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Theoretical calculation of zero field splitting parameters of Cr3+ doped ammonium oxalate monohydrate
Physica B ∎ (∎∎∎∎) ∎∎∎–∎∎∎
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Theoretical calculation of zero field splitting parameters of Cr3 þ doped ammonium oxalate monohydrate Ram Kripal n, Awadhesh Kumar Yadav EPR Laboratory, Department of Physics, University of Allahabad, Allahabad 211002, India
art ic l e i nf o
a b s t r a c t
Article history: Received 3 February 2015 Received in revised form 24 February 2015 Accepted 20 March 2015
Zero field splitting parameters (ZFSPs) D and E of Cr3 þ ion doped ammonium oxalate monohydrate (AOM) are calculated with formula using the superposition model. The theoretically calculated ZFSPs for Cr3 þ in AOM crystal are compared with the experimental value obtained by electron paramagnetic resonance (EPR). Theoretical ZFSPs are in good agreement with the experimental ones. The energy band positions of optical absorption spectra of Cr3 þ in AOM crystal calculated with CFA package are in good match with the experimental values. & 2015 Elsevier B.V. All rights reserved.
Keywords: Organic compounds Crystal fields Electron paramagnetic resonance Optical properties
1. Introduction Electron paramagnetic resonance (EPR) yields a great deal of information about the local site symmetry and zero field splitting parameters (ZFSPs) of transition metal ions in crystals [1]. It also enables to identify and characterize the defects responsible for the charge compensation in the impurity doped crystals [2]. EPR study is a powerful tool to study the dynamical aspects of the crystalline state and nature of bonding in crystals [3]. The optical absorption study provides knowledge of the energy levels and crystal field parameters. Cr3 þ is one of the most investigated metal ions. It has 3d3 electronic configuration and 4A2 ground state [4]. The mostly used perturbation procedure treats cubic field and diagonal parts of free ion Hamiltonian as unperturbed Hamiltonian, leaving the perturbation as the spin–orbit coupling, the low symmetry field, and off diagonal part of free ion Hamiltonian. This procedure was used by Macfarlane for F state ions yielding better results [5]. EPR of Cr3 þ doped impurity in ammonium oxalate monohydrate (AOM) crystal at liquid nitrogen temperature has been reported [6]. There are two possibilities of Cr3 þ ion entering the crystal of AOM; substitution at NH+4 ion site and/or structural vacancy. This is interesting to determine the site of this paramagnetic impurity. In the present investigation, the ZFSPs for Cr3 þ ion are calculated using superposition model (SPM) considering Cr3 þ ion to be present at the site of NH+4 ion. The result derived is
consistent with the experimental observation.
2. Crystal structure AOM single crystals are orthorhombic [7]. These belong to the space group P21212 and contain two molecules in the unit cell. The unit cell parameters are: a¼ 8.04 Å, b¼10.27 Å, and c ¼3.82 Å. The ammonium ion is six coordinated by oxygen atoms as shown in Fig. 1. The site symmetry at Cr3 þ ion is approximately orthorhombic.
3. Theoretical investigations EPR spectra of Cr3 þ doped single crystals of AOM were analyzed using the spin Hamiltonian in a crystal field of orthorhombic symmetry. The ground state of transition metal ion in crystal can be described using the spin Hamiltonian having Zeeman electronic (Ze) and ZFS terms [8,9]. The ZFS terms for Cr3 þ ion (S¼ 3/2) at orthorhombic symmetry sites are written as
/ = B20 O20+B22 O22 1 0 0 1 2 2 b2 O2 + b2 O2 3 3 1 2 = D (S z − S (S + 1)) + E (S x2 + S y2 ) 3 =
(1)
n
Corresponding author. Fax: þ 91 532 2460993. E-mail addresses: [email protected] (R. Kripal), [email protected] (A.K. Yadav).
The ZFSPs in Eq. (1) together with conventional zero field splitting parameters D and E are obtained using SPM as [10–14]
http://dx.doi.org/10.1016/j.physb.2015.03.016 0921-4526/& 2015 Elsevier B.V. All rights reserved.
