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EPR zero-field splitting parameters and structural distortion study of Mn2+-doped (CH3)4NCdCl3 crystal in high-temperature phases
Chemical Physics Letters 426 (2006) 77–80 www.elsevier.com/locate/cplett
EPR zero-field splitting parameters and structural distortion study of Mn2+-doped (CH3)4NCdCl3 crystal in high-temperature phases Die Dong a, Kuang Xiao-Yu b
d
b,d,*
, Guo Jian-Jun a, Wang Hui b, Zhou Kang-Wei
c,d
a Institute of Applied Physics, Xihua University, Chengdu 610039, China Institute of Atomic and Molecular Physics, Sichuan University, Chengdu 610065, China c Department of Physics, Sichuan University, Chengdu 610065, China International Centre for Materials Physics, Academia Sinica, Shengyang 110016, China
Received 11 January 2006; in final form 12 April 2006 Available online 25 May 2006
Abstract The EPR zero-field splitting parameters and structural distortion of Mn2+-doped (CH3)4NCdCl3 crystal in high-temperature phases have been studied by diagonalizing the complete energy matrices. The zero-field splitting parameters D and (a F) are demonstrated to be negative and positive, respectively, and obtain a reasonable explanation together. Simultaneously, the distortion magnitude of local ˚ and Dh = 2.975 for T = 124 K; lattice structure around the Mn2+ ion in this crystal is determined, namely, DR = 0.13 A ˚ ˚ DR = 0.12 A and Dh = 2.610 for T = 297 K; DR = 0.26 A and Dh = 2.870 for T = 573 K. From the structural distortion, we deduce that a new structural phase transition should occur to the (CH3)4NCdCl3 crystal at temperatures ranging from 297 to 573 K. This is also in agreement with recent differential scanning calorimetric measurements. 2006 Elsevier B.V. All rights reserved.
1. Introduction The crystals with chemical formula (CH3)4NMX3, where M is a transition metal and X is a halogen, have fascinated many physicists and chemists due to the quasi-ideal one-dimensional magnetic and thermal properties [1–12]. The basic structural features of these crystals are that infinite linear chains of face-sharing [MX6]4 octahedra are arrayed along the hexagonal c axis, and the (CH3)4N]+ cations occupy the space between the linear chains. In order to understand the influence of material structure on its properties, the (CH3)4NCdCl3 crystal as a representative of the family has been studied extensively [3–12]. The EPR investigation of (CH3)4NCdCl3:Mn2+ system which is regarded as the magnetically diluted (CH3)4NMnCl3-type systems has been performed in the 77–573 K temperature range * Corresponding author. Address: Institute of Atomic and Molecular Physics, Sichuan University, Chengdu 610065, China. E-mail addresses: [email protected] (D. Die), [email protected] (X.-Y. Kuang).
0009-2614/$ - see front matter 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2006.05.068
[11]. It is shown that the Mn2+ ion substitutes for host Cd2+ ion whose site has a C3i symmetry for above 118 K and a Ci or C1 symmetry for below 118 K. At the same time, the relative signs and absolute values of zero-field splitting parameters, D and (a F), were determined. For the (CH3)4NCdCl3:Mn2+ system, Edgar et al. pointed out that the parameter D should be positive and an ab initio calculation based on the crystal-field theory is not capable of providing a reasonable explanation for it [12]. In addition, their calculated result based on the empirical superposition model still has a quite large departure from the positive experimental findings. Up to now, the zero-field splitting parameters, D and (a F), of Mn2+ ion in (CH3)4NCdCl3:Mn2+ system have not got a reasonable interpretation. In general, the radius of Mn2+ ion is smaller than that of Cd2+ ion. The local lattice structure around Mn2+ ion in (CH3)4NCdCl3:Mn2+ system should be different from that of Cd2+ ion in (CH3)4NCdCl3 crystal. On the other hand, the EPR zero-field splitting parameters are extremely sensitive to the structural changes around the paramagnetic ion, and these parameters may help us to
78
D. Die et al. / Chemical Physics Letters 426 (2006) 77–80 2
Eð1=2Þ ¼ D=3 ða F Þ=2 ½ð18D þ a F Þ þ 80a2 Eð3=2Þ ¼ 2D=3 þ ða F Þ;
1=2
obtain the information of structural distortion and dynamic aspects about crystalline state. Therefore, in this Letter, the EPR zero-field splitting parameters and structural distortion of Mn2+ in the (CH3)4NCdCl3 crystal in high-temperature phases above 118 K will be studied simultaneously with the use of the complete energy matrices for a d5 configuration ion in a trigonal ligand field, and a previously unknown phase transition is predicted to occur.
