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Study of the local distortion of the tetragonal charge-compensation defect sites in Cr3+:MgO
7 October 1996 PHYSICS LETTERS
ELSEVIER
A
Physics Letters A 221(1996) 355-358
Study of the local distortion of the tetragonal charge-compensation defect sites in Cr 3+:MgO Wan-Lun Yu Deparrmeni
ofPhysics,
Sichuan Normal
Uniuersity,
Chengdu 610066,
China
Received 13 May 1996; revised manuscript 9 July 1996; accepted for publication IO July 1996 Communicated by J. Flouquet
Abstract A relation is established between the zero-field splitting and the local distortion parameters for CT’+ at the tetragonal sites in MgO. This is used to derive the ligand positions from the experimental data of the zero-field splitting parameter. The results obtained are well consistent with those calculated by Groh et al. using the embedded-quantum-cluster ICECAP method. PACS:
76.30.Mi; 76.3O.F~;71.7O.Ch
1. Introduction
2. Theory
The tetragonal (C,) defect Cr3+ center in MgO was first identified by Wertz and Auzins [l] in analyzing their EPR spectra, and they proposed that the site is formed by a next-nearest-neighbor Mg*+ vacancy; see Fig. 1. Subsequently, Fairbank and Klauminzer [2] and McDonagh et al. [3] have carried out optical studies for this center. An attempt has been made by Du and Zhao [4] to derive information on the vacancy-induced lattice distortion from the observed value of the ZFS parameter bt. The treatment was oversimplified as was criticized by Yeung [5]. In this work we presents another treatment. The results obtained are well consistent with those calculated recently by Groh et al. 161 using the embedded-quantum-cluster ICECAP method and those observed by Asakura and Iwasawa [7] from the extended X-ray absorption fine structure experiments.
For a 3d3 ion in octahedrally tetragonal symmetry, the EPR ZFS parameter bt is related to the splitting Dc4A2> of the ground state 4A2 by the relation D(4A,)=E(f1/2)-E(+3/2)=
0375~9601/%/$12.00 Copyright 0 1996 Elsevier Science B.V. All rights reserved. PI1 SO375-9601(96)00543-9
-2b;.
(001,
$JMg” -vacancy
Fig. I. Tetragonal site in C?:MgO.
(1)
356
W.-L. Yu/ Physics Letters A 221 (19961355-358
The ZFS parameter 6: has been observed to be - 0.08 194 cm-’ for Cr3+ at the tetragonal sites in MgO [l]. Clearly this value represents the netcharge-compensation ZFS contribution, since bi equals zero at the cubic sites. We note that the ZFS is a result of the actual Hamiltonian acting on Cr3+, which can be written as P=%,(B,
CY a) +&F+G.O.U)T
(2)
where terms in the right side are the electrostatic, crystal-field (CF), and the spin-orbit interactions, respectively. Fairbank and Klauminzer [2] have found B=570,C=3165,cr=7O,and~=24O,allincm-’ for Cr3+:Mg0. The crystal- field can be written as zc,
= B,,C&2’ + B&h4) + B,,( Cy) + C!!;)
(3)
for C,, symmetry ( z 11C,). It is convenient to define Bk, = B,, - FB,, Dq=$[B,+gB,,].
