Microscopic spin-Hamiltonian parameters and crystal field energy levels for the low C3 symmetry Ni2+ centre in LiNbO3 crystals

ARTICLE IN PRESS

Physica B 348 (2004) 151–159

Microscopic spin-Hamiltonian parameters and crystal field energy levels for the low C3 symmetry Ni2þ centre in LiNbO3 crystals Zi-Yuan Yanga,b, Czeslaw Rudowiczc,*, Yau-Yuen Yeungd a Microelectronics Institute, Xidian University, Xi’an 710071, PR China Institute of Chemistry and Physics, Department of Physics, Baoji University of Arts and Science, Baoji 721007, PR China c Department of Physics and Materials Science, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong SAR, China d Department of Science, The Hong Kong Institute of Education, 10 Lo Ping Road, Tai Po, New Territories, Hong Kong SAR, China b

Received 26 November 2003; received in revised form 26 November 2003; accepted 27 November 2003

Abstract The microscopic spin-Hamiltonian (MSH) parameters and the crystal field (CF) energy levels for Ni2þ ions in LiNbO3 crystals have been investigated using the crystal field analysis/microscopic spin-Hamiltonian package recently developed. The investigations considered for the first time the spin–spin (SS) and spin-other-orbit (SOO) interactions. The low-symmetry effects (LSE) arising from the additional terms ðImðB43 Þa0Þ induced at the C3 symmetry sites by the distortion angle j; which have been omitted in earlier works, have also been dealt with. This study shows that for LiNbO3 : Ni2þ the contributions arising from SS and SOO interactions to the zero-field splitting parameter D are appreciable, whereas those to gjj and g> are quite small. Since the distortion angle j ðD0:68 Þ for LiNbO3 : Ni2þ is rather small, the contributions to the spin-Hamiltonian (SH) parameters arising from LSE are also small. Feasibility of application of the superposition model is also discussed. A good overall agreement between the theoretical and experimental results for the SH parameters and the CF energy levels has been obtained. r 2003 Elsevier B.V. All rights reserved. PACS: 76.30.F; 71.70.C; 75.10.D Keywords: Microscopic spin-Hamiltonian (MSH) parameters; Spin–spin (SS) interaction; Spin-other-orbit (SOO) interaction; Low symmetry effects (LSE); LiNbO3 : Ni2þ crystals

1. Introduction LiNbO3 is an important technological crystal because of its applications in optoelectronics as an optical waveguide substrate [1], non-linear materi*Corresponding author. Tel.: +852-27887787; fax: 85227887830. E-mail address: [email protected] (C. Rudowicz).

al [2], and as solid-state laser host matrix [3]. In particular, LiNbO3 crystals doped with the transition-metal (TM) ions, e.g., Ti3þ [4,5], Cr3þ [6–9], Ni2þ [10], Mn2þ [11,12], and Fe3þ [13,14], and rare-earth (RE) ions, e.g., Er3þ [15], have attracted much attention. The TM or RE ions in such crystals are responsible for modifications of the optical properties of the host matrix. Hence these impurity ions in LiNbO3 crystals play a major

0921-4526/$ - see front matter r 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2003.11.085

