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Study of EPR zero-field splitting of iron–sulfur clusters in tetrahedral ZnS:FeIII system
Physica B 325 (2003) 184–188
Study of EPR zero-field splitting of iron–sulfur clusters in tetrahedral ZnS:FeIII system$ Die Donga, Kuang Xiao-Yua,b,*, Lu Weia, Zhou Kang-Weib,c,d a
Institute of Atomic and Molecular Physics, Sichuan University, Chengdu 610065, China International Centre for Materials Physics, Academia Sinica, Shenyang 110015, China c Department of Physics, Sichuan University, Chengdu 610065, China d CCAST(World Laboratory), Box 8730, Beijing 100080, China
b
Received 16 April 2002
Abstract The EPR zero-field splitting of the iron–sulfur cluster in the ZnS:FeIII system has been studied on the basis of the energy matrix for the electron–electron repulsion, the ligand–field and the spin–orbit coupling of a d5 configuration ion with a trigonal symmetry. It is demonstrated that in order to reasonably explain the EPR zero-field splitting parameters a; D and (a F ), a positive ligand–field strength Dq for a d5 electron configuration ion in a tetrahedron has to be employed. This means that the effective charge of each sulfur ion in ZnS is positive. This unusual result leads to the conclusion that in ZnS each sulfur ion may occur a quadricovalent argon state S2+ with sp3 hybrid configuration and this conclusion is in accord with Pauling’s speculation. r 2002 Elsevier Science B.V. All rights reserved. Keywords: Electron-paramagnetic resonance; Ligand–field theory
The electronic and magnetic properties of iron– sulfur clusters in complexes have been received extensive interest in the last decades. Recently, the interest has been intensified since some iron–sulfur clusters were found in the active sites of metalloproteins such as oxidized ferredoxin [1]. The iron– sulfur clusters usually play an important role for the electron exchange and electron transfer in metalloproteins. In understanding the characteristic of iron–sulfur clusters in complexes, each $
This project was supported by National Natural Science Foundation of China. *Corresponding author. Institute of Atomic and Molecular Physics, Sichuan University, Chengdu 610065, China. E-mail address: [email protected] (K. Xiao-Yu).
sulfur ion is usually treated as an anion S2. This treatment seems suitable for sulfur ions in most complexes. However, for the iron–sulfur clusters in ZnS:FeIII, we found by the analysis of the EPR spectra that if each sulfur ion is treated as an anion S2 in the calculations, the theoretical value of EPR parameter a will deviate far from the experimental finding. Up to now, the EPR zerofield splitting parameters a; D and (a F ) for iron–sulfur clusters in the ‘‘hexagonal’’ ZnS:FeIII have not yet been understood [2]. In the present work, we will show that a reasonable calculation result of the EPR spectra for the iron–sulfur clusters in ZnS:FeIII may be obtained by using a positive ligand–field strength Dq for the d5 electron configuration FeIII ion in the tetrahedron.
0921-4526/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 0 2 ) 0 1 5 2 1 - 1
D. Dong et al. / Physica B 325 (2003) 184–188
This positivity of Dq means that the effective charge of sulfur ions in ZnS is positive. This unusual result will support Pauling’s speculation that each of the sulfur ions in ZnS may be looked upon as an electron donor that forms a quadricovalent argon state of S2+ with sp3 hybrid configuration [3]. It is well known that the EPR spectra of d5 configuration FeIII ion in a trigonal ligand field may be analyzed by the spin Hamiltonian [4,5] ~ þ D½S 2 1SðS þ 1Þ þ 1a½S 4 þ S4 ~ S H# S ¼ gbH Z
