Spectrochimica Acta Part A 67 (2007) 694–696
Studies of the defect structure for Mn2+ in KTaO3 crystal from the calculation of EPR zero-field splitting Zheng Wen-Chen a,b,∗ a
b
Department of Material Science, Sichuan University, Chengdu 610064, People’s Republic of China International Center for Materials Physics, Chinese Academy of Sciences, Shenyang 110016, People’s Republic of China Received 11 May 2006; accepted 25 July 2006
Abstract There are several mistakes in the recent paper about the theoretical studies of defect structure for Mn2+ ion at the 12-fold tetrakaidecahedral K+ site in KTaO3 by calculating the spin Hamiltonian (SH) parameters, so the calculated defect structure (which is smaller than those obtained from the local density approximation (LDA) method, density functional theory in the generalized gradient approximation (GGA) and the dipole moment study (DMS)) is doubtful. Therefore, we restudy the defect structure in this paper by using the reasonable expressions and parameters. The present result is in agreement with those based on LDA, GGA and DMS methods and can be regarded as reasonable. It appears that the reliability of the defect structure of impurity center determined from the calculation of SH parameter depends strongly upon reasonableness of the used expressions and parameters. © 2006 Elsevier B.V. All rights reserved. Keywords: Detect structure; Electron paramagnetic resonance (EPR); Crystal-field theory; Mn2+ ; KTaO3
The determination of the defect structures for the extrinsic defects in crystals is an interesting and significant problem because the defects can influence strongly host material properties. Considering that the spin Hamiltonian (SH) parameters (in particular, the zero-field splitting D) of a paramagnetic defect in crystals are sensitive to its defect structure, one can study the defect structure of paramagnetic defect by calculating its SH parameters. The reliability of results depends upon the reasonableness of the used formulas and parameters. Recently, Wu et al. [1] calculated the SH parameters of the tetragonal Mn2+ impurity center in KTaO3 from two defect models by using the high-order perturbation formulas based on the strong cubic field approximation. In model I, Mn2+ replaces the host Ta5+ ion, associated with a captive oxygen vacancy (V0 ) in its first-neighbour shell. Since the effective charge of V0 is positive, the Mn2+ ion shifts away from the ideal Ta5+ site by ZI along C4 axis because of the electrostatic interaction, so the defect structure in this Mn2+ –V0 center is characterized by ZI . In Model II, Mn2+ substitutes for K+ ion and has an off-center displacement ZII along C4 axis ∗
Correspondence address: Department of Material Science, Sichuan University, Chengdu 610064, People’s Republic of China. Fax: +86 28 85416050. E-mail address:
[email protected]. 1386-1425/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.saa.2006.07.050
because the ionic radius of Mn2+ is much smaller than that of K+ , the defect structure in this model is characterized by ZII . From the calculations, they found that the calculated SH param˚ show slightly better eters based on model II (with ZII ≈ 0.6 A) agreement with the observed values than those based on model I ˚ They therefore thought that model II sug(with ZI ≈ −0.27 A). gested in the previous papers [2–4] is reasonable. Noteworthily, ˚ obtained from the the ZII is smaller than those (≈0.8–0.9 A) local density approximation (LDA) study [2], the density functional theory in generalized gradient approximation (GGA) [3] and the dipole moment study (DMS) [4]. More importantly, there are several mistakes in their calculations: (1) They thought that the K+ replaced by Mn2+ in KTaO3 is at a dodecahedral site, it is surprising why they apply the parameters B, C, Dq and ζ and the relation between the ¯ 4 (R) and Dq for Mn2+ ion in a tetraheintrinsic parameter A dron rather than in a dodecahedron. In fact, K+ ion in KTaO3 is at a 12-fold coordinated tetrakaidecahedral rather than dodecahedral site. For 3dn ions in whether a tetrakaidecahedron or dodecahedron, the above parameters and relation are unlike those in a tetrahedron because of the different coordination number and different metal–ligand distance. In
Z. Wen-Chen / Spectrochimica Acta Part A 67 (2007) 694–696
the case of tetrakaidecahedron under study, from the super¯ 4 (R0 ) or position model [5], one can find Dq = −(2/3)A ¯ A4 (R0 ) = −(3/2)Dq . So, in Ref. [1], the applications of ¯ 4 (R0 ) = −(27/16)Dq and the parameters B, the relation A C, ζ and Dq obtained for Mn2+ in tetrahedron to the case of Mn2+ in tetrakaidecahedron are unsuitable. (2) In superposition model [5], the crystal field parameters: ¯ k (Rj )Kkq (θj , φj ) Bkq = (1) A j