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role, e.g. some dopants are used to increase the photorefractive sensitivity to light. The spinHamiltonian (SH) parameters and, to a lesser extent, the crystal field (CF) ones (see, e.g. Refs. [16–18]), are known to reflect very sensitively even small variations in the coordination of the TM impurity ions in such materials. Thus the theoretical studies of the SH and CF parameters as well as their experimental studies using electron paramagnetic resonance (EPR) and optical spectroscopy, respectively, can provide a great deal of microscopic insights concerning the crystal structure, structural disorder, phase transitions, pressure behavior as well as the observed magnetic and spectroscopic properties of TM ions in crystals [4–18]. The SH parameters and CF energy levels have been reported for Ni2þ ions doped into LiNbO3 crystals [19,20]. Ni2þ ions exhibit the ground state 3 A2 at the C3 symmetry sites in LiNbO3 and show anisotropic EPR spectra [19,20] with the zero-field splitting (ZFS) parameter D ¼ 5:31 cm1 and the Zeeman factor Dg ¼ gjj  g> ¼ 0:04 [19]. These values are remarkably larger in magnitude than those of Cr3þ (D ¼ 0:39 cm1 ; DgE0 [21]), Mn2þ (D ¼ 0:07245 cm1 ; Dg ¼ 0:012 [11]), and Fe3þ (D ¼ 0:1640ð5Þ cm1 ; Dg ¼ 0:008 [14]) ions in LiNbO3 : In order to investigate the SH parameters and the CF energy levels of Ni2þ ions in LiNbO3 crystals, Zhou et al. [22] developed a complete diagonalization method (CDM) for 3d8 ion at C3v symmetry using the strong CF scheme. The CDM [22] results were criticized as incorrect by Li [23], who independently developed a similar CDM. However, more recent studies [24,25] reveal that the results [22,23] are incorrect, most probably due to errors in the matrix elements as suggested by Zhang et al. [25] concerning Li’s results [23]. So far, no satisfactory theoretical interpretation for the experimental findings [19,20] has been proposed. Recently, in order to provide a better understanding of the electronic structure of 3d2 ð3d8 Þ ions in crystals, an extended crystal-field analysis/ microscopic spin-Hamiltonian (CFA/MSH) computer package has been developed by us. This package is based on the CFA package for 3dN ions at arbitrary symmetry sites [26–28] and its recent

Windows version [24], whereas the MSH modules at present are applicable for 3d2 ð3d8 Þ ions at trigonal type I (C3v ; D3 ; D3d ) and type II (C3 ; C3i ) symmetry sites including the ‘imaginary’ CF terms [29]. The Hamiltonian adopted in the CFA/MSH package includes all terms considered earlier [26–28] and, additionally, the spin–spin (SS) and spin–other-orbit (SOO) [29,30] interactions, which have not been considered in the previous microscopic studies [22–25]. The CFA/MSH package enables to study not only the CF energy levels and wave functions but also the SH parameters as a function of the CF parameters (B20 ; B40 ; ReB43 ; ImðB43 Þ) for 3d2 ð3d8 Þ ions at trigonal types I and II symmetry sites. In the present work, the CFA/MSH package is used to investigate the SH and the CF energy levels taking into account the actual C3 symmetry of the Ni2þ – O6 complex in LiNbO3 : Ni2þ crystals.

2. Theoretical background of the CFA/MSH package for 3d2 and 3d8 ions A large amount of the recent work has been devoted to the microscopic studies of the SH parameters for the transition-metal 3dN ions at various symmetry sites in crystals. The incentive comes from the need to explain the experimental results accumulated due to extensive applications of the electron magnetic resonance (EMR) techniques. However, the theories published so far appear not to be fully satisfactory. In particular, the SS interaction, SOO interaction, and C3 low symmetry effects have as yet not been considered mainly due to computational difficulties. Hence, it is worth investigating the role of these interactions in explaining the MSH parameters. The CFA/ MSH package enables such comprehensive theoretical studies, since it includes these interactions on top of those considered earlier [19,22–25] as well as takes into account all 45 states in the 3d2 ð3d8 Þ configuration. 2.1. Energy matrices The Ni2þ ions doped into LiNbO3 experience a distorted octahedral CF with the local site

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symmetry given by C3 point group. In the CF framework, the total Hamiltonian is written as [26–29] H ¼ Hee ðB; CÞ þ HTrees ðaÞ þ HCF ðBkq Þ þ Hm ðz; M0 ; M2 Þ;

ð1Þ

where the respective terms represent the Coulomb interactions, the Trees correction, CF interactions, and magnetic interactions. The latter include the SO, SOO, and SS interactions [29,30]: Hm ¼ Hso ðzd Þ þ Hsoo ðM0 ; M2 Þ þ Hss ðM0 ; M2 Þ; ð2Þ the explicit form of which has been given in Eqs. (2)–(4) of Ref. [29]. In Eq. (2), zd is the spin– orbit interaction parameter whereas M0 and M2 are the Marvin’s radial integrals used for representing the SS and SOO interactions. The CF Hamiltonian for trigonal symmetry in the Wybourne notation [17,31] is given as [32] HCF ¼ B20 C0ð2Þ þ B40 C0ð4Þ þ B43 C3ð4Þ ð4Þ þ B43 C3 ;