So, the ground-state zero-field splitting energies, DE1 and DE2, may be expressed as a function of the EPR parameters a, D, and (a F) [17]
2. Theory
DE1 ¼ Eð5=2Þ Eð1=2Þ ¼ ½ð18D þ a F Þ2 þ 80a2 1=2 =3;
=6;
Eð5=2Þ ¼ D=3 ða F Þ=2 ½ð18D þ a F Þ2 þ 80a2 1=2 =6: ð4Þ
DE2 ¼ Eð3=2Þ Eð1=2Þ ¼ 3ða F Þ=2 D The method of diagonalizing complete energy matrix has been confirmed to be a powerful tool in the studies of EPR zero-field splitting parameters and local lattice structure [13–15]. For a d5-configuration ion in a ligand field with C3 symmetry, the complete energy matrix, which is composed of three 84 · 84 diagonal blocks corresponding to the irreducible representations C4(C5) and C6 of the C 3 double group, has been constructed in terms of the perturbation Hamiltonian [13,15] X X X ^ ¼ H e2 =ri;j þ f li s i þ V i; ð1Þ i
i
i
where the first, second and third terms represent, respectively, the electron–electron repulsion energy, the spinorbit coupling energy and the ligand-field potential energy. The matrix elements are the function of the Racah parameters B and C, Racah-Trees correction a, seniority correction b, the spin-orbit coupling coefficient f, and the ligand-field parameters ðB20 ; B40 ; Bc43 ; Bs43 Þ. For the (CH3)4NCdCl3:Mn2+ system in high-temperature phase, the local lattice structure around the Mn2+ ion has a C3i symmetry. Based on the point charge and superposition model, the ligand-field parameter Bs43 will vanish and the rests can be derived as [15] B20 ¼ ð3e2 hr2 i=R3 Þð3 cos2 h 1Þ; 2
4
5
4
ð2Þ
where R and h represent, respectively, the Mn2+–Cl distance and the angle between Mn2+–Cl direction and C3 axis. The EPR spectra of Mn2+ (3d5, S = 5/2) ion in a trigonal ligand field may be described by the following spin Hamiltonian [16] pffiffiffi ^ S ¼ gbH ~ ~ H S þ ð 2a=36Þ½S 2z ðS 3þ þ S 3 Þ þ ðS 3þ þ S 3 ÞS 2z þ DS 2z þ ½ða F Þ=180 ð3Þ
where the a, D and (a F) are EPR zero-field splitting parameters. From Eq. (3) the energy level splittings in the ground state 6A1 for a zero magnetic field are given as
1=2
=6; ð5Þ
where the signs ‘+’ and ‘’ correspond to D P 0 and D < 0, respectively. For the Mn2+ ion in (CH3)4NCdCl3 crystal, the parameter a is quite insignificant and may be neglected. Moreover, Kuang had shown that the parameters D and (a F) are nearly independent of the parameter a [18], and Yu had also given the expressions of the EPR parameters a, D, and F by using high order perturbation method [19] pffiffiffi a ¼ 3W ð5=2; 1=2Þ=2 5; D ¼ ½5W ð5=2; 5=2Þ W ð3=2; 3=2Þ 4W ð1=2; 1=2Þ=28; pffiffiffi F ¼ 3W ð5=2; 1=2Þ=2 5 þ 3½W ð5=2; 5=2Þ þ 2W ð1=2; 1=2Þ 3W ð3=2; 3=2Þ=14; ð6Þ where W ðM S ; M 0S Þ denotes perturbation matrix elements. From Eq. (6), it is evident that the parameter (a F) is not related to cubic parameter a. Hence, the EPR zero-field splitting parameters, D and (a F), can be determined by the following formulae [18] 6D þ ða F Þ=3 ¼ DE1 ;
2
B40 ¼ ð3e hr i=4R Þð35 cos h 30 cos h þ 3Þ; pffiffiffiffiffi Bc43 ¼ ð3 35e2 hr4 i=2R5 Þ sin3 h cos h;
ð35S 4z 475S 2z =2Þ;
2
½ð18D þ a F Þ þ 80a2
2D þ 5ða F Þ=3 ¼ DE2 ;
ð7Þ
where DE1 and DE2 can be obtained by diagonalizing the complete energy matrices. 3. Calculations The (CH3)4NCdCl3 crystal at room temperature possesses a hexagonal structure with the space group P63/m and Z = 2 formula units per unit cell. When Mn2+ ions are doped in the (CH3)4NCdCl3 crystal, the Mn2+ ions will substitute for the host Cd2+ ions. The Mn2+ ion is surrounded by six negative univalent chlorine ions. According to the covalence theory of Curie et al. [20], the Racah parameters B and C, Racah-Trees correction a, seniority correction b, and the spin-orbit coupling coefficient f are related to the free-ion parameters B0, C0, a0, b0, and f0, and the relations are