3
6
x
Z
þ Sz4 15SðS þ 1Þð3S 2 þ 3S 1Þ 1 þ 180 F ½35SZ4 30SðS þ 1ÞSZ2 þ 25SZ2
6SðS þ 1Þ þ 3S 2 ðS þ 1Þ2 ;
ð1Þ
where the parameters D and F relate to the second-order and fourth-order spin operators, respectively, and represent a component of the crystalline electric field which is axially symmetric about the C3-axis, the parameter a relates to a fourth-order spin operator and represents a cubic component of the crystalline electric field. From Eq. (1) the zero-field-splitting DE1 and DE2 in the ground-state 6A1 may be explicitly expressed as a function of the EPR parameters a; D and (a F ) [6]: DE1 ¼ 713½ða DE2 ¼ 32ða F Þ 716½ða
2
2 1=2
F þ 18DÞ þ 80a
; ð2Þ
The positive and negative signs in Eq. (2) correspond to D > 0 and Do0; respectively. The EPR zero-field splitting parameters a; D and (a F ) can be determined by using Eq. (2) and taking a cubic approximation. The energy matrix for the d5 configuration ion with C3 symmetry have been derived based on the following perturbation Hamiltonian [7]: X e2 X X H# ¼ þz l i si þ Vi ; ð3Þ r ioj ij i i where z is the spin–orbit coupling coefficient; Vi is the ligand potential, which may be expressed as, Vi ¼ g20 r2i Z20 ðyi ; fi Þ þ g40 r4i Z40 ðyi ; fi Þ c s ðyi ; fi Þ þ gs43 r4i Z43 ðyi ; fi Þ: þ gc43 r4i Z43
Each matrix element is a function of the Racah parameters B; and C; the Trees correction a; the Racah correction b; the spin–orbit coupling coefficient z; and the ligand–field parameters that are in the following forms [8]: D20 ¼ ð5=196pÞ1=2 g20 /r2 S; D40 ¼ ð1=196pÞ1=2 g40 /r4 S; Dc43 ¼ ð5=56pÞ1=2 gc43 /r4 S; Ds43 ¼ ið5=56pÞ1=2 gs43 /r4 S: III
ð5Þ III
For the Fe ions in ZnS:Fe system, the local symmetry is C3V. In this case the explicit expressions of Dkq may be derived by use of the superposition model [8,9] as, 4 1X D20 ¼ G2 ðtÞK20 ðtÞ; 7 t¼1 D40 ¼
4 1 X G4 ðtÞK40 ðtÞ; 21 t¼1
Dc43 ¼
4 1 X G4 ðtÞK43 ðtÞ 84 t¼1
ð6Þ
with K20 ðtÞ ¼ 12ð3 cos2 yt 1Þ; K40 ðtÞ ¼ 18ð35 cos2 yt 30 cos2 yt þ 3Þ; K43 ðtÞ ¼ 35 cos yt sin3 yt cos 3ft ;
D F þ 18DÞ2 þ 80a2 1=2 :
185
ð4Þ
G2 ðtÞ ¼ qt eG 2 ðtÞ; G4 ðtÞ ¼ qt eG 4 ðtÞ; Z Rt rk R23d ðrÞr2 kþ1 dr G k ðtÞ ¼ Rt 0 Z N Rkt R23d ðrÞr2 kþ1 dr; þ r Rt where t and qt represent the tth ligand and its effective charge, respectively. For FeIII in ‘‘hexagonal’’ ZnS:FeIII, if the z-axis is along the C3axis, we have yt ¼ yt0 þ Dy; yt0 ¼ cos1 13 (for t ¼ 1; 2, 3), y4 ¼ 1801 and G4 ðtÞ ¼ ð27 2 ÞDq (for t ¼ 1; 2, 3, 4). We will use Dy and G2 ðtÞ=G4 ðtÞ ¼ 3 to describe the trigonal ligand–field strength. A detail optical spectrum of MnII in ZnS:MnII has been studied by Kushida et al. [10] and Pohl et al. [11]. The ligand–field strength for ZnS:MnII
186
D. Dong et al. / Physica B 325 (2003) 184–188
has been reported to be Dq ¼ 600 cm1 [12]. As for ZnS:FeIII, although we do not know its optical spectrum, however, we can estimate its ligand–field strength Dq by use of the following relationship [13]:
Table 1 The EPR cubic parameter a as a function of spin–orbit coupling coefficient z for negative Dq and positive Dq, respectively, where B¼ 650; C¼ 2400 cm1, all values are in units of cm1
Dq ¼ f ðMÞgðLÞ;
z 200 250 300 350 400 450 Expt. [2]
where f ðMÞ is a function of the metal ion M and gðLÞ is a function of the ligand ions L: From Eq. (7) we have DqðZnS : FeIII Þ DqðMgO : FeIII Þ ¼ : II DqðZnS : Mn Þ DqðMgO : MnII Þ
ð8Þ