ð3Þ

where Bkq are the CF parameters. In general, the B20 and B40 are always real, whereas for the trigonal symmetry B43 and B43 are real for type I, while complex for type II. Since in the Wybourne notation the relation B ¼ ð1Þq B ð4Þ kq

kq

holds [32], the two components Re and Im of either B43 or B43 are enough for full parameterization; we chose here B43 ¼ ReðB43 Þ þ i ImðB43 Þ: The CFA/MSH package constructs the complete 45  45 energy matrix for 3d2 ð3d8 Þ ion at trigonal type II symmetry and, for the first time, incorporates the SS and SOO interactions omitted in previous studies [19,22–25]. The complete energy matrix can be partitioned into three smaller matrices, each of dimension 15  15: Since the ð10  NÞ-electron system can be regarded as the N-hole system (see, e.g. Ref. [33]), one can obtain the d8 matrix by changing the signs of only the CF and SO matrix elements within the complete energy matrix for the d2 configuration, whereas no such change is required for the SS and SOO matrix elements. The methods of calculation of the matrix elements for Hes ; Hso ; and HCF have been

153

described in Ref. [26], whereas those for HSS and HSOO in Ref. [29]. The Hamiltonian matrices obtained in this way are the functions of the Racah parameters B and C; CF parameters Bkq ; SO interactions constant zd ; and SS (or SOO) interactions parameters M0 ; M2 : Provided the values of these microscopic parameters are available, diagonalization of the full Hamiltonian matrices yields the energy levels and eigenvectors, including the ground state eigenvectors to be used in the calculations of the MSH parameters. 2.2. MSH parameters for d 8 ions at C3 symmetry The cubic orbital singlet ground state 3 A2 ð3d8 Þ of Ni2þ ion is not spilt by the C3 symmetry CF, whereas the magnetic interactions, Eq. (2), split this state into the spin states jE71 ð3 F k3 A2 k3 AÞS and jAð3 F k3 A2 k3 AÞS: We adopt here the labeling of the final states [24]: jGC ð2Sþ1 Lk2Sþ1 GOh k2Sþ1 GC3 ÞS; which indicates 3 explicitly the parentage of the states. Using the CFA/MSH package, the ground spin ðS ¼ 1Þ states of the d8 configuration are obtained by complete diagonalization of the three 15  15 matrices in the form of linear combinations of the basis LS states as [26,29] jcþ1 S jEþ1 ð3 F k3 A2 k3 AÞS ¼

15 X

aþ1;j jjj S;

ð5aÞ

j¼1

jc1 S jE1 ð3 F k3 A2 k3 AÞS ¼

15 X

a1;j jjj S;

ð5bÞ

j¼1

jc0 S jAð3 F k3 A2 k3 AÞS ¼

15 X

a0;j jjj S:

ð5cÞ

j¼1

The states jcþ1 S; jc1 S; and jc0 S are represented by real functions for the trigonal type I symmetry used in [24], whereas complex ones for the trigonal type II symmetry used here. For Ni2þ ions at C3 symmetry, the effective spin Hamiltonian, taking into account the ZFS and

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Zeeman terms [17,18], can be written as [24]   HS ¼ HZFS þ HZe ¼ D Sz2  13 SðS þ 1Þ þ mB gjj Bz Sz þ mB g> ðBx Sx þ By Sy Þ

with the z-axis along a [1 1 1] direction. For 3d8 ions at trigonal symmetry sites the CFA/MSH package computes the MSH parameters in Eq. (6) in the following way. The ZFS parameter D is directly related to the ZFS between the spin singlet ðMS ¼ 0Þ and doublet ðMS ¼ 71Þ and is computed using the built-in MSH expression [29]

using the optical absorption data [19]. The Trees correction a is chosen as 43:48 cm1 for free Ni2þ ion [36]. The SS or SOO parameter values M0 ¼ 0:3382 cm1 and M2 ¼ 0:0264 cm1 are available for Ni2þ ions from atomic data [35]. Having fixed the values of these input parameters, the MSH parameters D; gjj ; and g> ; which can be experimentally measured by EPR, as well as the energy levels, which can be derived from optical spectroscopy measurements, become functions of the CF parameters B20 ; B40 ; and B43 only.