,
B,,(LD)
= 2 A2
(4)
Eqs. (3) and (4) are applicable to the cubic sites for Cr3+:Mg0, where B,, = Bk, = 0. Let Dq, denote the value of Dq for the cubic site, we may write Dq = Dq, + Dq’
these contributions. Regarding the Mg’+-vacancy as an effective negative charge of 2e in the perfect cubic Cr3+:Mg0 lattice, we obtain B,,(D) = 1260 cm-‘, B&(D) = 59.4 cm-‘, and Dq’ (D) = 1.4 cm-’ as the defect (Mg*+ -vacancy) contributions. Another net-charge-compensation CF contribution arises from the lattice distortion (LD) caused by the vacancy. It is clear that the distortion of cluster Cr3+-60*gives the main contribution. The ions in the cluster may displace in different ways. Among them the ligand 0’ lying between the vacancy and Cr3+ should move towards Cr 3+, from a simple electrostatic point of view; see Fig. 1. Let A denote this displacement. It must be much greater than the displacements of other ions since 0, is closest to the vacancy. By adopting the superposition model [S], we obtain
(5)
for the tetragonal sites. Thus the parameters B,,, B&9 and Dq’ altogether represent the net charge compensation CF contribution. The ground-state splitting Dc4A,), and consequently the ZFS parameter bi, can be calculated by means of simultaneous diagonalization of all the actual Hamiltonian terms given in Eq. (2). For the cubic sites, the splitting is zero. When the next-nearest-neighbor cation Mg*+ is absent to form the tetragonal sites, the net charge compensation CF parameters B,,, Bk,, and Dq’ arise, and consequently, the splitting becomes nonzero. As the next step we establish the relationship between the net charge compensation CF contribution and the lattice distortion. We first note that the next-nearest-neighbor Mg*+ vacancy at the (OOl)axis must have contributions. Since the defect (D) is distant from the central magnetic Cr3+ ion, the interaction between the open-shell 3d3 electrons of Cr3+ should be mainly electrostatic, and the overlap effect should be negligible. Thus it is reasonable to adopt the point charge model in the calculation of
Dq’(LD) = -Bk,(LD)/42,
(6) as the contributions of the displacement of O,, providing other ligands, as well as the central metal ion, keep their positions as in the perfect Cr3+:Mg0 lattice. R, is the Cr-0 distance for the perfect Cr3+:Mg0 lattice; it is taken as the reference distance. By applying the superposition model [8] to the cubic sites we obtain Dq, = $i4. It then follows that A,= 1193 cm-’ from the experimental _value Dq, = 1590 cm-’ [2]. We take &T 10.8A, = 12880 cm-‘, considering that the ratio A2/x4 tends to be a constant of 10.8 * 2.0Jor iron-group ions [IO-I 21; a change of It 30% in A, will not give a great change in the final result, since the ZFS parameter is very insensitive to B,, [9]. The power-law exponents are taken to be t2 = 3 and t, = 5, which have been found from studies of the uniaxial and uniform stress effects of the g-factor [13] and the pressure dependence of Dq, [6] for the cubic sites of Cr3+:Mg0. Through the relationship between the net-chargecompensation ZFS and CF contributions, we have reached a reliable relation between the net-chargecompensation ZFS effect and the displacement A of 0’.
357
W.-L. Vu/ Physics Letters A 221 (1996) 355-358
3. Results and discussion The ground-state splitting DC4A2> of Cr3+ at the tetragonal sites in MgO is plotted as a function of A/R, in Fig. 2. We see a sensitive and almost a linear dependence, in the range A/R, < 0.05. The value of A/R, has to be 0.046 to account for the experimental value Dc4A,) = 0.1639 cm-’ [I]. The Cr-0 distance R, has been obtained to be 2.02 ,&by Groh et al. in an embedded-quantum-cluster calculation [6]. With the use of it, our result can be expressed as A = 0.093 A or R(Cr-0,) = 1.927 A. The latter is very well consistent with the 1.92 A calculated by Groh et al. [6] using the embeddedOquantum-cluster ICECAP method and 1.90 + 0.03 A observed from the extended X-ray absorption fine structure experiments [7]. The net-charge-compensation contributions to CF parameters are calculated using A/R, = 0.046 to be B,, = 5 170, Bk, = 2590, and Dq’ = Dq - Dq, = 62, which are in good agreement with B,, = 4550, Rio = 2520, and Dq’= Dq - Dqc= 60 obtained by Fairbank and Klauminzer [2] in fitting to the optical spectra, all in units of cm-‘. We obtain g,, = 1.978 and g, = 1.979 as the EPR g-factors by using the orbital reduction factor k = 0.6 [ 131 and D(*E) = 82 cm-’ as the splitting of the excited state ‘E. These are in good agreement with the experimental values 811= g _L= 1.9782 [l] and D(*E) = 93.5 cm-’ [3]. The spin-spin interaction [14,15] has been neglected in our determination of A/R, = 0.046. This interaction is found by us to contribute positively to the ground-state splitting. Hence taking it into account will make the value of A/R, decrease somewhat. By assuming the free-ion values for the spinspin interaction parameters [I 41 we obtain A/R, = 0.042. If we took values of these parameters smaller than the free-ion ones, a result would be obtained in the range 0.042 < A/R, < 0.046.