D. Die et al. / Chemical Physics Letters 426 (2006) 77–80
B ¼ B 0 N 4 ; C ¼ C 0 N 4 ; a ¼ a 0 N 4 ; b ¼ b0 N 4 ; f ¼ f 0 N 2 ;
ð8Þ
where N is the average covalency factor. The free-ion parameter values for the Mn2+ ion have been gotten as: B0 = 918 cm1, C0 = 3273 cm1, a0 = 65 cm1, b0 = 131 cm1, and f0 = 347 cm1 [21]. With regard to Mn2+ ion in the (CH3)4NCdCl3:Mn2+ system, the optical spectra data have not been reported. But, it is well known that the energy levels, 4A1(4G) and 4E(4G), of Mn2+ ion in complex are independent of the ligand-field parameters ðB20 ; B40 ; Bc43 Þ [20]. Thus, the parameters B, C, a, b, and f of Mn2+ ion in (CH3)4NCdCl3:Mn2+ system can be estimate by employing the energy levels, 4A1(4G) and 4E(4G), of Mn2+ ion in MnCl2 crystal [22], and their values corresponding to N = 0.969 are determined on the basis of the complete energy matrices. The electronic configuration and radius of Mn2+ ion are obviously different from those of Cd2+ ion. The local lattice structure around Mn2+ ion in (CH3)4NCdCl3: Mn2+ system should exhibit a distortion from that of Cd2+ ion in ˚ and (CH3)4NCdCl3 crystal. If one uses R0 = 2.644 A 2+ h0 = 50.53 [23] to denote the Cd –Cl bond length and the angle between Cd2+–Cl bond and the C3 axis, respectively, the local structure parameters R and h for the Mn2+ ion replaced the host Cd2+ ion can be written as R ¼ R0 þ DR;
ð9Þ
h ¼ h0 þ Dh;
where DR and Dh describe the distortion of bond length and bond angle. By using the above average covalency factor N, the radial expectation values of Ær2æ and Ær4æ for Mn2+ ion in (CH3)4NCdCl3:Mn2+ system are obtained as: hr2 i ¼ hr2 i0 N 2 ¼ 2:6061 a:u:
ð10Þ
hr4 i ¼ hr4 i0 N 2 ¼ 21:8397 a:u:
where Ær2æ0 = 2.7755 a.u. and Ær4æ0 = 23.2594 a.u. are the values of free Mn2+ ion [24]. Consequently, the ligand-field parameters ðB20 ; B40 ; Bc43 Þ in Eq. (2) become only the function of distortion parameters DR and Dh. By using the Eq. (7) and our complete energy matrices, the EPR zero-
79
field splitting parameters D and (a F) can be simulated with the use of the parameters DR and Dh. For the (CH3)4NCdCl3:Mn2+ system in high-temperature phase, the absolute signs of zero-field splitting parameters D and (a F) are still indefinite. Whereas, their relative signs had been established [11], i.e. if D > 0, then (a F) < 0 or if D < 0, then (a F) > 0. So, the parameters D and (a F) measured at 124, 297, 573 K may be studied by considering D > 0 and D < 0. When the D < 0 and (a F) > 0 are taken, the D and (a F) as the function of DR and Dh are calculated by diagonalizing the complete energy matrices. The calculated results are given in Table 1. It can be seen from Table 1 that the calculated values are in good agreement with the experimental findings. The DR < 0 means that local lattice structure around the Mn2+ ion in (CH3)4NCdCl3:Mn2+ system has a compressed structural distortion. This may be ascribed to the fact that the ˚ ) is smaller than that of radius of Mn2+ ion (R = 0.80 A 2+ ˚ Cd ion (R = 0.97 A) [25]. Oppositely, when the D > 0 and (a F) < 0 are supposed, in any case, the D and (a F) can’t always get a unified interpretation. The calculated results, especially (a F), deviate far from the experimental findings. Furthermore, the parameter DR must be a positive and large number. This indicates that the local lattice structure around Mn2+ ion in this crystal has a big expansion distortion, which is in contradiction with the size of Mn2+ and Cd2+ ions. Therefore, the zero-field splitting parameters, D and (a F), should be negative and positive, respectively. Simultaneously, these parameters get a satisfactory explanation, and the structural distortions of the linear chains ½–Cd–Cl 3 n in the ˚ , Dh = 2.975 high-temperature phases, i.e. DR = 0.13 A ˚ , Dh = 2.610 for T = for T = 124 K, and DR = 0.12 A ˚ , Dh = 2.870 for T = 573 K, 297 K, and DR = 0.26 A are determined. As a rule, the local lattice structure around the Mn2+ ion in crystal has a thermal expansion when the temperature increases [26]. Nevertheless, it is clear from our calculated results that the distortion magnitude at 573 K, whose