Substituting Dq(MgO:FeIII)=1316, Dq(MgO: MnII)=995 [14] and Dq(ZnS:MnII)=600 cm1 [12] into Eq. (8), we obtain Dq(ZnS:FeIII)= 794 cm1. We suppose that the typical Racah parameters B ¼ 650 and C ¼ 2400 cm1 for the FeIII in the tetrahedron in YGG determined by Zhou and co-workers [15] are also suitable for the ZnS:FeIII system here. Using the parameters B ¼ 650; C ¼ 2400; Dq ¼ 794 cm1 and Dy ¼ 0 in our calculation, and diagonalizing the corresponding energy matrix, we obtained the EPR cubic parameter a as a function of the spin–orbit coupling coefficient z: It is shown that in the possible range of the spin–orbit coupling coefficient z (zoz0 ; where z0 ¼ 470 cm1 for a free FeIII ion [14]), the theoretical value of the EPR cubic parameter a is much smaller than that of the experimental finding, as displayed in Table 1 and plotted in Fig. 1. Due to this difficulty, the EPR spectra of iron–sulfur clusters in ‘‘hexagonal’’ ZnS:FeIII has not yet been interpreted. According to the ligand–field theory, the negative Dq (Dq ¼ 794 cm1) for the d5 electron configuration ion FeIII in ZnS:FeIII corresponds to a negative effective charge for sulfur ions in ZnS. As stated above, from a negative Dq we cannot get a reasonable explanation of the EPR cubic parameter a: In order to overcome this difficulty, a positive ligand–field strength Dq is suggested and taken in our calculation. Again, by taking B ¼ 650; C ¼ 2400; Dq ¼ 794 cm1 and Dy ¼ 0 in our energy matrix and by diagonalizing those matrices, we can perform the calculation for the EPR cubic parameter a as a function of the spin–orbit coupling coefficient z . We find that in the case
Dq ¼ 794
104 ðaÞ 3.33 7.83 15.59 27.72 45.22 69.14 104 ðaÞ ¼ 12775
104 ðaÞ 4.36 10.96 23.40 44.59 78.07 128.33
150
120 ΙΙ 10 4 a (cm-1)
ð7Þ
Dq ¼ 794
90
60
30
0 200
I
250
300
350 ζ
400
450
(cm -1 )
Fig. 1. The EPR cubic parameter a as a function of spin–orbit coupling coefficient z: B ¼ 650 and C ¼ 2400 [15]. I: Dq ¼ 794: II: Dq ¼ þ794 (in units cm1).
of positive Dq the experimental EPR cubic parameter a can be reasonably explained (see Table 1 and Fig. 1). For instance, for z ¼ 449 cm1 the theoretical value is a ¼ 127:1 104 cm1, which is in good agreement with the experimental data aðexptÞ ¼ ð127:470:5Þ 104 cm1 [2]. A positive value of Dq has also been found in the study of EPR spectrum of MnII in cubic ZnS:MnII system by Zhou and co-workers [12]. To
D. Dong et al. / Physica B 325 (2003) 184–188 Table 2 The ground-state splittings DE1 ; DE2 and the EPR zero-field splitting parameters a, D, and (a-F) for FeIII ion in ZnS:FeIII as a function angle Dy; where 6 5of trigonal 6 1distortion 6 3 DE ¼ E A 7 A 7 E ; DE 1 1 1 2 ¼ E A1 72 2 2 6 1 E A1 72 ; and 104 ðDE1 Þ; 104 ðDE2 Þ; 104 ðaÞ; 104 ðDÞ and 104 ða F Þ are in units of cm1 ZnS:FeIII Dy ðdeg:Þ 104 ðDE1 Þ 104 ðDE2 Þ 104 ðaÞ 104 ðDÞ 0.5000 0.5500 0.5614 0.6000 0.6500 Expt. [2]
2539.0 2800.8 2860.0 3061.9 3326.0 2860.3
654.9 742.2 761.9 829.3 916.7 751.2
127.1 127.1 127.1 127.1 127.1 12775
425.4 469.5 479.5 513.4 557.7 479.975
104 ða F Þ 126.1 125.8 125.8 125.5 125.7 132.772
understand the origin of the positive Dq, Zhou et al. have proposed a possible local structure, in which the MnII ion is assumed in an octahedron formed by six anions S2. Zhou et al.’s suggestion seems a reasonable one for cubic ZnS:MnII system. However, in hexagonal wurtzite ZnS [11], we noted that the octahedral local structure does not exist. Stavrev and Nikolov have pointed out that in ZnS:MnII systems the MnII ion prefers to occupy the center of a tetrahedron formed by four sulfur ions [16]. The Nikolov et al.’s analysis is in accord with the experimental finding for MnII in ‘‘hexagonal’’ ZnS:MnII reported by Pohl and