  2 a 0 x h i 8 ðaa0 Þ2 þ x62 þ ðxþ2Þ 2

3 4  ðxþ2Þ 2 x2

i

h i 2ka 12 8 12 a 4 þ ðaa0 Þ2 v4 þ ðxþ2Þ 4 ðaa0 Þ2 þ xþ2 þ xðxþ2Þ 2 v5 þ xðxþ2Þ v6  ða0 Þ ðxþ2Þ v7 h i g? ¼ 2 8 ðaa0 Þ þ x62 þ ðxþ2Þ 2 h i h i 9 8 2 3 4 4 < = 8 x32  ðxþ2Þ 4ka x32  ðxþ2Þ 2 2 i5 þ h  i Ak ¼ P ðj=2Þ42 þ h 2 2 : ; a 8 a 8 þ x62 þ ðxþ2Þ þ x62 þ ðxþ2Þ 2 2 a0 a0 i h i 9 8 h     <2 x92  4 2 W X þ aa0 2 W Z  4 aa0 x32  4 2 W XZ = ðxþ2Þ ðxþ2Þ 0 h  i þP ; : a 2 6 8 þ x2 þ ðxþ2Þ2 a0 h  i 8 9 12 8ka = <ð2jÞ aa0 2 þ xðxþ2Þ þ xþ2 h  i A? ¼ P : ; a 2 8 þ x62 þ ðxþ2Þ 2 a0 i 9 8h  2 a 4 12 32 = <  xðxþ2Þ W X  aa0 W Z  ðxþ2Þ 2 W XY þ a0 ðxþ2Þ W XZ h  i þP0 ; : a 2 8 þ x62 þ ðxþ2Þ 2 a0

ð1Þ Table 1 g factors and hyperfine structure constants for Co2+ ion in rhombohedral BaTiO3 crystal a

Calculation Calculationb Experiment [9] a b

gk

g?

Ak (104 cm1)

A? (104 cm1)

6.211 4.286 4.262 (5)

3.233 4.394 4.346 (5)

214.4 99.0 99.7 (10)

38.7 105.7 104.5 (10)

Calculated by use of the off-center displacement of the host ion Ti4+. Calculated by use of the off-center displacement of impurity ion Co2+.

found for Co2+ in BaTiO3, suggesting that the required compensator, for example, oxygen vacancy V0, is in a distant sphere, as in the case of Cu2+ in Pb[Zr0.54Ti0.46]O3 [16]), however, no study for the defect structure of Co2+ ion in BaTiO3 crystal has been made by analyzing these EPR data. Since the anisotropy of g factor (characterized by Dg = gk  g?) and that of constant A (DA = Ak  A?) are very small (see Table 1), we suggest that similar to the case of Fe3+ ion [13], Co2+ ion in rhombohedral BaTiO3 does not occupy the exact Ti4+ site, but has much smaller off-center displacement S than the replaced Ti4+ ion along C3 axis in the oxygen octahedron. In order to check the suggestion and to explain reasonably the spin-Hamiltonian parameters gk, g?, Ak and A? for Co2+ in rhombohedral BaTiO3, in this paper, we calculate these spin-Hamiltonian parameters from the perturbation formulas based on the cluster approximation for 3d7 ions in trigonal octahedral site. The results are discussed. 2. Calculation For a Co2+ (3d7) ion in trigonal octahedral sites of crystals, the perturbation formulas of spin-Hamiltonian parameters gk, g?, Ak and A? based on the cluster approach can be expressed as [17]

with   k 0 f 15f12 2q21 10k 0 f0 f12 þ ; v2 ¼ 3 2E1X E2X 3E2X     k 0 f0 5f 1 f2 5f 3 f4 2q1 q2 k 0 f0 5f22 4q22 v3 ¼ þ þ þ ; v4 ¼ 3 2E2X E2Z E1X 3 2E2X E1X   0 0 0 0 2 2 2 k f 5f3 4q3 4q4 k f 5f52 5f32 2q23 2q24 v5 ¼ þ þ þ þ þ ; v6 ¼ 3 E2X E3 E1X 3 E2X E2Z E3 E1Z  0 0 k f 5f 1 f2 5f 3 f4 4q1 q2 v7 ¼ þ þ 3 E2X E2Z E1X

v1 ¼

ð2Þ in which j is the core polarization constant. Eij, x, a, a 0 , fj, qj and Wij are defined in [17]. These parameters are related to the trigonal field parameters v and v 0 and hence to the defect structure of Co2+ impurity center. From the cluster approach, the spin-orbit coupling parameters f, f 0 , the orbital reduction factors k, k 0 and the dipolar hyperfine parameters P and P 0 in the above formulas for a 3dn MX6 cluster in crystals can be written as [17] k ¼ N t ð1 þ k2t =2Þ; f ¼ N t ðf0d þ k2t f0p =2Þ; P ¼ N tP 0;

k 0 ¼ ðN t N e Þ1=2 ð1  kt ke =2Þ f0 ¼ ðN t N e Þ1=2 ðf0d  kt ke f0p =2Þ;

P 0 ¼ ðN t N e Þ

1=2

ð3Þ

P0

where f0d and f0p are, respectively, the spin-orbit coupling parameters of free 3dn ion and ligand ion, P0 is the dipolar hyperfine constant of a free 3dn ion. Nc(c = eg or t2g) and kc are the normalization factors and mixing coefficients in molecular orbitals. They can be obtained from the normalization condition [17] N c ð1  2kc S dp ðcÞ þ k2c Þ ¼ 1

