Spin-Hamiltonian parameters and defect structures for two tetragonal Gd3+ centers in Gd3+-dpoed Tl2ZnF4 crystal

Journal of Fluorine Chemistry 153 (2013) 7–11

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Spin-Hamiltonian parameters and defect structures for two tetragonal Gd3+ centers in Gd3+-dpoed Tl2ZnF4 crystal Yang Wei-Qing a,b,*, Zhang Ying a, Zheng Wen-Chen c, Lin Yuan a,** a

State Key Laboratory of Electronic Thin Films and Integrated Devices, University of Electronic Science and Technology of China, Chengdu 610054, PR China Department of Photoelectric Technology, Chengdu University of Information Technology, Chengdu 610225, PR China c Department of Material Science, Sichuan University, Chengdu 610064, PR China b

A R T I C L E I N F O

A B S T R A C T

Article history: Received 23 March 2013 Received in revised form 3 June 2013 Accepted 4 June 2013 Available online 13 June 2013

Seven spin-Hamiltonian parameters (g factors g//, g? and zero-field splittings b02 , b04 , b44 , b06 , b46 ) of two tetragonal Gd3+ centers, denoted A and B, in layered perovskite fluoride Tl2ZnF4 crystals doped only with Gd3+ ion and co-doped with Gd3+ and Li+ are calculated using the diagonalization (of energy matrix) method based on the one-electron crystal-field mechanism. In the calculations, the defect models suggested in the previous paper that center A is due to Gd3+ ion at the octahedral Zn2+ site without any local charge compensation and center B is due to Gd3+ ion at the nine-coordinated Tl2+ site associated with a Li+ ion at the nearest Zn2+ site along C4 axis for charge compensation are applied. The calculated results are in reasonable agreement with the experimental values. The suggested defect models of both Gd3+ centers are therefore confirmed and the respective defect structural data are obtained. The results, including the validity of defect structural data, are discussed. ß 2013 Elsevier B.V. All rights reserved.

Keywords: Perovskite fluorides Trivalent gadolinium ion Electron paramagnetic resonance Crystal- and ligand-field theory Defect structure Defect models

1. Introduction A2MF4 layered perovskite fluorides with K2NiF4 structure have attracted considerable attention because they are two-dimensional ferromagnets (when M = Cu) [1,2], antiferromagnets (M = Mn, Co) [3,4] and the most frequently investigated superconducting phase in the high Tc oxide superconductors [5,6]. Since the impurities can influence strongly the optical and magnetic properties of doped crystals, the defect models of impurity centers in A2MF4 crystals are of importance. The spectroscopic techniques are the powerful tools to study the defect structures of transition metal and rare earth ion impurities in crystals, including doped A2MF4 crystals [7–12]. The room temperature electron paramagnetic resonance (EPR) study indicated a tetragonal Gd3+ center (A) in Gd3+:Tl2ZnF4 and a new tetragonal Gd3+ center (B) in Tl2ZnF4 codoped Gd3+ and Li+ [12]. Arakawa et al. [12] have suggested that the center A is due to the substitutional Gd3+ ion at the octahedral Zn2+ site without any local charge compensation [see Fig. 1(A)], and the center B may be attributed to a Gd3+ ion substituted at a

* Corresponding author at: State Key Laboratory of Electronic Thin Films and Integrated Devices, University of Electronic Science and Technology of China, Chengdu 610054, PR China. Tel.: +86 28 83203901; fax: +86 28 83208813. ** Corresponding author. Tel.: +86 28 83203901; fax: +86 28 83208813. E-mail addresses: [email protected] (Y. Wei-Qing), [email protected] (L. Yuan). 0022-1139/$ – see front matter ß 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jfluchem.2013.06.002

nine-fold coordinated Tl2+ site, where divalent excess positive charge on Gd3+ is compensated by a Li+ ion at the nearest Zn2+ site along C4-axis [see Fig. 1(B)]. The g factors g//, g? and the zero-field splitting (ZFS) parameters b02 , b04 , b44 , b06 , b46 of the two tetragonal Gd3+ centers in Tl2ZnF4 were determined by EPR [12]. The ZFS parameters bqk were analyzed in Ref. [12] using the superposition model (SPM) of ZFS [13–18]. However, up to date, no theoretical microscopic calculations of these spin-Hamiltonian (SH) parameters have been performed. Additionally, although the defect models of both Gd3+ centers were suggested [12], their structures were not considered. In order to explain theoretically these SH parameters and confirm the defect models and their structures for the two Gd3+ centers in Tl2ZnF4, the quantitative calculations should be made. In this paper, we calculate the pertinent SH parameters using the diagonalization (of energy matrix) method based on the one-electron crystal-field (CF) mechanism [13,14,19,20]. 2. Calculation For the S-state ions, like Gd3+ (4f7) ion with the ground multiplet 8S7/2, due to the quenching of orbital angular momentum (i.e., L = 0) in crystals, the microscopic derivation of ZFS parameters is cumbersome [13–15,21,22]. Several mechanisms contribute to the ZFS parameters of 4f7 ions in crystals. Besides the conventional one-electron CF mechanism, the other CF mechanisms, such as