coworkers [11]. If a FeIII ion in ZnS:FeIII or a MnII ion in ZnS:MnII are surrounded by four sulfur ions, the local structure will be necessarily a tetrahedron. From this tetrahedron structure and the positive ligand–field strength Dq, we can deduce that the effective charge of the sulfur ions in ZnS is positive. This unusual result may be explained as that in ZnS system each sulfur ion prefers to produce a sp3 hybrid configuration and causes a tetrahedral structure. The positive effective charge as well as sp3 hybrid configuration has also been reported in the work of Pauling for the sulfur ions in the ZnS system [3]. In the following we will show that the positive Dq is also suitable for explaining the EPR spectrum of iron-sulfur clusters in ‘‘hexagonal’’ ZnS:FeIII system. In reality, the so-called ‘‘hexagonal’’ crystals are of mixed-poly-type structure [2], and one of axial symmetry in these crystals has a slight distortion
187
along the C3-axis. We will use the Dya0 to describe the trigonal ligand–field. Using the parameters B ¼ 650; C ¼ 2400; z ¼ 449 and Dq ¼ 794 cm1 in our calculation, we can derive the zero-field splitting values DE1 and DE2 as functions of the distortion angle Dy: The EPR zero-field splitting parameters D and (a F ) may also be calculated by Eq. (2), the results are listed in Table 2. It can be seen from Table 2 that the theoretical values 104 ðaÞ ¼ 127:1; 104 ðDÞ ¼ 479:5; and 104 ða F Þ ¼ 125:8 cm1 (for Dy= 0.56141) are in good agreement with the experimental findings 104 ðaÞ ¼ 12775; 104 ðDÞ ¼ 479:975; and 104 ða F Þ ¼ 132:772 cm1 [2]. This result means that the view of positive effective charge is also reasonable for analyzing the EPR spectra of iron–sulfur clusters in a trigonal distorted tetrahedron. In conclusion, the EPR zero-field splitting of iron–sulfur clusters in the ZnS:FeIII system has been studied by diagonalizing the energy matrix for the electron–electron repulsion, the ligand– field and the spin–orbit coupling interaction of the d5 electron configuration with trigonal ligand field. It is shown that only a positive Dq may offer a reasonable explanation of the EPR spectra. The positive Dq for FeIII in tetrahedron means that the effective charge of the sulfur ions is positive. This result implies that in tetrahedral ZnS structure each sulfur ion may occur a quadricovalent argon state with sp3 hybrid configuration and this is also in agreement with Pauling’s speculation [3].
Acknowledgements The authors express their gratitude to Prof. Gou Qing-Quan, Chengdu University of Science and Technology, for many helpful discussions. This project was supported by National Natural science Foundation of China.
References [1] G. Blondin, J.J. Girerd, Chem. Rev. 90 (1990) 1359. [2] T. Buch, B. Clerjaud, B. Lambert, P. Kovacs, Phys. Rev. B 7 (1973) 184.
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D. Dong et al. / Physica B 325 (2003) 184–188
[3] L. Pauling, Mineral. Soc. Am. Spec. Pap. 3 (1970) 125; A.S. Marfunin, in: N.G. Egorova, A.G. Mishchenko (Transl), Physics of Minerals and Inorganic Materials, Springer, Berlin, Heidelberg, New York, 1979, p. 304–305. [4] P.B. Dorain, Phys. Rev. 112 (1958) 1058. [5] R.S. Title, Phys. Rev. 131 (1963) 2503. [6] A. Abragam, B. Bleaney, in Electron Paramagnetic Resonance of Transition Ions, Oxford University Press, Oxford, 1986. [7] X.Y. Kuang, Ph.D. Thesis, Universite de Paris-sud., 1994. [8] D.J. Newman, W. Urban, Adv. Phys. 24 (1975) 793. [9] S. Hufner, in Optical Spectra of Transparent Rare Earth Compounds, Academic Press, New York, 1978.