Please cite this article as: R. Kripal, A.K. Yadav, Physica B (2015), http://dx.doi.org/10.1016/j.physb.2015.03.016i
R. Kripal, A.K. Yadav / Physica B ∎ (∎∎∎∎) ∎∎∎–∎∎∎
2
Fig. 1. Crystal structure of AOM in which symmetry adopted axis system (SAAS) is shown.
D = b20 =
− ⎤ ⎡ t2 b2 (R 0 ) ⎢ ⎛ R 0 ⎞ ⎜ ⎟ ∑ (3 cos2 θi − 1) ⎥ ⎥⎦ 2 ⎢⎣ ⎝ Ri ⎠ i
− ⎡ t2 b2 b2 (R 0 ) ⎢ ⎛ R 0 ⎞ E= 2 = ⎜ ⎟ 3 2 ⎢⎣ ⎝ Ri ⎠ 3þ
∑ i
(2)
D¼313 10-4 cm 1, E ¼97 10 4 cm 1 and D ¼309 10 4 cm 1, E¼ 96 10 4 cm 1 for Site I and II, respectively. For orthorhombic symmetry, the ratio b22 /b20 should be within the range (0, 1) [16]. In the present study, the ratio b22 /b20 = 0. 932 and E/D¼ 0.309 for Site
⎤ sin2 θi cos 2ϕi ⎥ ⎥⎦
(3)
3
For Cr (3d , S ¼3/2) ions, there exist crystal field parameters (CFPs) of the rank k¼ 2 and 4, while ZFSPs only of the rank k ¼2.
I, b22 /b20 = 0. 935 and E/D ¼ 0.310 for Site II, which is consistent with above. The calculated ZFSPs, and experimental ZFSPs for Cr3 þ ion are given in Table 2. The theoretical ZFSPs thus obtained are in good agreement with experimental ones [6]. The CFPs for Cr3 þ in crystals are obtained by the following formula [15]
4. Result and discussion
−
3þ
NH+4
ion substitutes the ion in AOM and has similar The Cr ligands environment. From crystal structure the local symmetry around Cr3 þ ion is C1, for which the 14 CF parameters Bkq are admitted by group theory. As some of CF parameters in C1 symmetry are very small [15], the calculations are done on the approximation of orthorhombic symmetry and 5 appreciable CF parameters are determined. For octahedral coordination of Cr3 þ −
ion in LiNbO3 having Cr3 þ –O2 bond, t2 ¼0.12 and b2 (R0 ) ¼ 2.34 cm 1 [13] were used for calculating b20 and b22. The position of Cr3 þ ion and spherical coordinates of ligands are given in Table 1. The conventional ZFSPs D and E of Cr3 þ ion in AOM crystal are determined using Eqs. (2) and (3). The reference distances of 1.95 Å for Site I and 1.93 Å for Site II are taken for the evaluation of ZFSPs [11], and the calculated conventional ZFSPs are
Bkq =
⎛ R 0 ⎞tk ⎟ Kkq (θi ϕi ) ⎝ Ri ⎠
∑ Bk ⎜ i
(4)
where R0 ¼1.95 Å and 1.93 Å (reference distances) for sites I and II, respectively; Ri, θi, ɸi are the polar coordinates of the ith ligand and Kkq is the coordination factor [2]. For calculating Bkq (k ¼2, 4; −
−
q¼ 0, 2, 4), B2 ¼ 40,400 cm 1, t2 ¼ 1.3, B4 ¼ 11,700 cm 1 and t4 ¼3.4 are taken from [2]. The calculated Bkq parameters are given in Table 3. Using these Bkq parameters and CFA program [17,18], the optical spectra of Cr3 þ doped AOM crystals are calculated. The energy levels of the Cr3 þ ion are obtained by diagonalizing the complete Hamiltonian within the 3dN basis of states in the intermediate crystal field coupling scheme. The calculated energy values are given in Table 4 together with the experimental ones [6] for comparison. There is good agreement between the two. Thus the theoretical investigation supports the experimental study [6].