8

Y. Wei-Qing et al. / Journal of Fluorine Chemistry 153 (2013) 7–11

relativistic CF, spin-correlated CF and quadratic CF mechanisms,

and for the external magnetic field Bjjx axis, DEi ð ? Þ

    5 3 3 5 15 0 35 0 5 4 7 4 ! b  b þ b  b  DE  !  ¼ 4b02 þ 2 2 2 4 4 6 2 4 4 6 2  2 7 5 5 7 15 0 3 b  5b44 þ b46 DE3 ð ? Þ ¼ DE !  DE  !  ¼ 6b02  15b04 þ 2 2 2 4 6 4   2 1 1 DE !  ¼ g ? mB Bx 2 2

DE2 ð ? Þ ¼ DE

were considered [13–15,21,22]. Since the latter contributions may partly cancel each other [13–15,21,22], and the former mechanism can explain well the SH parameters for Gd3+ ions in some crystals, especially if the CF parameters Bkq [13–15,20] used are estimated by means of the superposition model [14,15] rather than the electrostatic model. For simplicity, we apply only the one-electron CF mechanism [19,23–26] here. For a tetragonal Gd3+ center in crystals, the tetragonal CF splits the ground multiplet 8S7/2 into four Kramers doublets. The external magnetic field used in EPR further splits these doublets into eight singlets with J = S = 7/2, 5/2, 3/2, 1/2, 1/2, 3/2, 5/2 and 7/2. Hence EPR spectra of tetragonal Gd3+ centers can be described by the effective spin-Hamiltonian [12,19,27]. 1 1 0 0 ðb O Hs ¼ g == mB Bz Sz þ g ? mB ðBx Sx þ By Sy Þ þ b02 O02 þ 3 60 4 4 1 ðb0 O0 þ b46 O46 Þ þ b44 O44 Þ þ (1) 1260 6 6 where Oqk represent the Stevens operators and bqk are the ZFS parameters [27,28]. The SH parameters g//, g? and bqk can be determined from the observed angular dependences of EPR transitions, e.g., for the effective spin S = 7/2 using second-order perturbation relations for the external magnetic field Bjjz (or C4) axis [19,23],     3 1 1 3 DE1 ð==Þ ¼ DE !  DE  !  ¼ 2ð2b02  12b04 þ 14b06 Þ 2 2 2  2 5 3 3 5 DE2 ð==Þ ¼ DE ! ! DE  !  ¼ 2ð4b02  10b04  14b06 Þ 2 2 2  2 7 5 5 7 DE3 ð==Þ ¼ DE !  DE  !  ¼ 2ð6b02 þ 20b04 þ 6b06 Þ 2 2 2  2 1 1 DE !  ¼ g == mB Bz 2 2 (2)

Fig. 1. Defect models of Gd3+ centers A and B in Gd3+-doped Tl2ZnF4 crystal.

(3)

Obviously, the SH parameters g//, g? and bqk can be calculated from the above EPR transitions and hence from the eight singlet energy levels due to the splittings of the ground multiplet 8S7/2 for Gd3+ ion in a tetragonal crystal-field and under an external magnetic field. So, the Hamiltonian of this system based on the one-electron crystal-field mechanism can be written as H ¼ H fi þ HCF þ Hze

(4)

where the three terms are, respectively, the free ion, the CF and Zeeman (or magnetic) interaction terms [28,29] X k H fi ¼ EAVE þ F f k þ z4 f ASO þ aLðL þ 1Þ þ bGðG2 Þ k¼2;4;6

þ g GðR7 Þ þ

k¼2;4;6 X t¼2;3;4;6;7;8

ti T k þ

X k¼0;2;4

mk M k þ

X

pk P k

(5)

k¼2;4;6

HZe ¼ g J mB S  B

(6)

HCF ¼ B20 C 20 þ B40 C 40 þ B44 ðC 44 þ C 4 ; 4Þ þ B60 C 60 þ B64 ðC 64 þ C 6 ; 4Þ