[10] T. Kushida, Y. Tanaka, Y. Oka, J. Phys. Soc. Japan. 37 (1974) 1341. [11] U.W. Pohl, H.E. Gumlich, W. Busse, Phys. Stat. Sol. B 125 (1984) 733. [12] K.W. Zhou, S.B. Zhao, Y.M. Ning, Phys. Rev. B 43 (1991) 3712. [13] M. Gerloch, R.C. Slade, Ligand–Field Parameters, Cambridge University Press, Cambridge, 1973, p. 10. [14] X.Y. Kuang, W. Zhang, I. Morgenstern-Badarau, Phys. Rev. B 45 (1992) 8104. [15] K.W. Zhou, J.K. Xie, Y.M. Ning, S.B. Zhao, P.F. Wu, Phys. Rev. B44 (1991) 7499. [16] K.K. Stavrev, G.S. Nikolov, Phys. Rev. B 47 (1993) 542.
Study of EPR zero-field splitting of iron–sulfur clusters in tetrahedral ZnS:FeIII system$ Die Donga, Kuang Xiao-Yua,b,*, Lu Weia, Zhou Kang-Weib,c,d a
Institute of Atomic and Molecular Physics, Sichuan University, Chengdu 610065, China International Centre for Materials Physics, Academia Sinica, Shenyang 110015, China c Department of Physics, Sichuan University, Chengdu 610065, China d CCAST(World Laboratory), Box 8730, Beijing 100080, China
b
Received 16 April 2002
Abstract The EPR zero-field splitting of the iron–sulfur cluster in the ZnS:FeIII system has been studied on the basis of the energy matrix for the electron–electron repulsion, the ligand–field and the spin–orbit coupling of a d5 configuration ion with a trigonal symmetry. It is demonstrated that in order to reasonably explain the EPR zero-field splitting parameters a; D and (a F ), a positive ligand–field strength Dq for a d5 electron configuration ion in a tetrahedron has to be employed. This means that the effective charge of each sulfur ion in ZnS is positive. This unusual result leads to the conclusion that in ZnS each sulfur ion may occur a quadricovalent argon state S2+ with sp3 hybrid configuration and this conclusion is in accord with Pauling’s speculation. r 2002 Elsevier Science B.V. All rights reserved. Keywords: Electron-paramagnetic resonance; Ligand–field theory
The electronic and magnetic properties of iron– sulfur clusters in complexes have been received extensive interest in the last decades. Recently, the interest has been intensified since some iron–sulfur clusters were found in the active sites of metalloproteins such as oxidized ferredoxin [1]. The iron– sulfur clusters usually play an important role for the electron exchange and electron transfer in metalloproteins. In understanding the characteristic of iron–sulfur clusters in complexes, each $
This project was supported by National Natural Science Foundation of China. *Corresponding author. Institute of Atomic and Molecular Physics, Sichuan University, Chengdu 610065, China. E-mail address: [email protected] (K. Xiao-Yu).
sulfur ion is usually treated as an anion S2. This treatment seems suitable for sulfur ions in most complexes. However, for the iron–sulfur clusters in ZnS:FeIII, we found by the analysis of the EPR spectra that if each sulfur ion is treated as an anion S2 in the calculations, the theoretical value of EPR parameter a will deviate far from the experimental finding. Up to now, the EPR zerofield splitting parameters a; D and (a F ) for iron–sulfur clusters in the ‘‘hexagonal’’ ZnS:FeIII have not yet been understood [2]. In the present work, we will show that a reasonable calculation result of the EPR spectra for the iron–sulfur clusters in ZnS:FeIII may be obtained by using a positive ligand–field strength Dq for the d5 electron configuration FeIII ion in the tetrahedron.