Table 1 Fractional coordinates of Cr3 þ ion together with spherical co-ordinates (R, θ, ɸ) of ligands in AOM single crystal. Position of Cr3 þ (fractional)
Site I: substitutional (0, 0, 0)
Site II: substitutional (0, 0, 0)
Ligands
O(1) O(2) O(3) Ow O,w O,(1) O(1) O(2) O(3) Ow O,w O,(1)
Spherical co-ordinates of ligands R (Å)
θ (deg)
ɸ (deg)
4.4341 2.7652 3.5670 4.0734 4.7498 4.9726 4.8839 5.4441 7.6074 8.1185 8.1185 3.3050
105 122 106 97 121 100 101 74 97 93 107 106
63 24 36 42 42 22 22 45 65 68 68 63
Table 2 Calculated and conventional zero field splitting parameters together with reference distance and experimental ZFSPs for Cr3 þ doped AOM single crystal. R0 (Å) Calculated ZFS parameters (cm 1)
Conventional ZFS parameters ( 10 4 cm 1)
b20
b22
b22/b20
D
E
E/D
1.95
0.0313
0.0292
0.932
Site II 1.93
0.0309
0.0289
0.935
313 309e 309 309e
97 103e 96 103e
0.309 0.323 0.310 0.323
Site I
e¼experimental.
Please cite this article as: R. Kripal, A.K. Yadav, Physica B (2015), http://dx.doi.org/10.1016/j.physb.2015.03.016i
R. Kripal, A.K. Yadav / Physica B ∎ (∎∎∎∎) ∎∎∎–∎∎∎
3
Table 3 Bkq parameters to be used in CFA program for calculating optical absorption spectra. R0 (Å)
Site I Site II
1.95 1.93
Calculated Bkq (cm 1) parameters used for CFA package B20
B22
B40
B42
B44
41512 40960
15564 15683
2694 2995
1243 1198
4991 4809
Table 4 Observed and calculated energy band positions of Cr3 þ doped AOM single crystal from CFA package. Transition from4A2g(F)
2
Experimentally observedband (cm 1) [6]
Eg(G) T1g(G)
16588 20681
4
T2g(F)
22083, 25882, 27457
4
T1g(F)
30292
2
A1g(G) T2g(H)
35257 39129
2
2
Calculated energy band from CFA (cm 1) Site I
Site II
16086, 16241 20630, 20690, 21064 21678, 21742, 22930, 23165, 25274, 27315 29399, 30281, 30484, 31204, 31369, 31459 35788 38911, 38876, 39043
16094, 16233 20503, 20611, 21242 21905, 21953, 23983, 24295, 25496, 27763 29305, 29340, 29490, 29607, 29890, 30044 35327 38608, 39098, 39107
Input parameters: numbers of free ion parameters¼ 5, number of d shell electrons¼ 3, number of fold for rotational site symmetry ¼1; Racah parameters in A, B and C, spin–orbit coupling constant and Trees correction are 0, 803, 3531, 276 and 70 cm 1, respectively; number of crystal field parameters ¼ 5; crystal field parameters for Site I, B20 ¼41512.00, B22 ¼ 15564.00, B40 ¼ 2694.00, B42 ¼1243.00, B44 ¼4991.00 cm 1; spin–spin interaction parameter, M0¼ 0.0000; spin–spin interaction parameter, M2¼ 0.2021; spin-other-orbit interaction parameter, M00¼ 0.0159; spin-other-orbit interaction parameter, M22¼ 0.2021; magnetic field, B¼0.0 Gauss; angle between magnetic field B and z-axis¼ 0.00 degree. Crystal field parameters for Site II, B20 ¼ 40960.00, B22 ¼15683.00, B40 ¼ 2995.00, B42 ¼1178.00, B44 ¼4809.00 cm 1; other parameters are the same as for Site I.
5. Conclusions The theoretical investigation of ZFSPs has been done using superposition model. The conventional ZFSPs for the Cr3 þ ion doped AOM are similar to the experimental ones. The calculated optical spectra using CFPs and CFA program are in agreement with
the experimental ones. The Cr3 þ ions are inferred to enter the lattice substitutionally by replacing NH+4 site and are bound electrically to neighboring vacancies necessary for the charge compensation. Thus our results support the conclusion derived from the experimental data.
Acknowledgment The authors are thankful to the Head, Department of Physics for providing the facilities. One of the authors, Awadhesh Kumar Yadav is thankful to Council of Scientific and Industrial Research (Grant no. GR38/31), New Delhi for financial assistance.