(7)

where the symbols have their standard meanings [28,29]. The complete energy matrix of the Hamiltonian in Eq. (4) has the dimension 3432  3432. The matrix is too large. However, lots of studies suggested that the splittings of ground multiplet 8S7/2 of 4f7 ion are related mainly to the interactions (or matrix elements) among it and the low-lying excited multiplets having the same J (=7/2) value [22,30,31]. As an approximation, a 56  56 energy matrix of the Hamiltonian in Eq. (4) including the ground multiplet 8 S7/2 and the excited multiplets 6L7/2 (L = P, D, F, G, H, I) is constructed by means of the equivalent and/or irreducible tensor operator methods [28,32]. The eight singlet energy levels (and hence the SH parameters g//, g? and bqk ) due to the splittings of the ground multiplet 8S7/2 can be calculated by diagonalization the energy matrix. For calculations, we take the mean values of the free-ion parameters for Gd3+ ions in many crystals [29] (see Table 1). Since the electrostatic model cannot produce reasonable crystal field parameters, we use the superposition model (SPM) [14,15], which is more appropriate for rare earth ions in crystals [14,15,33–37]. In the model, the CF parameters Bkq are treated as a sum of contributions from the ligands [14,15]:  t k q X Kk ðu i ; fi Þ R0 (8) A¯ k ðR0 Þ Bkq ¼ Ri ak0 i where A¯ k ðR0 Þ (k = 2, 4, 6) are the intrinsic parameters with the reference distance R0, which are taken as the adjustable parameters because they depend upon the central metal ion, the ligand, the reference distance R0, the coordination number and the nature of metal–ligand cluster, whereas tk are the power-law exponents which are also adjustable. For rare earth ions in crystals, in particular, in fluorides, the studies of optical spectra and hence CF parameters suggested that t2  5, t4  6 and t6  10 [36,37]. We apply them to the studied Gd3+:Tl2ZnF4. The coefficients ak0 are

Y. Wei-Qing et al. / Journal of Fluorine Chemistry 153 (2013) 7–11

9

Table 1 The average free-ion parameters (in cm1) of Gd3+ ion [29]. F2 85,300 T7 338

F4 60,517 T8 335

F6 44,731

z4f 1504

a

b

g

18.95 M0 2.99

–620 M2 1.67

1658 M4 1.14

given in Ref. [15]. Ri are the metal–ligand distances and Kkq (ui, fi) are the coordination factors [34,35]. So the calculations of the CF parameters Bkq (and hence the SH parameters) depend upon the defect model and their structure.

T2 308 P2 542

T3 43 P4 407

T4 51 P6 271

T6 –298

Table 2) are determined by fitted the calculated SH parameters, using the diagonalization method. The CF parameters Bkq obtained from Eq. (9) with these parameters are collected in Table 3. The SH parameters obtained in this way are in reasonable agreement with experiment (see Table 4).

2.1. Calculation for center A 2.2. Calculation for center B The center A for Gd3+-doped Tl2ZnF4 crystal is a tetragonal octahedral cluster. Thus, from Fig. 1(A) and Eq. (8), we have   t 2 # R0 2 R0  R== R? "    t4 # R0 t4 R0 ¼ 4A¯ 4 ðR0 Þ 4 þ3 R== R?  t4 pffiffiffiffiffiffi R0 ¼ 2 70A¯ 4 ðR0 Þ ? "  R  t6 # R0 t6 R0 ¯ ¼ 4A6 ðR0 Þ 8 5 R== R?  t6 pffiffiffiffiffiffi R0 ¼ 6 14A¯ 6 ðR0 Þ R?

B20 ¼ 4A2 ðR0 Þ B40 B44 B60 B64

"

(9)

where R//and R? represent the metal–ligand distances parallel with and perpendicular to the z (or C4)-axis. For A2MF4 crystal,

In center B, Gd3+ ion replaces the nine-coordinated Tl2+ ion. According to the X-ray diffraction data for A2MF4 [38,39], one of the nine F ligands around A2+ ion is at the z-(or C4) axis with the metal–ligand distance R3 = (ZA  ZF)c, where ZA is the atomic position parameter of A+ ion. No value of ZA was reported for Tl2ZnF4, hence it is taken as an adjustable parameter. Since in center B the effective charge of Li+ ion at the Zn2+ site is negative, the F ion between Gd3+ and Li+ should be displaced far away Li+ and toward Gd3+ by DR(>0) [see Fig. 1(b)]. Thus, R3 in center B should be R3 = (ZA  ZF)c  DR. The other eight F ligands are divided into two groups. The four F ligands in each group have the same metal–ligand distance Ri (i = 1, 2) and polar angle ui (between Ri and C4 axis), but the azimuthal angles fi of the four F ligands in group 1 are: 0, 908, 1808, 2708, whereas in group 2: 458, 1358, 2258 and 3158 [see Fig. 1(B)]. Thus, the expressions of Bkq for center B from Eq. (8) are:

" #  t2 X R0 t2 R0 ð3 cos2 ui  1Þ þ 2A¯ 2 ðR0 Þ Ri R3 i¼1;2 " #  t 4 X R0 t4 R0 4 2 ¯ ¼ 4A4 ðR0 Þ ð35 cos u i  30 cos u i þ 3Þ þ 8A¯ 4 ðR0 Þ R R3 i i¼1;2 "  #  t 4 t4 pffiffiffiffiffiffi R0 R0 4 4 ¼ 2 70A¯ 4 ðR0 Þ sin u1  sin u2 R1 R2 " #  t6 X R0 t6 R0 ¼ 4A¯ 6 ðR0 Þ ð231 cos6 u i  315 cos4 u i þ 105 cos2 ui  5Þ þ 16A¯ 6 ðR0 Þ Ri R3 i¼1;2 "  #  t 6 pffiffiffiffiffiffi R0 t6 R0 4 4 2 2 ¯ ¼ 6 14A6 ðR0 Þ ð11 cos u1  1Þsin u1  ð11 cos u 2  1Þsin u 2 R1 R2

B20 ¼ 4A2 ðR0 Þ B40 B44 B60 B64

(10)

R? = a/2 and R// = ZFc, where a and c are the lattice constants and ZF is the atomic position parameter of F ion [38–42]. For Tl2ZnF4 crystal studied, we have a  0.4105 nm (then R?  0.2053 nm) and c  1.410 nm [10–12,40], but the parameter ZF has not been reported. In fact, even if ZF of Tl2ZnF4 is known, the ZF for the impurity center may be unlike the corresponding value in the host crystal because of the size and/or charge mismatch. So we take the parameter ZF in Gd3+ center A as an adjustable parameter. The reference distance for this center is taken as R0 = R?. Thus, in the above formulas and hence in the energy matrix, we have four adjustable parameters A¯ 2 ðR0 Þ, A¯ 4 ðR0 Þ, A¯ 6 ðR0 Þ, and ZF. They (see

in which we take the reference distance R0 = R2  0.2903 nm. Thus, in the above formulas and hence in the energy matrix, there are five parameters A¯ 2 ðR0 Þ, A¯ 4 ðR0 Þ, A¯ 6 ðR0 Þ, ZA and DR left as adjustable parameters. By matching the calculated spin-Hamiltonian

Table 2 The intrinsic parameters A¯ k ðR0 Þ (in cm1) and the defect structural data of tetragonal centers A and B for Gd3+ ions in Tl2ZnF4 crystals.

Table 3 The crystal field parameters Bkq (in cm1) of tetragonal centers A and B for Gd3+ ions in Tl2ZnF4 crystals.

Center A Center B

A¯ 2 ðR0 Þ

A¯ 4 ðR0 Þ

A¯ 6 ðR0 Þ

ZF

ZA

DR (nm)

890 463

336 151

49 23

0.143 0.143

0.369

0.037

with  a 2 1=2 ð0:5  zA Þc ; u1 ¼ arccos R1 ¼ ð0:5  zA Þ2 c2 þ 2 R1 pffiffiffi 2 ; u2 ¼ 90 ; R3 ¼ ðzA  zF Þc  DR R2 ¼ 2

Center A Center B

(11)

B20

B40

B44

B60

B64

336 5165

10,022 3341

5622 –534

898 –1509

–1100 697

Y. Wei-Qing et al. / Journal of Fluorine Chemistry 153 (2013) 7–11

10

Table 4 The g factors and ZFS parameters bqk (in 104 cm1) of tetragonal centers A and B for Gd3+ ions in Tl2ZnF4 crystals.