Table 1 The EPR zero-field splitting parameters, D and (a F), for the Mn2+ ion in (CH3)4NCdCl3:Mn2+ system as a function of DR and Dh ˚) DR (A Dh () 104DE1 (cm1) 104DE2 (cm1) 104D (cm1) 104(a F) (cm1) T = 124 K
0 0 0 0.13 0.13 0.13 0.26 0.26 0.26 Experiment [11]
2.379 2.579 2.779 2.775 2.975 3.175 3.124 3.324 3.524
217.6 191.4 166.4 225.2 191.3 158.9 236.9 191.3 146.1
71.1 62.1 54.0 72.7 61.2 50.7 75.2 60.0 45.0
36.3 32.0 27.8 37.6 32.0 26.6 39.6 32.0 24.5 32.0
0.9 1.1 0.9 1.5 1.6 1.5 2.4 2.4 2.4 1.7
T = 297 K
0.12 Experiment [11]
2.610
247.1
79.9
41.3 41.4
1.6 1.7
T = 573 K
0.26 Experiment [11]
2.870
296.3
94.7
49.5 49.6
2.6 2.7
80
D. Die et al. / Chemical Physics Letters 426 (2006) 77–80
absolute values are expected to be smaller than those at 124 and 297 K, has a significantly anomalous change. This implies that a new structural phase transition of the (CH3)4NCdCl3 crystal will taken place when the temperature varies from 297 to 573 K. Recently, the new phase transition at about T = 400 K has been found to be of second order, and the phase transition mechanism has not been interpreted entirely so far [7,10]. This present work is also useful to gain a better insight into the phase transition mechanism of these materials. 4. Conclusion The EPR zero-field splitting parameters and structural distortion of Mn2+-doped (CH3)4NCdCl3 crystal in hightemperature phases have been studied on the basis of the complete energy matrices for a d5 configuration ion in a trigonal ligand field. The parameters, D and (a F), are proved to be negative and positive, respectively, and get a satisfactory explanation together. Simultaneously, the distortion magnitude of local lattice structure around ˚ and the Mn2+ ion is determined, that is, DR = 0.13 A ˚ Dh = 2.975 for T = 124 K; DR = 0.12 A and ˚ and Dh = Dh = 2.610 for T = 297 K; DR = 0.26 A 2.870 for T = 573 K. Considering the structural distortion, we conclude that a new structural phase transition should occur to the (CH3)4NCdCl3 crystal at temperatures ranging from 297 to 573 K. The result is also in accord with recent differential scanning calorimetric measurements [10]. Acknowledgements This project was supported by National Natural Science Foundation of China (No. 10374068) and by the Doctoral Education Fund of Education Ministry of China (No. 20050610011).
References [1] J.L. Musfeldt, M. Poirier, S. Jandl, J.P. Renard, J. Chem. Phys. 100 (1994) 7677. [2] L. Allam, G. Ablart, J. Pescia, S. Cle´ment, J.P. Renard, Phys. Rev. B 40 (1989) 8654. [3] A. Paduan-Filho, N.F. Oliveira Jr., V. Bindilatti, S. Foner, Y. Shapira, Phys. Rev. B 68 (2003) 224417. [4] S. Mulla-Osman, D. Michel, G. Vo¨lkel, I. Peral, G. Madariaga, J. Phys.: Condens. Matter 13 (2001) 1119. [5] T. Breczewski, I. Peral, G. Madariaga, Eur. Phys. J. B 19 (2001) 171. [6] I. Peral, G. Madariaga, A. Pe´rez-Etxebarria, T. Breczewski, Acta Crystallogr. B 56 (2000) 215. [7] S. Mulla-Osman, D. Michel, Z. Czapla, W.D. Hoffmann, J. Phys.: Condens. Matter 10 (1998) 2465. ´ az-Herna´ndez, G. Aguirre-Zamalloa, A. Lo´pez-Echarri, I. Ruiz[8] J. Dı Larrea, T. Breczewski, M.J. Tello, J. Phys.: Condens. Matter 9 (1997) 3399. [9] J.T. Yu, K.T. Liu, Y.H. Jeng, Solid State Commun. 