ð4Þ

716

W.-C. Zheng et al. / Optical Materials 29 (2007) 714–717

and the approximate relation [17] fc ¼ ðB=B0 þ C=C 0 Þ=2 ¼ N 2c ½1 þ k2c S 2dp ðcÞ  2kc S dp ðcÞ

ð5Þ

in which B0 and C0 are the Racah parameters in free state and B and C are those in the studied crystal. Sdp(c) is the group overlap integrals. The parameters B, C and the cubic field parameters Dq can be obtained by analyzing the optical spectra of the studied system. For BaTiO3:Co2+, no optical spectral data were reported, we estimate reasonably the above parameters as follows: Considering that for 3dn cluster Dq / R5 is approximately valid [18–21] and that the Racah parameters B and C decreases slightly with decreasing metal–ligand distance R0 [22], from the optical spectra of similar (CoO6)10 clusters in MgO:Co2+ [23] and the distance ˚ [24] and 2.002 A ˚ [13] for MgO and BaTiO3 R0 = 2.105 A (rhombohedral phase), respectively, we can estimate for BaTiO3:Co2+ B  770 cm1 ; 2+

C  3930 cm1 ;

Dq  1208 cm1

1

ð6Þ

Ti4+ ion in oxygen octahedron along C3 axis for the pure crystal and that of Co2+ ion for the impurity center in Co2+-doped crystal. The off-center displacement S of ˚ [1]. If we assume that Co2+ ion in rhomboTi4+ is 0.18 A hedral BaTiO3 occupies the exact Ti4+ site, from the structural parameters Ri and hi obtained from the displacement ˚ . We can calculate the g factors and A constants for 0.18 A BaTiO3:Co2+ by using the above formulas and parameters. The results are in poor agreement with the observed values (see Table 1), suggesting that the off-center displacement S of Co2+ is different from that of Ti4+ ion it replaces. We take the displacement S of Co2+ as an adjustable parameter. Thus, by fitting the calculated spin-Hamiltonian parameters to the observed values, we obtain  S  0:0075ð15Þ A

ð9Þ

The comparisons between the calculated and experimental spin-Hamiltonian parameters are shown in Table 1. 3. Discussion

1

For free Co ion, B0  1115 cm and C0  4366 cm [25], so we have fr  0.792. From the Slater-type SCF functions [26,27] and the above distance R0, we calculate the group overlap integral Sdp(t2g)  0.0145, Sdp(eg)  0.0457. The parameters f0d  533 cm1 [25] and P0  254 · 104 cm1 [28] for free Co2+ ion and f0p  150 cm1 [29] for free O2 ion. Applying these parameters to Eqs. (4), (5) and then to Eq. (3), we obtain f  485:42 cm1 ; f0  219:89 cm1 ; k  0:952; k 0  0:378 P  227:23  104 cm1 ; P 0  102:86  104 cm1 ð7Þ The core polarization constant j  0.325 ± 0.01 for Co2+ ion [30], within the ranges of error, we take j = 0.326 here. The trigonal field parameters v and v 0 can be calculated from the superposition model [31],

From the above studies, one can find that by use of the defect structure, which is different from the corresponding structure in the host crystal, the spin-Hamiltonian parameters gk, g?, Ak and A? for Co2+ in rhombohedral BaTiO3 crystal can be explained reasonably from the perturbation formulas based on the cluster approach (see Table 1). The above studies also give the conclusive evidence that the offcenter displacement of impurity Co2+ along C3 axis in rhombohedral BaTiO3 is much smaller than that of the replaced Ti4+ ion. That is say, Co2+ ion remains at the approximate center of the oxygen octahedron in BaTiO3. This point is very similar to the case of Fe3+ ion in rhombohedral BaTiO3, where the very small displacement of Fe3+ along C3 axis was found by analyzing the EPR zero-field splitting from superposition model [13]. It appears that some useful information of the defect struc-

" # pffiffiffi  t 2  t4  t 4 2 X 9 R0 20  R0 20 2  R0 3 2 4 2 A2 ðR0 Þ A4 ðR0 Þ v¼ ð3 cos h  1Þ þ A4 ðR0 Þ ð35 cos h  30 cos h þ 3Þ þ sin h cos h 7 21 3 Ri Ri Ri i¼1 " pffiffiffi # pffiffiffi  t2  t4  t4 2 X 3 2 R0 5 2 R0 10  R0 3 0 2 4 2 v ¼ A2 ðR0 Þ A4 ðR0 Þ  ð3 cos h  1Þ þ ð35 cos h  30 cos h þ 3Þ þ A4 ðR0 Þ sin h cos h 7 21 3 Ri Ri Ri i¼1 ð8Þ where the power-law exponents t2  3 and t4  5 [17,32].  2 ðR0 Þ and A  4 ðR0 Þ are the intrinsic parameters with the refA ˚ for BaTiO3 as mentioned erence distance R0 (R0  2.002 A n  4 ðR0 Þ  3Dq/4 for 3d ions in octahedral clusters above). A  2 ðR0 Þ  (9–12)A  4 ðR0 Þ obtained for 3dn ions [17,31] and A  2 ðR0 Þ  ð10:5 in many crystals [32–35]. We take A  1:5ÞA4 ðR0 Þ within the range of uncertainty. Ri (i = 1 or 2) is the metal–ligand distance and hi is the angle between the direction of Ri and C3 axis. The structure parameters Ri and hi depend upon the off-center displacement S of

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