0921-4526/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 0 2 ) 0 1 5 2 1 - 1
D. Dong et al. / Physica B 325 (2003) 184–188
This positivity of Dq means that the effective charge of sulfur ions in ZnS is positive. This unusual result will support Pauling’s speculation that each of the sulfur ions in ZnS may be looked upon as an electron donor that forms a quadricovalent argon state of S2+ with sp3 hybrid configuration [3]. It is well known that the EPR spectra of d5 configuration FeIII ion in a trigonal ligand field may be analyzed by the spin Hamiltonian [4,5] ~ þ D½S 2 1SðS þ 1Þ þ 1a½S 4 þ S4 ~ S H# S ¼ gbH Z
3
6
x
Z
þ Sz4 15SðS þ 1Þð3S 2 þ 3S 1Þ 1 þ 180 F ½35SZ4 30SðS þ 1ÞSZ2 þ 25SZ2
6SðS þ 1Þ þ 3S 2 ðS þ 1Þ2 ;
ð1Þ
where the parameters D and F relate to the second-order and fourth-order spin operators, respectively, and represent a component of the crystalline electric field which is axially symmetric about the C3-axis, the parameter a relates to a fourth-order spin operator and represents a cubic component of the crystalline electric field. From Eq. (1) the zero-field-splitting DE1 and DE2 in the ground-state 6A1 may be explicitly expressed as a function of the EPR parameters a; D and (a F ) [6]: DE1 ¼ 713½ða DE2 ¼ 32ða F Þ 716½ða
2
2 1=2
F þ 18DÞ þ 80a
; ð2Þ
The positive and negative signs in Eq. (2) correspond to D > 0 and Do0; respectively. The EPR zero-field splitting parameters a; D and (a F ) can be determined by using Eq. (2) and taking a cubic approximation. The energy matrix for the d5 configuration ion with C3 symmetry have been derived based on the following perturbation Hamiltonian [7]: X e2 X X H# ¼ þz l i si þ Vi ; ð3Þ r ioj ij i i where z is the spin–orbit coupling coefficient; Vi is the ligand potential, which may be expressed as, Vi ¼ g20 r2i Z20 ðyi ; fi Þ þ g40 r4i Z40 ðyi ; fi Þ c s ðyi ; fi Þ þ gs43 r4i Z43 ðyi ; fi Þ: þ gc43 r4i Z43
Each matrix element is a function of the Racah parameters B; and C; the Trees correction a; the Racah correction b; the spin–orbit coupling coefficient z; and the ligand–field parameters that are in the following forms [8]: D20 ¼ ð5=196pÞ1=2 g20 /r2 S; D40 ¼ ð1=196pÞ1=2 g40 /r4 S; Dc43 ¼ ð5=56pÞ1=2 gc43 /r4 S; Ds43 ¼ ið5=56pÞ1=2 gs43 /r4 S: III
ð5Þ III
For the Fe ions in ZnS:Fe system, the local symmetry is C3V. In this case the explicit expressions of Dkq may be derived by use of the superposition model [8,9] as, 4 1X D20 ¼ G2 ðtÞK20 ðtÞ; 7 t¼1 D40 ¼
4 1 X G4 ðtÞK40 ðtÞ; 21 t¼1
Dc43 ¼
4 1 X G4 ðtÞK43 ðtÞ 84 t¼1
ð6Þ
with K20 ðtÞ ¼ 12ð3 cos2 yt 1Þ; K40 ðtÞ ¼ 18ð35 cos2 yt 30 cos2 yt þ 3Þ; K43 ðtÞ ¼ 35 cos yt sin3 yt cos 3ft ;
D F þ 18DÞ2 þ 80a2 1=2 :
185
ð4Þ
G2 ðtÞ ¼ qt eG 2 ðtÞ; G4 ðtÞ ¼ qt eG 4 ðtÞ; Z Rt rk R23d ðrÞr2 kþ1 dr G k ðtÞ ¼ Rt 0 Z N Rkt R23d ðrÞr2 kþ1 dr; þ r Rt where t and qt represent the tth ligand and its effective charge, respectively. For FeIII in ‘‘hexagonal’’ ZnS:FeIII, if the z-axis is along the C3axis, we have yt ¼ yt0 þ Dy; yt0 ¼ cos1 13 (for t ¼ 1; 2, 3), y4 ¼ 1801 and G4 ðtÞ ¼ ð27 2 ÞDq (for t ¼ 1; 2, 3, 4). We will use Dy and G2 ðtÞ=G4 ðtÞ ¼ 3 to describe the trigonal ligand–field strength. A detail optical spectrum of MnII in ZnS:MnII has been studied by Kushida et al. [10] and Pohl et al. [11]. The ligand–field strength for ZnS:MnII