89 (1994) 543. [10] M.N. Braud, M. Couzi, N.B. Chanh, C. Courseille, B. Gallois, C. Hauw, A. Meresse, J. Phys.: Condens. Matter 2 (1990) 8209. [11] G.L. Mcpherson, L.M. Henling, R.C. Koch, H.F. Quarls, Phys. Rev. B 16 (1977) 1893. [12] A. Edgar, E. Siegel, W. Urban, J. Phys. C: Solid State Phys. 13 (1980) 6649. [13] X.Y. Kuang, Phys. Rev. B 36 (1987) 797. [14] K.W. Zhou, S.B. Zhao, Y.M. Ning, Phys. Rev. B 43 (1991) 3712. [15] D. Die, X.Y. Kuang, J.J. Guo, H. Wang, K.W. Zhou, Phys. Rev. B 72 (2005) 073101. [16] J. Kreissl, W. Gehlhoff, P. Omling, P. Emanuelsson, Phys. Rev. B 42 (1990) 1731. [17] A. Abragam, B. Bleaney, Electron Paramagnetic Resonance of Transition Ions, Oxford University Press, London, 1986. [18] X.Y. Kuang, Phys. Rev. B 36 (1987) 712. [19] W.L. Yu, Chin. Sci. Bull. 38 (1993) 1283. [20] D. Curie, C. Barthon, B. Canny, J. Chem. Phys. 61 (1974) 3048. [21] X.Y. Kuang, W. Zhang, M.B. Ire`ne, Phys. Rev. B 45 (1992) 8104. [22] J.S. Griffith, The Theory of Transition-Metal Ions, Cambrige University Press, Cambrige, 1964. [23] B. Morosin, Acta Crystallogr. B 28 (1972) 2303. [24] M.G. Zhao, G.R. Bai, H.C. Jin, J. Phys. C: Solid State Phys. 18 (1982) 5959. [25] X.Z. Cao, T.Y. Song, X.Q. Wang, Inorganic Chemistry, High Educational Press, China, 1997. [26] F. Rodrı´guez, M. Moreno, J. Phys. C: Solid State Phys. 19 (1986) L513.
EPR zero-field splitting parameters and structural distortion study of Mn2+-doped (CH3)4NCdCl3 crystal in high-temperature phases Die Dong a, Kuang Xiao-Yu b
d
b,d,*
, Guo Jian-Jun a, Wang Hui b, Zhou Kang-Wei
c,d
a Institute of Applied Physics, Xihua University, Chengdu 610039, China Institute of Atomic and Molecular Physics, Sichuan University, Chengdu 610065, China c Department of Physics, Sichuan University, Chengdu 610065, China International Centre for Materials Physics, Academia Sinica, Shengyang 110016, China
Received 11 January 2006; in final form 12 April 2006 Available online 25 May 2006
Abstract The EPR zero-field splitting parameters and structural distortion of Mn2+-doped (CH3)4NCdCl3 crystal in high-temperature phases have been studied by diagonalizing the complete energy matrices. The zero-field splitting parameters D and (a F) are demonstrated to be negative and positive, respectively, and obtain a reasonable explanation together. Simultaneously, the distortion magnitude of local ˚ and Dh = 2.975 for T = 124 K; lattice structure around the Mn2+ ion in this crystal is determined, namely, DR = 0.13 A ˚ ˚ DR = 0.12 A and Dh = 2.610 for T = 297 K; DR = 0.26 A and Dh = 2.870 for T = 573 K. From the structural distortion, we deduce that a new structural phase transition should occur to the (CH3)4NCdCl3 crystal at temperatures ranging from 297 to 573 K. This is also in agreement with recent differential scanning calorimetric measurements. 2006 Elsevier B.V. All rights reserved.
1. Introduction The crystals with chemical formula (CH3)4NMX3, where M is a transition metal and X is a halogen, have fascinated many physicists and chemists due to the quasi-ideal one-dimensional magnetic and thermal properties [1–12]. The basic structural features of these crystals are that infinite linear chains of face-sharing [MX6]4 octahedra are arrayed along the hexagonal c axis, and the (CH3)4N]+ cations occupy the space between the linear chains. In order to understand the influence of material structure on its properties, the (CH3)4NCdCl3 crystal as a representative of the family has been studied extensively [3–12]. The EPR investigation of (CH3)4NCdCl3:Mn2+ system which is regarded as the magnetically diluted (CH3)4NMnCl3-type systems has been performed in the 77–573 K temperature range * Corresponding author. Address: Institute of Atomic and Molecular Physics, Sichuan University, Chengdu 610065, China. E-mail addresses: [email protected] (D. Die), [email protected] (X.-Y. Kuang).