D ¼ eðjE71 ð3 F k3 A2 k3 AÞSÞ

3.1. Crystal structure and CF parameters

 eðjAð3 F k3 A2 k3 AÞSÞ

ð6Þ

ð7Þ

with the ground state energies taken as obtained within the CFA module by diagonalization of the complete energy matrices. In the external magnetic field B the energy levels are further split by the actual Zeeman interaction HZe ¼ mB ðkL þ ge SÞ B;

ð8Þ

where ge ¼ 2:0023; and k is the orbital reduction factor, and the angular momenta: orbital L and electronic spin S; represent the summation over single electron variables. The CFA/MSH package computes the axial components of the Zeeman gfactors gjj and g> in Eq. (6) using the built-in MSH expressions [24] ð1Þ gjj ¼ k/cþ1 jLð1Þ 0 jcþ1 S þ ge /cþ1 jS0 jcþ1 S;

ð9aÞ

ð1Þ g> ¼ kð/cþ1 jLð1Þ 1 jc0 S  /cþ1 jLþ1 jc0 SÞ

The LiNbO3 structure has been determined by X-ray and neutron diffraction [37–39]. The centers of the oxygen octahedra are occupied by cations, whereas the structural vacancy (SV) forms an alternating sequence Liþ –Nb5þ –SV–Liþ –Nb5þ – SV [8,38–41]—see Fig. 1 in Ref. [8]. It has been reported [42] that in LiNbO3 : Ni2þ crystals the divalent Ni2þ ions occupy Nb5þ sites with C3 point group symmetry. However, the previous studies for LiNbO3 : Ni2þ were based on the approximated C3v [22,23,25] or Oh [20] symmetry rather than on the actual C3 symmetry. Such approximations (C3v or Oh ) may not provide a reliable insight into the energy level structure, and the MSH parameters for Ni2þ ions in LiNbO3 crystals. In the present work, we have considered the contributions to the MSH parameters and the CF

ð1Þ ð1Þ þ ge ð/cþ1 jS1 jc0 S  /cþ1 jSþ1 jc0 SÞ: ð9bÞ

3. Applications to Ni2+ ions in LiNbO3 crystals Using the MSH expressions derived in Section 2 and the energy levels and wave functions obtained from the CFA module, the MSH parameters can be estimated for any set of the input values of B & C; Bkq ; zd ; k; and M0 & M2 : For Ni2þ in LiNbO3 : Ni2þ crystals, B ¼ 816 cm1 ; C ¼ 3224 cm1 ; zd ¼ 540 cm1 ; and k ¼ 0:83 have been obtained [24]

-5.24

ZFS parameter D (cm-1)

The matrix elements of the irreducible tensor operators in Eq. (9) are obtained using the Wigner–Eckart Theorem [24,34].

-5.20

-5.28

-5.32

-5.36

-5.40 260

280

300

320

340

360

380

-1

ImB43 (cm ) Fig. 1. The variation of SFS parameter D with CF parameter IMðB43 Þ:

ARTICLE IN PRESS Z.-Y. Yang et al. / Physica B 348 (2004) 151–159

energy levels arising from the low symmetry effects due to the actual C3 symmetry as well as the SS and SOO interactions omitted in the previous studies [20,22–25]. With the z-axis for HCF chosen along the [1 1 1] axis, we adopt the definition of the x- and y-axis as given in Ref. [29]. Then from the X-ray data [37] we obtain the structural parameters for the Nb centers in the undistorted LiNbO3 crystals: R1 ¼ 0:1889 nm; R2 ¼ 0:2112 nm; a ¼ 61:65 ; b ¼ 47:99 ; and j ¼ 0:68 (see, Fig. 1 in Refs. [8,29]). In principle, these values of the structural parameters could be used as starting values within the superposition model (SPM) [43–47], which provides quantitative relationships between the structural parameters and CF ones, for modeling the lattice distortions as well as the CF parameters for various structural distortion configurations (see, e.g. Refs. [7,8,11,14,24,29]). Since the application of SPM for the present ion/host system is technically feasible, we have initially considered ‘‘fitting’’ or actually matching the structural parameters for the distorted LiNbO3 : Ni2þ host via the SPM relationships. Various sets of the CF parameters were calculated by successive SPM calculations and subsequently used in the CFA/ MSH package to obtain the theoretical CF energy levels and states as well as the SH parameters, which were then compared with the respective experimental data. In fact, we have obtained a perfect agreement between the theory and experiment using this SPM-based ‘‘fitting’’ approach. However, in view of the inherent uncertainties in the input data, we have finally limited usage of this approach to consideration of the CF parameter ImðB43 Þ (see below). Note that the value of the intrinsic SPM parameter A% 2 is unknown for Ni2þ in LiNbO3 and can only be approximated from the ratio A% 2 =A% 4 : Hence the SPM-calculated values of the CF parameters could hardly have uncertainties less than 10%. This would induce much greater uncertainties in the final ‘‘fitted’’ quantities, rendering this approach unreliable. Thus we refrain from providing the SPM results in full here. In order to consider the C3 low symmetry effect (LSE), the knowledge of the CF parameter ImðB43 Þ is necessary. The differences in crystal structure between the C3v and C3 symmetry can be

155

described by the distortion angle j of the rotation of the upper and lower oxygen triangles in the octahedron away from the sv plane (see Fig. 1 of Ref. [29]). For j ¼ 0; ImðB43 Þ ¼ 0 and C3 symmetry reduces to C3v : In view of the small j ðD0:68 Þ; the magnitude of ImðB43 Þ may be expected to be quite small and thus its effect on the CF energy levels and states as well as the SH parameters may be insignificant. To verify this expectation, we may employ SPM, since ImðB43 Þ does not depend on the intrinsic parameter A% 2 and such estimates may be more reliable than in the case of other CF parameters. Using the SPM expression [29] pffiffiffiffiffi ImðB43 Þ ¼ 6 35A% 4 Qt4 sin3 b cos b sin 6j; ð10Þ where Q is the radial ratio ðR0 =R2 Þ (see below), t4 is the power-law exponent, A% 4 is the intrinsic parameter [44,47], and b is the bond angle within the oxygen octahedron defined in Fig. 1 of Ref. [8]. Note that in Eq. (18) of Ref. [29] the sign at the imaginary term inside the bracket (+i) is misprinted and should be replaced by ðiÞ; consequently the RHS in Eq. (10) above is positive. We adopt the values of R1 ; R2 ; b; and j [35,37] obtained above for the undistorted LiNbO3 crystals. The reference distance R0 is approximated as R0 EðR1 þ R2 Þ=2: A% 4 can be found from the relation for the cubic CF parameter Dq [48]: A% 4 E3Dq=4; whereas we take t4 ¼ 5 [44,49]. Then Eq. (10) yields ImðB43 Þ ¼ 314 cm1 ; i.e. a small value indeed. In order to check the influence of ImðB43 Þ on the SH parameters, we vary ImðB43 Þ by 720%: The dependence of the SH parameters on ImðB43 Þ is plotted in Figs. 1 and 2 for D and gfactors, respectively. It turns out that the effect of about 20% uncertainty in the value ImðB43 Þ on D; gjj ; and g> is indeed very small. 3.2. Results and discussions For the reasons discussed above, instead of the full-scale SPM approach, we utilize the CF parameters obtained from the optical data, i.e. v ¼ 950 cm1 ; v0 ¼ 600 cm1 ; and Dq ¼ 792 cm1 [19,24]. This approach should be more reliable as it involves no a priori assumed values. Substituting the parameter values selected above for B; C; zd ; k;

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a; M0 ; and M2 together with the values of Bkq (obtained using the relationships [24] between Bkq in Eq. (3) and v; v0 ; and Dq —as listed in Table 1) into the CFA/MSH package, we obtain for Ni2þ ions in LiNbO3 crystals the SH parameters listed in Table 1 and the CF energy levels in Table 2. Note that calculations including the SOO interactions require using instead zd the effective value [29] of the SO coupling constant z0 ð¼ zd 7ð2N  3ÞM0 þ 42M2 ¼ zd  7M0 þ 42M2 ¼ 538:7414 cm1 for Ni2þ ). This is done internally in the CFA/MSH package. Our previous calculations [24] were aimed at comparative analysis of earlier results, which did not include the Trees correction, and hence used a ¼ 0: The present calculations have been carried out for both a ¼ 0 and 43:48 cm1 however, only