186
D. Dong et al. / Physica B 325 (2003) 184–188
has been reported to be Dq ¼ 600 cm1 [12]. As for ZnS:FeIII, although we do not know its optical spectrum, however, we can estimate its ligand–field strength Dq by use of the following relationship [13]:
Table 1 The EPR cubic parameter a as a function of spin–orbit coupling coefficient z for negative Dq and positive Dq, respectively, where B¼ 650; C¼ 2400 cm1, all values are in units of cm1
Dq ¼ f ðMÞgðLÞ;
z 200 250 300 350 400 450 Expt. [2]
where f ðMÞ is a function of the metal ion M and gðLÞ is a function of the ligand ions L: From Eq. (7) we have DqðZnS : FeIII Þ DqðMgO : FeIII Þ ¼ : II DqðZnS : Mn Þ DqðMgO : MnII Þ
ð8Þ
Substituting Dq(MgO:FeIII)=1316, Dq(MgO: MnII)=995 [14] and Dq(ZnS:MnII)=600 cm1 [12] into Eq. (8), we obtain Dq(ZnS:FeIII)= 794 cm1. We suppose that the typical Racah parameters B ¼ 650 and C ¼ 2400 cm1 for the FeIII in the tetrahedron in YGG determined by Zhou and co-workers [15] are also suitable for the ZnS:FeIII system here. Using the parameters B ¼ 650; C ¼ 2400; Dq ¼ 794 cm1 and Dy ¼ 0 in our calculation, and diagonalizing the corresponding energy matrix, we obtained the EPR cubic parameter a as a function of the spin–orbit coupling coefficient z: It is shown that in the possible range of the spin–orbit coupling coefficient z (zoz0 ; where z0 ¼ 470 cm1 for a free FeIII ion [14]), the theoretical value of the EPR cubic parameter a is much smaller than that of the experimental finding, as displayed in Table 1 and plotted in Fig. 1. Due to this difficulty, the EPR spectra of iron–sulfur clusters in ‘‘hexagonal’’ ZnS:FeIII has not yet been interpreted. According to the ligand–field theory, the negative Dq (Dq ¼ 794 cm1) for the d5 electron configuration ion FeIII in ZnS:FeIII corresponds to a negative effective charge for sulfur ions in ZnS. As stated above, from a negative Dq we cannot get a reasonable explanation of the EPR cubic parameter a: In order to overcome this difficulty, a positive ligand–field strength Dq is suggested and taken in our calculation. Again, by taking B ¼ 650; C ¼ 2400; Dq ¼ 794 cm1 and Dy ¼ 0 in our energy matrix and by diagonalizing those matrices, we can perform the calculation for the EPR cubic parameter a as a function of the spin–orbit coupling coefficient z . We find that in the case
Dq ¼ 794
104 ðaÞ 3.33 7.83 15.59 27.72 45.22 69.14 104 ðaÞ ¼ 12775
104 ðaÞ 4.36 10.96 23.40 44.59 78.07 128.33
150
120 ΙΙ 10 4 a (cm-1)
ð7Þ
Dq ¼ 794
90
60
30
0 200
I
250
300
350 ζ
400
450
(cm -1 )
Fig. 1. The EPR cubic parameter a as a function of spin–orbit coupling coefficient z: B ¼ 650 and C ¼ 2400 [15]. I: Dq ¼ 794: II: Dq ¼ þ794 (in units cm1).