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18]
D.J. Newman, B. Ng, Rep. Prog. Phys. 52 (1989) 699–763. Y.Y. Yeung, D.J. Newman, Phys. Rev. B 34 (1986) 2258–2265. O.S. Venger, R. Valiente, H.U. Gudel, J. Chem. Phys. 115 (2002) 3819. M.G. Brik, C.N. Avram, N.M. Avram, Physica B 384 (2006) 78–81. R.M. Macfarlane, J. Chem. Phys. 47 (1967) 2066–2073; R.M. Macfarlane, Phys. Rev. B 1 (1970) 9891004. R. Kripal, M. Bajpai, A.K. Shukla, Physica B 404 (2009) 82–88. B.F. Pedersen, Acta Crystallogr. B 28 (1972) 746–754. M. Acikgoz, Spectrochim. Acta A 86 (2012) 417–422. M. Acikgoz, P. Gnutek, C. Rudowicz, Chem. Phys. Lett. 524 (2012) 49–55. K.A. Muller, W. Berlinger, J. Phys.C: Solid State Phys. 16 (1983) 6861–6874. T.H. Yeom, J. Phys., Condens. Matter 13 (2001) 10471–10476. P. Gnutek, M. Acikgoz, C. Rudowicz, Opt. Mater. 32 (2010) 1161–1169. T.H. Yeom, Y.M. Chang, C. Rudowicz, Solid State Commun. 87 (1993) 245–249. E. Siegel, K.A. Muller, Phys. Rev. B 19 (1979) 109–120. Y.Y. Yeung, C. Rudowicz, Y.M. Chang, J. Qin, J. Lumin. 60–61 (1994) 108–111. C. Rudowicz, R. Bramley, J. Chem. Phys. 83 (1985) 5192–5197. Y.Y. Yeung, C. Rudowicz, J. Comput. Phys. 109 (1993) 150–152. Y.Y. Yeung, C. Rudowicz, Comput. Chem. 16 (1992) 207–216.
Please cite this article as: R. Kripal, A.K. Yadav, Physica B (2015), http://dx.doi.org/10.1016/j.physb.2015.03.016i
Contents lists available at ScienceDirect
Physica B journal homepage: www.elsevier.com/locate/physb
Theoretical calculation of zero field splitting parameters of Cr3 þ doped ammonium oxalate monohydrate Ram Kripal n, Awadhesh Kumar Yadav EPR Laboratory, Department of Physics, University of Allahabad, Allahabad 211002, India
art ic l e i nf o
a b s t r a c t
Article history: Received 3 February 2015 Received in revised form 24 February 2015 Accepted 20 March 2015
Zero field splitting parameters (ZFSPs) D and E of Cr3 þ ion doped ammonium oxalate monohydrate (AOM) are calculated with formula using the superposition model. The theoretically calculated ZFSPs for Cr3 þ in AOM crystal are compared with the experimental value obtained by electron paramagnetic resonance (EPR). Theoretical ZFSPs are in good agreement with the experimental ones. The energy band positions of optical absorption spectra of Cr3 þ in AOM crystal calculated with CFA package are in good match with the experimental values. & 2015 Elsevier B.V. All rights reserved.
Keywords: Organic compounds Crystal fields Electron paramagnetic resonance Optical properties
1. Introduction Electron paramagnetic resonance (EPR) yields a great deal of information about the local site symmetry and zero field splitting parameters (ZFSPs) of transition metal ions in crystals [1]. It also enables to identify and characterize the defects responsible for the charge compensation in the impurity doped crystals [2]. EPR study is a powerful tool to study the dynamical aspects of the crystalline state and nature of bonding in crystals [3]. The optical absorption study provides knowledge of the energy levels and crystal field parameters. Cr3 þ is one of the most investigated metal ions. It has 3d3 electronic configuration and 4A2 ground state [4]. The mostly used perturbation procedure treats cubic field and diagonal parts of free ion Hamiltonian as unperturbed Hamiltonian, leaving the perturbation as the spin–orbit coupling, the low symmetry field, and off diagonal part of free ion Hamiltonian. This procedure was used by Macfarlane for F state ions yielding better results [5]. EPR of Cr3 þ doped impurity in ammonium oxalate monohydrate (AOM) crystal at liquid nitrogen temperature has been reported [6]. There are two possibilities of Cr3 þ ion entering the crystal of AOM; substitution at NH+4 ion site and/or structural vacancy. This is interesting to determine the site of this paramagnetic impurity. In the present investigation, the ZFSPs for Cr3 þ ion are calculated using superposition model (SPM) considering Cr3 þ ion to be present at the site of NH+4 ion. The result derived is
consistent with the experimental observation.