0009-2614/$ - see front matter 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2006.05.068
[11]. It is shown that the Mn2+ ion substitutes for host Cd2+ ion whose site has a C3i symmetry for above 118 K and a Ci or C1 symmetry for below 118 K. At the same time, the relative signs and absolute values of zero-field splitting parameters, D and (a F), were determined. For the (CH3)4NCdCl3:Mn2+ system, Edgar et al. pointed out that the parameter D should be positive and an ab initio calculation based on the crystal-field theory is not capable of providing a reasonable explanation for it [12]. In addition, their calculated result based on the empirical superposition model still has a quite large departure from the positive experimental findings. Up to now, the zero-field splitting parameters, D and (a F), of Mn2+ ion in (CH3)4NCdCl3:Mn2+ system have not got a reasonable interpretation. In general, the radius of Mn2+ ion is smaller than that of Cd2+ ion. The local lattice structure around Mn2+ ion in (CH3)4NCdCl3:Mn2+ system should be different from that of Cd2+ ion in (CH3)4NCdCl3 crystal. On the other hand, the EPR zero-field splitting parameters are extremely sensitive to the structural changes around the paramagnetic ion, and these parameters may help us to
78
D. Die et al. / Chemical Physics Letters 426 (2006) 77–80 2
Eð1=2Þ ¼ D=3 ða F Þ=2 ½ð18D þ a F Þ þ 80a2 Eð3=2Þ ¼ 2D=3 þ ða F Þ;
1=2
obtain the information of structural distortion and dynamic aspects about crystalline state. Therefore, in this Letter, the EPR zero-field splitting parameters and structural distortion of Mn2+ in the (CH3)4NCdCl3 crystal in high-temperature phases above 118 K will be studied simultaneously with the use of the complete energy matrices for a d5 configuration ion in a trigonal ligand field, and a previously unknown phase transition is predicted to occur.
So, the ground-state zero-field splitting energies, DE1 and DE2, may be expressed as a function of the EPR parameters a, D, and (a F) [17]
2. Theory
DE1 ¼ Eð5=2Þ Eð1=2Þ ¼ ½ð18D þ a F Þ2 þ 80a2 1=2 =3;
=6;
Eð5=2Þ ¼ D=3 ða F Þ=2 ½ð18D þ a F Þ2 þ 80a2 1=2 =6: ð4Þ
DE2 ¼ Eð3=2Þ Eð1=2Þ ¼ 3ða F Þ=2 D The method of diagonalizing complete energy matrix has been confirmed to be a powerful tool in the studies of EPR zero-field splitting parameters and local lattice structure [13–15]. For a d5-configuration ion in a ligand field with C3 symmetry, the complete energy matrix, which is composed of three 84 · 84 diagonal blocks corresponding to the irreducible representations C4(C5) and C6 of the C 3 double group, has been constructed in terms of the perturbation Hamiltonian [13,15] X X X ^ ¼ H e2 =ri;j þ f li s i þ V i; ð1Þ i
i
i
where the first, second and third terms represent, respectively, the electron–electron repulsion energy, the spinorbit coupling energy and the ligand-field potential energy. The matrix elements are the function of the Racah parameters B and C, Racah-Trees correction a, seniority correction b, the spin-orbit coupling coefficient f, and the ligand-field parameters ðB20 ; B40 ; Bc43 ; Bs43 Þ. For the (CH3)4NCdCl3:Mn2+ system in high-temperature phase, the local lattice structure around the Mn2+ ion has a C3i symmetry. Based on the point charge and superposition model, the ligand-field parameter Bs43 will vanish and the rests can be derived as [15] B20 ¼ ð3e2 hr2 i=R3 Þð3 cos2 h 1Þ; 2
4
5
4
ð2Þ
where R and h represent, respectively, the Mn2+–Cl distance and the angle between Mn2+–Cl direction and C3 axis. The EPR spectra of Mn2+ (3d5, S = 5/2) ion in a trigonal ligand field may be described by the following spin Hamiltonian [16] pffiffiffi ^ S ¼ gbH ~ ~ H S þ ð 2a=36Þ½S 2z ðS 3þ þ S 3 Þ þ ðS 3þ þ S 3 ÞS 2z þ DS 2z þ ½ða F Þ=180 ð3Þ
where the a, D and (a F) are EPR zero-field splitting parameters. From Eq. (3) the energy level splittings in the ground state 6A1 for a zero magnetic field are given as
1=2
=6; ð5Þ