of positive Dq the experimental EPR cubic parameter a can be reasonably explained (see Table 1 and Fig. 1). For instance, for z ¼ 449 cm1 the theoretical value is a ¼ 127:1 104 cm1, which is in good agreement with the experimental data aðexptÞ ¼ ð127:470:5Þ 104 cm1 [2]. A positive value of Dq has also been found in the study of EPR spectrum of MnII in cubic ZnS:MnII system by Zhou and co-workers [12]. To
D. Dong et al. / Physica B 325 (2003) 184–188 Table 2 The ground-state splittings DE1 ; DE2 and the EPR zero-field splitting parameters a, D, and (a-F) for FeIII ion in ZnS:FeIII as a function angle Dy; where 6 5of trigonal 6 1distortion 6 3 DE ¼ E A 7 A 7 E ; DE 1 1 1 2 ¼ E A1 72 2 2 6 1 E A1 72 ; and 104 ðDE1 Þ; 104 ðDE2 Þ; 104 ðaÞ; 104 ðDÞ and 104 ða F Þ are in units of cm1 ZnS:FeIII Dy ðdeg:Þ 104 ðDE1 Þ 104 ðDE2 Þ 104 ðaÞ 104 ðDÞ 0.5000 0.5500 0.5614 0.6000 0.6500 Expt. [2]
2539.0 2800.8 2860.0 3061.9 3326.0 2860.3
654.9 742.2 761.9 829.3 916.7 751.2
127.1 127.1 127.1 127.1 127.1 12775
425.4 469.5 479.5 513.4 557.7 479.975
104 ða F Þ 126.1 125.8 125.8 125.5 125.7 132.772
understand the origin of the positive Dq, Zhou et al. have proposed a possible local structure, in which the MnII ion is assumed in an octahedron formed by six anions S2. Zhou et al.’s suggestion seems a reasonable one for cubic ZnS:MnII system. However, in hexagonal wurtzite ZnS [11], we noted that the octahedral local structure does not exist. Stavrev and Nikolov have pointed out that in ZnS:MnII systems the MnII ion prefers to occupy the center of a tetrahedron formed by four sulfur ions [16]. The Nikolov et al.’s analysis is in accord with the experimental finding for MnII in ‘‘hexagonal’’ ZnS:MnII reported by Pohl and coworkers [11]. If a FeIII ion in ZnS:FeIII or a MnII ion in ZnS:MnII are surrounded by four sulfur ions, the local structure will be necessarily a tetrahedron. From this tetrahedron structure and the positive ligand–field strength Dq, we can deduce that the effective charge of the sulfur ions in ZnS is positive. This unusual result may be explained as that in ZnS system each sulfur ion prefers to produce a sp3 hybrid configuration and causes a tetrahedral structure. The positive effective charge as well as sp3 hybrid configuration has also been reported in the work of Pauling for the sulfur ions in the ZnS system [3]. In the following we will show that the positive Dq is also suitable for explaining the EPR spectrum of iron-sulfur clusters in ‘‘hexagonal’’ ZnS:FeIII system. In reality, the so-called ‘‘hexagonal’’ crystals are of mixed-poly-type structure [2], and one of axial symmetry in these crystals has a slight distortion
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along the C3-axis. We will use the Dya0 to describe the trigonal ligand–field. Using the parameters B ¼ 650; C ¼ 2400; z ¼ 449 and Dq ¼ 794 cm1 in our calculation, we can derive the zero-field splitting values DE1 and DE2 as functions of the distortion angle Dy: The EPR zero-field splitting parameters D and (a F ) may also be calculated by Eq. (2), the results are listed in Table 2. It can be seen from Table 2 that the theoretical values 104 ðaÞ ¼ 127:1; 104 ðDÞ ¼ 479:5; and 104 ða F Þ ¼ 125:8 cm1 (for Dy= 0.56141) are in good agreement with the experimental findings 104 ðaÞ ¼ 12775; 104 ðDÞ ¼ 479:975; and 104 ða F Þ ¼ 132:772 cm1 [2]. This result means that the view of positive effective charge is also reasonable for analyzing the EPR spectra of iron–sulfur clusters in a trigonal distorted tetrahedron. In conclusion, the EPR zero-field splitting of iron–sulfur clusters in the ZnS:FeIII system has been studied by diagonalizing the energy matrix for the electron–electron repulsion, the ligand– field and the spin–orbit coupling interaction of the d5 electron configuration with trigonal ligand field. It is shown that only a positive Dq may offer a reasonable explanation of the EPR spectra. The positive Dq for FeIII in tetrahedron means that the effective charge of the sulfur ions is positive. This result implies that in tetrahedral ZnS structure each sulfur ion may occur a quadricovalent argon state with sp3 hybrid configuration and this is also in agreement with Pauling’s speculation [3].
Acknowledgements The authors express their gratitude to Prof. Gou Qing-Quan, Chengdu University of Science and Technology, for many helpful discussions. This project was supported by National Natural science Foundation of China.
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