2. Crystal structure AOM single crystals are orthorhombic [7]. These belong to the space group P21212 and contain two molecules in the unit cell. The unit cell parameters are: a¼ 8.04 Å, b¼10.27 Å, and c ¼3.82 Å. The ammonium ion is six coordinated by oxygen atoms as shown in Fig. 1. The site symmetry at Cr3 þ ion is approximately orthorhombic.
3. Theoretical investigations EPR spectra of Cr3 þ doped single crystals of AOM were analyzed using the spin Hamiltonian in a crystal field of orthorhombic symmetry. The ground state of transition metal ion in crystal can be described using the spin Hamiltonian having Zeeman electronic (Ze) and ZFS terms [8,9]. The ZFS terms for Cr3 þ ion (S¼ 3/2) at orthorhombic symmetry sites are written as
/ = B20 O20+B22 O22 1 0 0 1 2 2 b2 O2 + b2 O2 3 3 1 2 = D (S z − S (S + 1)) + E (S x2 + S y2 ) 3 =
(1)
n
Corresponding author. Fax: þ 91 532 2460993. E-mail addresses: [email protected] (R. Kripal), [email protected] (A.K. Yadav).
The ZFSPs in Eq. (1) together with conventional zero field splitting parameters D and E are obtained using SPM as [10–14]
http://dx.doi.org/10.1016/j.physb.2015.03.016 0921-4526/& 2015 Elsevier B.V. All rights reserved.
Please cite this article as: R. Kripal, A.K. Yadav, Physica B (2015), http://dx.doi.org/10.1016/j.physb.2015.03.016i
R. Kripal, A.K. Yadav / Physica B ∎ (∎∎∎∎) ∎∎∎–∎∎∎
2
Fig. 1. Crystal structure of AOM in which symmetry adopted axis system (SAAS) is shown.
D = b20 =
− ⎤ ⎡ t2 b2 (R 0 ) ⎢ ⎛ R 0 ⎞ ⎜ ⎟ ∑ (3 cos2 θi − 1) ⎥ ⎥⎦ 2 ⎢⎣ ⎝ Ri ⎠ i
− ⎡ t2 b2 b2 (R 0 ) ⎢ ⎛ R 0 ⎞ E= 2 = ⎜ ⎟ 3 2 ⎢⎣ ⎝ Ri ⎠ 3þ
∑ i
(2)
D¼313 10-4 cm 1, E ¼97 10 4 cm 1 and D ¼309 10 4 cm 1, E¼ 96 10 4 cm 1 for Site I and II, respectively. For orthorhombic symmetry, the ratio b22 /b20 should be within the range (0, 1) [16]. In the present study, the ratio b22 /b20 = 0. 932 and E/D¼ 0.309 for Site
⎤ sin2 θi cos 2ϕi ⎥ ⎥⎦
(3)
3
For Cr (3d , S ¼3/2) ions, there exist crystal field parameters (CFPs) of the rank k¼ 2 and 4, while ZFSPs only of the rank k ¼2.