Zeeman g-factors: g// andg⊥

2.30

2.25

2.20

g // g⊥

2.15

2.10

2.05

2.00 260

280

300

320

340

360

380

-1

ImB43 (cm ) Fig. 2. The variation of gjj and g> with CF parameter ImðB43 Þ:

the latter results are provided. We note that neglecting the Trees correction induces about less than 1% difference in the calculated values of D; whereas negligible differences in the g-factors. Table 1 reveals that taking into account the SO, SS, and SOO interactions yields a good agreement between the theoretical values of D and g-factors (row (1) or (5)) and the experimental ones. On the other hand, using the same input parameters as in row (1) of Table 1, a good agreement between theory and experiment is also obtained for the CF energy levels of Ni2þ in LiNbO3 crystals (see Eð1Þ in Table 2). The assignment of the optical transitions in Table 2 has been based on the energy-level calculations and the selection rules. In Table 2, we also present the energy levels shifts due to the SO, SS, and SOO interactions, as well as LSE. The average values of the energy levels shifts induced by a given contribution are 1.81, 5.36, and 2:06 cm1 for the SS, SOO interactions, and LSE, respectively. It can be seen from Table 2 that the combined contributions arising from the SS and SOO interactions to various multiplet energy levels for Ni2þ ions in LiNbO3 crystal were estimated to be in the range of several cm1 ; respectively. This range is comparable with that for V3þ ions in Al2 O3 [29]. Concerning the magnetic interactions, our study reveals that the contributions to D from the SO, SS, and SOO interaction are 90.4%, 3.9%, and 5.7%, respectively (see Tables 1 and 3). These results show that the ZFS parameter D is mostly induced by the SO interaction, whereas the combined (SS+SOO) contributions are also

Table 1 The values of the ZFS parameter D (in cm1 ) and g-factors (unitless), calculated with B ¼ 816 cm1 ; C ¼ 3224 cm1 ; zd ¼ 540 cm1 ; M0 ¼ 0:3382 cm1 ; M2 ¼ 0:0264 cm1 ; k ¼ 0:83; a ¼ 43:48 cm1 ; B20 ¼ 2647:1 cm1 ; B40 ¼ Dq ¼ 792 cm1 ; 1 10657:6 cm ; ReðB43 Þ ¼ 13432:7 cm1 as well as ImðB43 Þ ¼ 314 cm1 for C3 symmetry and ImðB43 Þ ¼ 0 cm1 for C3v symmetry for Ni2þ ions in LiNbO3 crystal Symmetry (1) (2) (3) (4) (5) Expt. at T

Interactions included

SO C3 C3 SO SO C3 C3 SO C3v SO ¼ 300 K (no uncertainties given) [19]:

SOO

SS SS

SOO SOO

SS

D

gjj

g>

Dg

5:293 4:785 4:993 5:086 5:296 5:31

2.2427 2.2373 2.2374 2.2426 2.2428 2.24

2.2035 2.1989 2.1990 2.2034 2.2035 2.20

0.0392 0.0384 0.0384 0.0392 0.0393 0.04

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Table 2 The calculated and observed CF energy levels for Ni2þ in LiNbO3 at C3 symmetry sites (cm1 ) Calculated in this work (see Table 1 for values of input parameters)

Observed

C3 ð2Sþ1 LÞ C3 E(1)b

E(2)c

E(3)d

E(4)e

E(5)f

DEðLSEÞg DEðSSÞh DEðSOOÞi

Oh

3

0 4.785 7576 7625 7949 8185 8308 8368 12145 12419 12692 12928 13455 13796 14030 19139 20015 21024 21433 21572 23303 23413 23525 23594 24366 24748 29909 31173 31716 51847

0 4.993 7575 7627 7950 8184 8306 8372 12145 12416 12694 12930 13456 13797 14029 19138 20015 21024 21436 21566 23303 23416 23533 23582 24366 24749 29910 31173 31716 51847