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From the superposition model [5], the tetragonal field parameters Bkq can be written as 3 R0 t2 2 ¯ 2 (R0 ) (3 cos θi − 1) , B20 = 4A Ri i=1 3 R0 t4 4 2 ¯ (35 cos θi − 30 cos θi + 3) , B40 = 4A4 (R0 ) Ri i=1 √ ¯ 4 (R0 ) B44 = 2 70A t4
t4 t4 R0 R0 R0 × sin4 θ1 − sin4 θ2 + sin4 θ3 R1 R2 R3 (5)
May be in the coordination factors Kkq (θ j , φj ), the 45◦ difference of the vectorial angle φj between the ligands in upper (or lower) plane and those in central plane is not considered, the expression of tetragonal field parameter Dt in Eq. (3) of Ref. [1] is incorrect. This point can be con¯ 2 (R0 ) ≈ 10.8A ¯ 4 (R0 ) [1]. A ¯ 4 (R0 ) = where t2 ≈ 3, t2 ≈ 5 and A firmed as follows: according to the crystal-field theory, for √ , as said before. The structure parameters Ri and θ i −(3/2)D q 3dn ion in cubic symmetry (i.e., R1 = R2 = R3 = ( 2/2)a, √ are defined in Ref. [1] (note: θ 3 should be corrected, as mencos θ1 = cos θ3 = 2/2, cos θ2 = 0 here), the tetragonal tioned above). The optical parameters B, C and ζ for Mn2+ at field parameter Dt should be equal to zero, however, the K+ site of KTaO3 should be slightly larger than those at Ta5+ parameter Dt in Ref. [1] cannot. The correct expression of site because of the larger metal–ligand distance. The value of Dt should be: Dq for Mn2+ at K+ site is much smaller than that at Ta5+ site √ 4 ¯ 70 1 Dt = − B40 − B44 = − A 4 (R0 ) 21 5 21 3 t4 t4 t4 R0 t4 R0 R0 R0 4 2 4 4 4 × (2) (35 cos θi − 30 cos θi + 3) − 7 sin θ1 − 7 sin θ3 + 7 sin θ2 Ri R1 R3 R2 i=1
(3) The expression of angle θ3 = (π/2) + tg−1 (a/(a + ZII )) is also incorrect. The correct expression should be θ3 = π − tg−1 (a/(a + ZII )) or θ3 = (π/2) + tg−1 ((a + ZII )/a).
(as said before). Considering that a ∝ |Dq |n (where n ≈ 2–4 [11,12], we take the average value n ≈ 3 here) and the values of a for the isoelectronic Fe3+ at K+ and Ta5+ sites of KTaO3 [9,10], we estimate reasonably for Mn2+ at K+ site:
Because of these mistakes, the calculated SH parameters and hence the defect structure in model II for KTaO3 :Mn2+ in Ref. [1] are doubtful and unreliable. It is worth notice that the above mistakes were also made by them in the studies of SH parameters and defect structure for Ni3+ [7] and Fe+ [8] at the K+ site of KTaO3 crystals. Obviously, these results in Refs. [7,8] are also unreliable. The cubic crystal field (characterized by the cubic field parameter Dq ) for 3d5 ions at K+ site of KTaO3 is much weaker than that at the Ta5+ site [9] because of the large metal–ligand distance. The very small cubic zero-field splitting a (≈30 × 10−4 cm−1 [9,10]) of Fe3+ at K+ site, compared to that (≈345 × 10−4 cm−1 [10]) of Fe5+ at Ta5+ site, reflects this point. So, for Mn2+ at K+ site the fourth-order perturbation formula of zero-field splitting D based on the spin-orbit coupling mechanism is preferable to the formula based on the strong field approximation used in Ref. [1]. For 3d5 ion in tetragonal symmetry, the fourth-order perturbation formula is [6]:
B ≈ 800 cm−1 ,
D=
3ζ 2 ζ2 2 2 2 (−B − 21ζB ) + + 14B44 ) (−5B40 20 20 70P 2 D 63P 2 G (3)
with P = 7B + 7C,
G = 10B + 5C,
D = 17B + 5C
(4)
Dq ≈ −635 cm−1 ,
C ≈ 2900 cm−1 ,
ζ ≈ 320 cm−1 , (6)
from the optical spectral parameters of Mn2+ at Ta5+ site [1]. Substituting all these parameters into the above formulas, we obtain ˚ ZII ≈ 0.926 A
(7)
by fitting the calculated zero-field splitting D to the observed ˚ based on value. The result is in agreement with that (≈0.81 A) ˚ based on the LDA [2] and GGA [3] studies and that (≈0.9 A) the dipole moment analysis from EPR and dielectric studies [4]. So, it is reasonable. For comparison, we also use the reasonable parameters in Eq. ¯ 4 (R0 ) = −(3/2)Dq ) and the correct (6) (including the relation A expressions of Dt and θ 3 given above to the calculation of zerofield splitting D of KTaO3 :Mn2+ from the formulas of D given in Ref. [1]. It is found that to reach a good fit between calculated and ˚ The value observed splitting D, the displacement ZII ≈ 0.47 A. (which is even smaller than that obtained in Ref. [1]) is too small to be regarded as reasonable. The causes may be due mainly to the fact that the formula based on the strong field approximation in Ref. [1] is effective only to the cases of strong cubic field parameter Dq and small tetragonal distortion. It appears that the
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Z. Wen-Chen / Spectrochimica Acta Part A 67 (2007) 694–696
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