I, b22 /b20 = 0. 935 and E/D ¼ 0.310 for Site II, which is consistent with above. The calculated ZFSPs, and experimental ZFSPs for Cr3 þ ion are given in Table 2. The theoretical ZFSPs thus obtained are in good agreement with experimental ones [6]. The CFPs for Cr3 þ in crystals are obtained by the following formula [15]
4. Result and discussion
−
3þ
NH+4
ion substitutes the ion in AOM and has similar The Cr ligands environment. From crystal structure the local symmetry around Cr3 þ ion is C1, for which the 14 CF parameters Bkq are admitted by group theory. As some of CF parameters in C1 symmetry are very small [15], the calculations are done on the approximation of orthorhombic symmetry and 5 appreciable CF parameters are determined. For octahedral coordination of Cr3 þ −
ion in LiNbO3 having Cr3 þ –O2 bond, t2 ¼0.12 and b2 (R0 ) ¼ 2.34 cm 1 [13] were used for calculating b20 and b22. The position of Cr3 þ ion and spherical coordinates of ligands are given in Table 1. The conventional ZFSPs D and E of Cr3 þ ion in AOM crystal are determined using Eqs. (2) and (3). The reference distances of 1.95 Å for Site I and 1.93 Å for Site II are taken for the evaluation of ZFSPs [11], and the calculated conventional ZFSPs are
Bkq =
⎛ R 0 ⎞tk ⎟ Kkq (θi ϕi ) ⎝ Ri ⎠
∑ Bk ⎜ i
(4)
where R0 ¼1.95 Å and 1.93 Å (reference distances) for sites I and II, respectively; Ri, θi, ɸi are the polar coordinates of the ith ligand and Kkq is the coordination factor [2]. For calculating Bkq (k ¼2, 4; −
−
q¼ 0, 2, 4), B2 ¼ 40,400 cm 1, t2 ¼ 1.3, B4 ¼ 11,700 cm 1 and t4 ¼3.4 are taken from [2]. The calculated Bkq parameters are given in Table 3. Using these Bkq parameters and CFA program [17,18], the optical spectra of Cr3 þ doped AOM crystals are calculated. The energy levels of the Cr3 þ ion are obtained by diagonalizing the complete Hamiltonian within the 3dN basis of states in the intermediate crystal field coupling scheme. The calculated energy values are given in Table 4 together with the experimental ones [6] for comparison. There is good agreement between the two. Thus the theoretical investigation supports the experimental study [6].
Table 1 Fractional coordinates of Cr3 þ ion together with spherical co-ordinates (R, θ, ɸ) of ligands in AOM single crystal. Position of Cr3 þ (fractional)
Site I: substitutional (0, 0, 0)
Site II: substitutional (0, 0, 0)
Ligands
O(1) O(2) O(3) Ow O,w O,(1) O(1) O(2) O(3) Ow O,w O,(1)
Spherical co-ordinates of ligands R (Å)
θ (deg)
ɸ (deg)
4.4341 2.7652 3.5670 4.0734 4.7498 4.9726 4.8839 5.4441 7.6074 8.1185 8.1185 3.3050
105 122 106 97 121 100 101 74 97 93 107 106
63 24 36 42 42 22 22 45 65 68 68 63
Table 2 Calculated and conventional zero field splitting parameters together with reference distance and experimental ZFSPs for Cr3 þ doped AOM single crystal. R0 (Å) Calculated ZFS parameters (cm 1)
Conventional ZFS parameters ( 10 4 cm 1)
b20
b22
b22/b20
D
E
E/D
1.95
0.0313
0.0292
0.932
Site II 1.93
0.0309
0.0289
0.935
313 309e 309 309e
97 103e 96 103e
0.309 0.323 0.310 0.323
Site I
e¼experimental.