where the signs ‘+’ and ‘’ correspond to D P 0 and D < 0, respectively. For the Mn2+ ion in (CH3)4NCdCl3 crystal, the parameter a is quite insignificant and may be neglected. Moreover, Kuang had shown that the parameters D and (a F) are nearly independent of the parameter a [18], and Yu had also given the expressions of the EPR parameters a, D, and F by using high order perturbation method [19] pffiffiffi a ¼ 3W ð5=2; 1=2Þ=2 5; D ¼ ½5W ð5=2; 5=2Þ W ð3=2; 3=2Þ 4W ð1=2; 1=2Þ=28; pffiffiffi F ¼ 3W ð5=2; 1=2Þ=2 5 þ 3½W ð5=2; 5=2Þ þ 2W ð1=2; 1=2Þ 3W ð3=2; 3=2Þ=14; ð6Þ where W ðM S ; M 0S Þ denotes perturbation matrix elements. From Eq. (6), it is evident that the parameter (a F) is not related to cubic parameter a. Hence, the EPR zero-field splitting parameters, D and (a F), can be determined by the following formulae [18] 6D þ ða F Þ=3 ¼ DE1 ;
2
B40 ¼ ð3e hr i=4R Þð35 cos h 30 cos h þ 3Þ; pffiffiffiffiffi Bc43 ¼ ð3 35e2 hr4 i=2R5 Þ sin3 h cos h;
ð35S 4z 475S 2z =2Þ;
2
½ð18D þ a F Þ þ 80a2
2D þ 5ða F Þ=3 ¼ DE2 ;
ð7Þ
where DE1 and DE2 can be obtained by diagonalizing the complete energy matrices. 3. Calculations The (CH3)4NCdCl3 crystal at room temperature possesses a hexagonal structure with the space group P63/m and Z = 2 formula units per unit cell. When Mn2+ ions are doped in the (CH3)4NCdCl3 crystal, the Mn2+ ions will substitute for the host Cd2+ ions. The Mn2+ ion is surrounded by six negative univalent chlorine ions. According to the covalence theory of Curie et al. [20], the Racah parameters B and C, Racah-Trees correction a, seniority correction b, and the spin-orbit coupling coefficient f are related to the free-ion parameters B0, C0, a0, b0, and f0, and the relations are
D. Die et al. / Chemical Physics Letters 426 (2006) 77–80
B ¼ B 0 N 4 ; C ¼ C 0 N 4 ; a ¼ a 0 N 4 ; b ¼ b0 N 4 ; f ¼ f 0 N 2 ;
ð8Þ
where N is the average covalency factor. The free-ion parameter values for the Mn2+ ion have been gotten as: B0 = 918 cm1, C0 = 3273 cm1, a0 = 65 cm1, b0 = 131 cm1, and f0 = 347 cm1 [21]. With regard to Mn2+ ion in the (CH3)4NCdCl3:Mn2+ system, the optical spectra data have not been reported. But, it is well known that the energy levels, 4A1(4G) and 4E(4G), of Mn2+ ion in complex are independent of the ligand-field parameters ðB20 ; B40 ; Bc43 Þ [20]. Thus, the parameters B, C, a, b, and f of Mn2+ ion in (CH3)4NCdCl3:Mn2+ system can be estimate by employing the energy levels, 4A1(4G) and 4E(4G), of Mn2+ ion in MnCl2 crystal [22], and their values corresponding to N = 0.969 are determined on the basis of the complete energy matrices. The electronic configuration and radius of Mn2+ ion are obviously different from those of Cd2+ ion. The local lattice structure around Mn2+ ion in (CH3)4NCdCl3: Mn2+ system should exhibit a distortion from that of Cd2+ ion in ˚ and (CH3)4NCdCl3 crystal. If one uses R0 = 2.644 A 2+ h0 = 50.53 [23] to denote the Cd –Cl bond length and the angle between Cd2+–Cl bond and the C3 axis, respectively, the local structure parameters R and h for the Mn2+ ion replaced the host Cd2+ ion can be written as R ¼ R0 þ DR;
ð9Þ
h ¼ h0 þ Dh;
where DR and Dh describe the distortion of bond length and bond angle. By using the above average covalency factor N, the radial expectation values of Ær2æ and Ær4æ for Mn2+ ion in (CH3)4NCdCl3:Mn2+ system are obtained as: hr2 i ¼ hr2 i0 N 2 ¼ 2:6061 a:u:
ð10Þ
hr4 i ¼ hr4 i0 N 2 ¼ 21:8397 a:u:
where Ær2æ0 = 2.7755 a.u. and Ær4æ0 = 23.2594 a.u. are the values of free Mn2+ ion [24]. Consequently, the ligand-field parameters ðB20 ; B40 ; Bc43 Þ in Eq. (2) become only the function of distortion parameters DR and Dh. By using the Eq. (7) and our complete energy matrices, the EPR zero-
79