0.20
,
0.15
-
:
---
Exjt: -_--_--_-----0.1639 cm-’
5
Fig. 2. Ground-state splittin,0 Dc4A,) as a function of the displacement of 0,.
The value obtained for A/R, could be further improved by taking into account the displacement of the central Cr3+ ion, which is expected to move towards the vacancy; see Fig. 1. Let A,, denote this movement; it is expected that A,, +K A. This movement is found by us to contribute to the ground-state splitting slightly. By assuming A/A,, = 2, 4, and 8, we obtain values of A/R,, which fit the experimental value of Dt4A,) [l]. These values as well as the deduced ligand positions by taking R, = 2.02 [6] are given in Table 1, together with those calculated using the embedded-quantum-cluster ICECAP method [6] and observed from the extended X-ray absorption fine structure experiments [7]. We see an excellent consistence among them.
4. Conclusion We have determined successfully the ligand positions for the tetragonal vacancy sites in Cr3+:Mg0 from the experimental value of the ZFS parameter. The results obtained are well consistent with the
Table 1 The ligand positions of the tetragonal site in @+:MgO Present work */*cr *A
2 0.040
R(Cr-0,)
(A,
R(Cr-0,)
(a&i>
R(Cr-0,)
(A,
O,-0-0,
(deg.)
Ref. 161 4 0.043
Ref. [7]
8 0.0445
1.899
1.911
1.919
1.92
1.w + 0.03
2.020 2.060 91.2
2.020 2.041 90.6
2.020 2.03 I 90.3
2.03 2.04 90.7
2.06 f 0.04
358
W.-L. Yu / Physics Letters A 22 1 (1996) 355-358
results calculated by using the embedded-quantumcluster ICECAP method and those observed from the extended X-ray absorption fine structure experiments. This work shows a successful application of the superposition model. Acknowledgement
This work was supported by the Sichuan Provincial Scientific Foundation. References [I] J.E. Werz and P.V. Auzins, Phys. Rev. 106 (1957) 484. [2] W.M. Fairbank and G.K. Klauminzer, Phys. Rev. B 7 (1973) 500.
[31C.M. McDonagh, B. Henderson, G.F. Imbusch and P. Dawson, J. Phys. C 13 (1980) 3309. [41 M.L. Du and M.G. Zhao, J. Phys. C 19 (1986) 2935. [51 Y.Y. Yeung, J. Phys. Condens. Matter 2 (1990) 2461. [61D.J. Groh. R. Pandey and J.M. Recio, Phys. Rev. B 50 (1994) 14860. Mater. Chem. Phys. 18 [71 K. Asakura and Y. Iwasawa, (1988) 499. [Sl D.J. Newman and B. Ng, Rep. Prog. Phys. 52 (1989) 699. [91W.L. Yu, X.M. Zhang, L.X. Yang and B.Q. Zen, Phys. Rev. B 50 ( 1994) 6756. [lOI Y.Y. Yeung and D.J. Newman, Phys. Rev. B 34(1986) 2258. [ill A. Edgar, J. Phys. C 9 (1976) 4304. 1121 D.J. Newman, D.C. Pryce and W.A. Runciman, Am. Mineral. 63 (1978) 1278. [I31 W.L. Yu and M.G. Zhao, J. Phys. C 20 (1987) 2923. [141 M. Bhtme and R.E. Watson, Proc. Phys. Sot. A 271 (1963) 565. 1151 R.E. Trees, Phys. Rev. 82 (1951) 683.