Please cite this article as: R. Kripal, A.K. Yadav, Physica B (2015), http://dx.doi.org/10.1016/j.physb.2015.03.016i
R. Kripal, A.K. Yadav / Physica B ∎ (∎∎∎∎) ∎∎∎–∎∎∎
3
Table 3 Bkq parameters to be used in CFA program for calculating optical absorption spectra. R0 (Å)
Site I Site II
1.95 1.93
Calculated Bkq (cm 1) parameters used for CFA package B20
B22
B40
B42
B44
41512 40960
15564 15683
2694 2995
1243 1198
4991 4809
Table 4 Observed and calculated energy band positions of Cr3 þ doped AOM single crystal from CFA package. Transition from4A2g(F)
2
Experimentally observedband (cm 1) [6]
Eg(G) T1g(G)
16588 20681
4
T2g(F)
22083, 25882, 27457
4
T1g(F)
30292
2
A1g(G) T2g(H)
35257 39129
2
2
Calculated energy band from CFA (cm 1) Site I
Site II
16086, 16241 20630, 20690, 21064 21678, 21742, 22930, 23165, 25274, 27315 29399, 30281, 30484, 31204, 31369, 31459 35788 38911, 38876, 39043
16094, 16233 20503, 20611, 21242 21905, 21953, 23983, 24295, 25496, 27763 29305, 29340, 29490, 29607, 29890, 30044 35327 38608, 39098, 39107
Input parameters: numbers of free ion parameters¼ 5, number of d shell electrons¼ 3, number of fold for rotational site symmetry ¼1; Racah parameters in A, B and C, spin–orbit coupling constant and Trees correction are 0, 803, 3531, 276 and 70 cm 1, respectively; number of crystal field parameters ¼ 5; crystal field parameters for Site I, B20 ¼41512.00, B22 ¼ 15564.00, B40 ¼ 2694.00, B42 ¼1243.00, B44 ¼4991.00 cm 1; spin–spin interaction parameter, M0¼ 0.0000; spin–spin interaction parameter, M2¼ 0.2021; spin-other-orbit interaction parameter, M00¼ 0.0159; spin-other-orbit interaction parameter, M22¼ 0.2021; magnetic field, B¼0.0 Gauss; angle between magnetic field B and z-axis¼ 0.00 degree. Crystal field parameters for Site II, B20 ¼ 40960.00, B22 ¼15683.00, B40 ¼ 2995.00, B42 ¼1178.00, B44 ¼4809.00 cm 1; other parameters are the same as for Site I.
5. Conclusions The theoretical investigation of ZFSPs has been done using superposition model. The conventional ZFSPs for the Cr3 þ ion doped AOM are similar to the experimental ones. The calculated optical spectra using CFPs and CFA program are in agreement with
the experimental ones. The Cr3 þ ions are inferred to enter the lattice substitutionally by replacing NH+4 site and are bound electrically to neighboring vacancies necessary for the charge compensation. Thus our results support the conclusion derived from the experimental data.
Acknowledgment The authors are thankful to the Head, Department of Physics for providing the facilities. One of the authors, Awadhesh Kumar Yadav is thankful to Council of Scientific and Industrial Research (Grant no. GR38/31), New Delhi for financial assistance.
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18]
D.J. Newman, B. Ng, Rep. Prog. Phys. 52 (1989) 699–763. Y.Y. Yeung, D.J. Newman, Phys. Rev. B 34 (1986) 2258–2265. O.S. Venger, R. Valiente, H.U. Gudel, J. Chem. Phys. 115 (2002) 3819. M.G. Brik, C.N. Avram, N.M. Avram, Physica B 384 (2006) 78–81. R.M. Macfarlane, J. Chem. Phys. 47 (1967) 2066–2073; R.M. Macfarlane, Phys. Rev. B 1 (1970) 9891004. R. Kripal, M. Bajpai, A.K. Shukla, Physica B 404 (2009) 82–88. B.F. Pedersen, Acta Crystallogr. B 28 (1972) 746–754. M. Acikgoz, Spectrochim. Acta A 86 (2012) 417–422. M. Acikgoz, P. Gnutek, C. Rudowicz, Chem. Phys. Lett. 524 (2012) 49–55. K.A. Muller, W. Berlinger, J. Phys.C: Solid State Phys. 16 (1983) 6861–6874. T.H. Yeom, J. Phys., Condens. Matter 13 (2001) 10471–10476. P. Gnutek, M. Acikgoz, C. Rudowicz, Opt. Mater. 32 (2010) 1161–1169. T.H. Yeom, Y.M. Chang, C. Rudowicz, Solid State Commun. 87 (1993) 245–249. E. Siegel, K.A. Muller, Phys. Rev. B 19 (1979) 109–120. Y.Y. Yeung, C. Rudowicz, Y.M. Chang, J. Qin, J. Lumin. 60–61 (1994) 108–111. C. Rudowicz, R. Bramley, J. Chem. Phys. 83 (1985) 5192–5197. Y.Y. Yeung, C. Rudowicz, J. Comput. Phys. 109 (1993) 150–152. Y.Y. Yeung, C. Rudowicz, Comput. Chem. 16 (1992) 207–216.
Please cite this article as: R. Kripal, A.K. Yadav, Physica B (2015), http://dx.doi.org/10.1016/j.physb.2015.03.016i