field splitting parameters D and (a F) can be simulated with the use of the parameters DR and Dh. For the (CH3)4NCdCl3:Mn2+ system in high-temperature phase, the absolute signs of zero-field splitting parameters D and (a F) are still indefinite. Whereas, their relative signs had been established [11], i.e. if D > 0, then (a F) < 0 or if D < 0, then (a F) > 0. So, the parameters D and (a F) measured at 124, 297, 573 K may be studied by considering D > 0 and D < 0. When the D < 0 and (a F) > 0 are taken, the D and (a F) as the function of DR and Dh are calculated by diagonalizing the complete energy matrices. The calculated results are given in Table 1. It can be seen from Table 1 that the calculated values are in good agreement with the experimental findings. The DR < 0 means that local lattice structure around the Mn2+ ion in (CH3)4NCdCl3:Mn2+ system has a compressed structural distortion. This may be ascribed to the fact that the ˚ ) is smaller than that of radius of Mn2+ ion (R = 0.80 A 2+ ˚ Cd ion (R = 0.97 A) [25]. Oppositely, when the D > 0 and (a F) < 0 are supposed, in any case, the D and (a F) can’t always get a unified interpretation. The calculated results, especially (a F), deviate far from the experimental findings. Furthermore, the parameter DR must be a positive and large number. This indicates that the local lattice structure around Mn2+ ion in this crystal has a big expansion distortion, which is in contradiction with the size of Mn2+ and Cd2+ ions. Therefore, the zero-field splitting parameters, D and (a F), should be negative and positive, respectively. Simultaneously, these parameters get a satisfactory explanation, and the structural distortions of the linear chains ½–Cd–Cl 3 n in the ˚ , Dh = 2.975 high-temperature phases, i.e. DR = 0.13 A ˚ , Dh = 2.610 for T = for T = 124 K, and DR = 0.12 A ˚ , Dh = 2.870 for T = 573 K, 297 K, and DR = 0.26 A are determined. As a rule, the local lattice structure around the Mn2+ ion in crystal has a thermal expansion when the temperature increases [26]. Nevertheless, it is clear from our calculated results that the distortion magnitude at 573 K, whose
Table 1 The EPR zero-field splitting parameters, D and (a F), for the Mn2+ ion in (CH3)4NCdCl3:Mn2+ system as a function of DR and Dh ˚) DR (A Dh () 104DE1 (cm1) 104DE2 (cm1) 104D (cm1) 104(a F) (cm1) T = 124 K
0 0 0 0.13 0.13 0.13 0.26 0.26 0.26 Experiment [11]
2.379 2.579 2.779 2.775 2.975 3.175 3.124 3.324 3.524
217.6 191.4 166.4 225.2 191.3 158.9 236.9 191.3 146.1
71.1 62.1 54.0 72.7 61.2 50.7 75.2 60.0 45.0
36.3 32.0 27.8 37.6 32.0 26.6 39.6 32.0 24.5 32.0
0.9 1.1 0.9 1.5 1.6 1.5 2.4 2.4 2.4 1.7
T = 297 K
0.12 Experiment [11]
2.610
247.1
79.9
41.3 41.4
1.6 1.7
T = 573 K
0.26 Experiment [11]
2.870
296.3
94.7
49.5 49.6
2.6 2.7
80
D. Die et al. / Chemical Physics Letters 426 (2006) 77–80
absolute values are expected to be smaller than those at 124 and 297 K, has a significantly anomalous change. This implies that a new structural phase transition of the (CH3)4NCdCl3 crystal will taken place when the temperature varies from 297 to 573 K. Recently, the new phase transition at about T = 400 K has been found to be of second order, and the phase transition mechanism has not been interpreted entirely so far [7,10]. This present work is also useful to gain a better insight into the phase transition mechanism of these materials. 4. Conclusion The EPR zero-field splitting parameters and structural distortion of Mn2+-doped (CH3)4NCdCl3 crystal in hightemperature phases have been studied on the basis of the complete energy matrices for a d5 configuration ion in a trigonal ligand field. The parameters, D and (a F), are proved to be negative and positive, respectively, and get a satisfactory explanation together. Simultaneously, the distortion magnitude of local lattice structure around ˚ and the Mn2+ ion is determined, that is, DR = 0.13 A ˚ Dh = 2.975 for T = 124 K; DR = 0.12 A and ˚ and Dh = Dh = 2.610 for T = 297 K; DR = 0.26 A 2.870 for T = 573 K. Considering the structural distortion, we conclude that a new structural phase transition should occur to the (CH3)4NCdCl3 crystal at temperatures ranging from 297 to 573 K. The result is also in accord with recent differential scanning calorimetric measurements [10]. Acknowledgements This project was supported by National Natural Science Foundation of China (No. 10374068) and by the Doctoral Education Fund of Education Ministry of China (No. 20050610011).
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