ELSEVIER
A
Physics Letters A 221(1996) 355-358
Study of the local distortion of the tetragonal charge-compensation defect sites in Cr 3+:MgO Wan-Lun Yu Deparrmeni
ofPhysics,
Sichuan Normal
Uniuersity,
Chengdu 610066,
China
Received 13 May 1996; revised manuscript 9 July 1996; accepted for publication IO July 1996 Communicated by J. Flouquet
Abstract A relation is established between the zero-field splitting and the local distortion parameters for CT’+ at the tetragonal sites in MgO. This is used to derive the ligand positions from the experimental data of the zero-field splitting parameter. The results obtained are well consistent with those calculated by Groh et al. using the embedded-quantum-cluster ICECAP method. PACS:
76.30.Mi; 76.3O.F~;71.7O.Ch
1. Introduction
2. Theory
The tetragonal (C,) defect Cr3+ center in MgO was first identified by Wertz and Auzins [l] in analyzing their EPR spectra, and they proposed that the site is formed by a next-nearest-neighbor Mg*+ vacancy; see Fig. 1. Subsequently, Fairbank and Klauminzer [2] and McDonagh et al. [3] have carried out optical studies for this center. An attempt has been made by Du and Zhao [4] to derive information on the vacancy-induced lattice distortion from the observed value of the ZFS parameter bt. The treatment was oversimplified as was criticized by Yeung [5]. In this work we presents another treatment. The results obtained are well consistent with those calculated recently by Groh et al. 161 using the embedded-quantum-cluster ICECAP method and those observed by Asakura and Iwasawa [7] from the extended X-ray absorption fine structure experiments.
For a 3d3 ion in octahedrally tetragonal symmetry, the EPR ZFS parameter bt is related to the splitting Dc4A2> of the ground state 4A2 by the relation D(4A,)=E(f1/2)-E(+3/2)=
0375~9601/%/$12.00 Copyright 0 1996 Elsevier Science B.V. All rights reserved. PI1 SO375-9601(96)00543-9
-2b;.
(001,
$JMg” -vacancy
Fig. I. Tetragonal site in C?:MgO.
(1)
356
W.-L. Yu/ Physics Letters A 221 (19961355-358
The ZFS parameter 6: has been observed to be - 0.08 194 cm-’ for Cr3+ at the tetragonal sites in MgO [l]. Clearly this value represents the netcharge-compensation ZFS contribution, since bi equals zero at the cubic sites. We note that the ZFS is a result of the actual Hamiltonian acting on Cr3+, which can be written as P=%,(B,
CY a) +&F+G.O.U)T
(2)
where terms in the right side are the electrostatic, crystal-field (CF), and the spin-orbit interactions, respectively. Fairbank and Klauminzer [2] have found B=570,C=3165,cr=7O,and~=24O,allincm-’ for Cr3+:Mg0. The crystal- field can be written as zc,
= B,,C&2’ + B&h4) + B,,( Cy) + C!!;)
(3)
for C,, symmetry ( z 11C,). It is convenient to define Bk, = B,, - FB,, Dq=$[B,+gB,,].