Center A Calc. Expt. [12] Center B Calc. Expt. [12]

g ==

g?

b02

b04

b44

b06

b46

1.9918 1.992 (1)

1.9901 1.992 (1)

558.8 577.6 (5)

4.4 3.8 (1)

45.9 47.9 (5)

0.69 0.8 (1)

16.1 18.6 (2)

1.9918 1.992 (1)

1.9910 1.992 (1)

286.1 288.9(4)

1.7 1.1 (1)

35.1 36.3 (7)

0.45 0.4 (2)

5.2 2.0 (2)

parameters g//, g? and bqk of center B from the diagonalization method to the experimental values, the five adjustable parameters are determined and the results are listed in Table 2. Based on these parameters, the calculated CF parameters Bkq are given in Table 3. The calculated and experimental SH parameters for Gd3+ center B in Tl2ZnF4 crystals are listed in Table 4. 3. Discussion A number of SPM studies [14,15,33–37,41–43] of CF parameters Bkq for various rare earth ions in crystals indicate the trend: A¯ 2 ðR0 Þ > A¯ 4 ðR0 Þ > A¯ 6 ðR0 Þ. Our values of A¯ k ðR0 Þ for both tetragonal Gd3+ centers in Tl2ZnF4 crystals (see Table 2) follow this trend. In addition, since A¯ k ðR0 Þ  R0 tk [14,15], the larger the reference distance R0, the smaller the intrinsic parameter A¯ k ðR0 Þ for similar rare earth ion clusters. Thus, the smaller values of A¯ k ðR0 Þ in center B (with the larger reference distance R0) compared with those in center A can be understood. So, these intrinsic parameters can be regarded as rational. From the atomic parameter ZF (see Table 2), for center A, we obtain R// = ZFc  0.2016 nm and then R// < R?. So, the Gd3+ center A in Tl2ZnF4 crystal is a tetragonally-compressed octahedron. This is consistent with the cases of other trivalent paramagnetic impurities, e.g., Cr3+ and Fe3+, in Tl2ZnF4 crystals [10,11]. In these crystals, similar to the Gd3+ center A, Cr3+ and Fe3+ occupy substitutionally the octahedral Zn2+ sites. The negative signs of the observed ZFS parameter b02 ð¼ DÞ for both Cr3+ and Fe3+ centers in Tl2ZnF4 suggested that these impurity centers represent also tetragonally compressed octahedra [10,11,44]. So the defect model of Gd3+ center A [12] is suitable. The displacement of F DR > 0 shows that the F ion between the Gd3+ center B and Li+ (at Zn2+ site) indeed shifts far away from Li+ and hence toward Gd3+. This is due to the electrostatic interaction between F and Li+ caused by the negative effective charge of Li+ at Zn2+ site. So the defect model of center B [12] is in agreement with the expectation based on the electrostatic interaction and can be regarded as reasonable. Thus, defect models of both centers A and B for Gd3+ in Tl2ZnF4 crystals are confirmed and their defect structures are obtained. Based on the reasonable defect models and suitably matched parameters (intrinsic parameters A¯ k ðR0 Þ and defect structural data), the seven SH parameters g//, g?, b02 , b04 , b44 , b06 and b46 calculated by diagonalization method for both centers A and B of Gd3+ in Tl2ZnF4 crystals are in reasonable agreement with the experimental values (see Table 4). This suggests that the diagonalization (of energy matrix) method based on the one-electron CF mechanism is useful for calculations of SH parameters of 4f7 ions in crystals. The small disparities between the calculated and experimental SH parameters in Table 4 may be due to the following reasons: (i) The contributions to the SH parameters from the other CF mechanisms except the one-electron CF mechanism are omitted. (ii) The relations in Eqs. (2) and (3) are approximate because they are obtained from a second-order perturbation calculation and the higher order terms are neglected.

(iii) The small effect of the high-lying excited multiplets on the splittings of ground multiplet 8S7/2 is not considered. (iv) The small contribution to the SH parameters due to electron– phonon interaction [45–48] is not taken into account.

Because of the above approximations, the small disparities are comprehensible. The complete and exact calculation of SH parameters for Gd3+ (4f7) ions in crystals is very complex and beyond the scope of this paper. 4. Conclusions The spin-Hamiltonian parameters (g factors g//, g? and ZFS parameters b02 , b04 , b44 , b06 , b46 ) of two tetragonal Gd3+ centers A and B in layered perovskite fluoride Tl2ZnF4 crystals doped only with Gd3+ ion and co-doped with Gd3+ and Li+ have been calculated and explained reasonably using the diagonalization (of energy matrix) method based on the one-electron crystal-field mechanism. The calculations enable to predict the structures of both Gd3+ centers. Acknowledgments This work is supported by the National Basic Research Program of China (973 Program) under Grant No. 2011CB301705, National Natural Science Foundation of China (Nos. 51202023 and 11028409), the Postdoctoral National Natural Science Foundation of China (No. 2012M511917) and the Scientific Research Foundation of CUIT (Nos. KYTZ201208 and J201221).

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