,
B,,(LD)
= 2 A2
(4)
Eqs. (3) and (4) are applicable to the cubic sites for Cr3+:Mg0, where B,, = Bk, = 0. Let Dq, denote the value of Dq for the cubic site, we may write Dq = Dq, + Dq’
these contributions. Regarding the Mg’+-vacancy as an effective negative charge of 2e in the perfect cubic Cr3+:Mg0 lattice, we obtain B,,(D) = 1260 cm-‘, B&(D) = 59.4 cm-‘, and Dq’ (D) = 1.4 cm-’ as the defect (Mg*+ -vacancy) contributions. Another net-charge-compensation CF contribution arises from the lattice distortion (LD) caused by the vacancy. It is clear that the distortion of cluster Cr3+-60*gives the main contribution. The ions in the cluster may displace in different ways. Among them the ligand 0’ lying between the vacancy and Cr3+ should move towards Cr 3+, from a simple electrostatic point of view; see Fig. 1. Let A denote this displacement. It must be much greater than the displacements of other ions since 0, is closest to the vacancy. By adopting the superposition model [S], we obtain
(5)
for the tetragonal sites. Thus the parameters B,,, B&9 and Dq’ altogether represent the net charge compensation CF contribution. The ground-state splitting Dc4A,), and consequently the ZFS parameter bi, can be calculated by means of simultaneous diagonalization of all the actual Hamiltonian terms given in Eq. (2). For the cubic sites, the splitting is zero. When the next-nearest-neighbor cation Mg*+ is absent to form the tetragonal sites, the net charge compensation CF parameters B,,, Bk,, and Dq’ arise, and consequently, the splitting becomes nonzero. As the next step we establish the relationship between the net charge compensation CF contribution and the lattice distortion. We first note that the next-nearest-neighbor Mg*+ vacancy at the (OOl)axis must have contributions. Since the defect (D) is distant from the central magnetic Cr3+ ion, the interaction between the open-shell 3d3 electrons of Cr3+ should be mainly electrostatic, and the overlap effect should be negligible. Thus it is reasonable to adopt the point charge model in the calculation of
Dq’(LD) = -Bk,(LD)/42,
(6) as the contributions of the displacement of O,, providing other ligands, as well as the central metal ion, keep their positions as in the perfect Cr3+:Mg0 lattice. R, is the Cr-0 distance for the perfect Cr3+:Mg0 lattice; it is taken as the reference distance. By applying the superposition model [8] to the cubic sites we obtain Dq, = $i4. It then follows that A,= 1193 cm-’ from the experimental _value Dq, = 1590 cm-’ [2]. We take &T 10.8A, = 12880 cm-‘, considering that the ratio A2/x4 tends to be a constant of 10.8 * 2.0Jor iron-group ions [IO-I 21; a change of It 30% in A, will not give a great change in the final result, since the ZFS parameter is very insensitive to B,, [9]. The power-law exponents are taken to be t2 = 3 and t, = 5, which have been found from studies of the uniaxial and uniform stress effects of the g-factor [13] and the pressure dependence of Dq, [6] for the cubic sites of Cr3+:Mg0. Through the relationship between the net-chargecompensation ZFS and CF contributions, we have reached a reliable relation between the net-chargecompensation ZFS effect and the displacement A of 0’.
357
W.-L. Vu/ Physics Letters A 221 (1996) 355-358
3. Results and discussion The ground-state splitting DC4A2> of Cr3+ at the tetragonal sites in MgO is plotted as a function of A/R, in Fig. 2. We see a sensitive and almost a linear dependence, in the range A/R, < 0.05. The value of A/R, has to be 0.046 to account for the experimental value Dc4A,) = 0.1639 cm-’ [I]. The Cr-0 distance R, has been obtained to be 2.02 ,&by Groh et al. in an embedded-quantum-cluster calculation [6]. With the use of it, our result can be expressed as A = 0.093 A or R(Cr-0,) = 1.927 A. The latter is very well consistent with the 1.92 A calculated by Groh et al. [6] using the embeddedOquantum-cluster ICECAP method and 1.90 + 0.03 A observed from the extended X-ray absorption fine structure experiments [7]. The net-charge-compensation contributions to CF parameters are calculated using A/R, = 0.046 to be B,, = 5 170, Bk, = 2590, and Dq’ = Dq - Dq, = 62, which are in good agreement with B,, = 4550, Rio = 2520, and Dq’= Dq - Dqc= 60 obtained by Fairbank and Klauminzer [2] in fitting to the optical spectra, all in units of cm-‘. We obtain g,, = 1.978 and g, = 1.979 as the EPR g-factors by using the orbital reduction factor k = 0.6 [ 131 and D(*E) = 82 cm-’ as the splitting of the excited state ‘E. These are in good agreement with the experimental values 811= g _L= 1.9782 [l] and D(*E) = 93.5 cm-’ [3]. The spin-spin interaction [14,15] has been neglected in our determination of A/R, = 0.046. This interaction is found by us to contribute positively to the ground-state splitting. Hence taking it into account will make the value of A/R, decrease somewhat. By assuming the free-ion values for the spinspin interaction parameters [I 41 we obtain A/R, = 0.042. If we took values of these parameters smaller than the free-ion ones, a result would be obtained in the range 0.042 < A/R, < 0.046.
0.20
,
0.15
-
:
---
Exjt: -_--_--_-----0.1639 cm-’
5
Fig. 2. Ground-state splittin,0 Dc4A,) as a function of the displacement of 0,.
The value obtained for A/R, could be further improved by taking into account the displacement of the central Cr3+ ion, which is expected to move towards the vacancy; see Fig. 1. Let A,, denote this movement; it is expected that A,, +K A. This movement is found by us to contribute to the ground-state splitting slightly. By assuming A/A,, = 2, 4, and 8, we obtain values of A/R,, which fit the experimental value of Dt4A,) [l]. These values as well as the deduced ligand positions by taking R, = 2.02 [6] are given in Table 1, together with those calculated using the embedded-quantum-cluster ICECAP method [6] and observed from the extended X-ray absorption fine structure experiments [7]. We see an excellent consistence among them.
4. Conclusion We have determined successfully the ligand positions for the tetragonal vacancy sites in Cr3+:Mg0 from the experimental value of the ZFS parameter. The results obtained are well consistent with the
Table 1 The ligand positions of the tetragonal site in @+:MgO Present work */*cr *A
2 0.040
R(Cr-0,)
(A,
R(Cr-0,)
(a&i>
R(Cr-0,)
(A,
O,-0-0,
(deg.)
Ref. 161 4 0.043
Ref. [7]
8 0.0445
1.899
1.911
1.919
1.92
1.w + 0.03
2.020 2.060 91.2
2.020 2.041 90.6
2.020 2.03 I 90.3
2.03 2.04 90.7
2.06 f 0.04
358
W.-L. Yu / Physics Letters A 22 1 (1996) 355-358
results calculated by using the embedded-quantumcluster ICECAP method and those observed from the extended X-ray absorption fine structure experiments. This work shows a successful application of the superposition model. Acknowledgement
This work was supported by the Sichuan Provincial Scientific Foundation. References [I] J.E. Werz and P.V. Auzins, Phys. Rev. 106 (1957) 484. [2] W.M. Fairbank and G.K. Klauminzer, Phys. Rev. B 7 (1973) 500.
[31C.M. McDonagh, B. Henderson, G.F. Imbusch and P. Dawson, J. Phys. C 13 (1980) 3309. [41 M.L. Du and M.G. Zhao, J. Phys. C 19 (1986) 2935. [51 Y.Y. Yeung, J. Phys. Condens. Matter 2 (1990) 2461. [61D.J. Groh. R. Pandey and J.M. Recio, Phys. Rev. B 50 (1994) 14860. Mater. Chem. Phys. 18 [71 K. Asakura and Y. Iwasawa, (1988) 499. [Sl D.J. Newman and B. Ng, Rep. Prog. Phys. 52 (1989) 699. [91W.L. Yu, X.M. Zhang, L.X. Yang and B.Q. Zen, Phys. Rev. B 50 ( 1994) 6756. [lOI Y.Y. Yeung and D.J. Newman, Phys. Rev. B 34(1986) 2258. [ill A. Edgar, J. Phys. C 9 (1976) 4304. 1121 D.J. Newman, D.C. Pryce and W.A. Runciman, Am. Mineral. 63 (1978) 1278. [I31 W.L. Yu and M.G. Zhao, J. Phys. C 20 (1987) 2923. [141 M. Bhtme and R.E. Watson, Proc. Phys. Sot. A 271 (1963) 565. 1151 R.E. Trees, Phys. Rev. 82 (1951) 683.