0 5.086 7574 7624 7946 8191 8316 8377 12153 12412 12692 12929 13464 13805 14038 19145 20022 21025 21433 21569 23289 23413 23551 23625 24368 24750 29912 31175 31718 51849

0 5.296 7571 7624 7945 8188 8313 8379 12152 12407 12693 12929 13463 13803 14034 19143 20020 21025 21433 21561 23286 23414 23557 23610 24366 24749 29908 31172 31716 51846

0 0.003 1.9 1.9 1.6 1.6 1.5 1.5 0.3 2.7 2.0 2.2 2.0 3.2 2.4 1.7 1.9 0.8 2.5 2.5 2.5 2.5 2.5 2.5 2.0 1.5 3.6 3.0 2.8 2.7 2.1

3

Að3 FÞ Að3 FÞ 3 Að3 FÞ 3 Að3 FÞ 3 Eð3 FÞ 3 Eð3 FÞ 3 Eð3 FÞ 3 Eð3 FÞ 1 Eð1 DÞ 3 Eð3 FÞ 3 Eð3 FÞ 3 Eð3 FÞ 3 Eð3 FÞ 3 Að3 FÞ 3 Að3 FÞ 1 Að1 DÞ 1 Eð1 DÞ 1 Að1 GÞ 3 Að3 PÞ 3 Að3 PÞ 3 Eð3 PÞ 3 Eð3 PÞ 3 Eð3 PÞ 3 Eð3 PÞ 1 Að1 GÞ 1 Eð1 GÞ 1 Eð1 GÞ 1 Eð1 GÞ 1 Að1 GÞ 1 Að1 SÞ Average 3

E A E A E E A A E A A E E A E A E A E A E E A A A E E E A A

0 5.293 7573 7626 7947 8190 8314 8381 12153 12409 12695 12931 13465 13806 14037 19145 20022 21025 21436 21564 23289 23416 23559 23612 24368 24750 29912 31175 31718 51849

0 0.208 1.1 1.8 0.7 1.2 1.5 3.9 0.3 2.8 2.3 1.9 0.7 0.4 1.7 0.2 0.1 0.1 2.6 5.2 0.1 2.7 8.1 12.2 0.3 0.2 0.1 0.1 0.1 0.1 1.8

0 0.301 1.3 1.3 2.5 3.6 2.1 1.4 7.7 6.8 0.4 1.1 8.9 9.2 8.0 6.7 6.7 1.5 0.2 3.1 13.3 0.1 25.8 30.9 1.9 1.6 2.1 2.3 2.4 2.1 5.4

s[20]

p[20]

s [22,54] p[22,54]

3

A2g 0 A2g

3

T2g

3

T2g

7968

7970

1

E

12120

12120

3

T1g

3

T1g T1g

3

T2g T2g 1 A1 3 3

T1g T1g

5.31a 7812

7810

12990 13333

12990 13333

13900

1 1

0

13773

19417 20408

19420 20450 20620

21978 23364

22220 23260

a

Ref. [19]. C3 symmetry with SO, SS, and SOO. c C3 symmetry with SO and without SS and SOO. d C3 symmetry with SO and SS without SOO. e C3 symmetry with SO and SOO without SS. f C3v approximation with SO, SS, and SOO. g DEðLSEÞ ¼ jEð1Þ  Eð5Þj; h DEðSSÞ ¼ jEð3Þ  Eð2Þj; i DEðSOOÞ ¼ jEð4Þ  Eð2Þj: b

appreciable reaching 9.6%. Hence the latter contributions to D shall not be neglected in the detailed investigations of the SH parameters, which are very sensitive to the lattice distortions [8,50–53]. However, the SS and SOO contributions to gjj ; g> ; and Dg are very small (see Table 3). Our study indicates that the

low symmetry effects induced by the angle j contribute negligibly to the SH parameters for Ni2þ in LiNbO3 crystals and hence the calculations based on C3v and C3 symmetry yield nearly the same results. However, these effects may be appreciable for V3þ in Al2 O3 crystal, especially for D and Dg [29], due to much

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158

larger jD3:0 than 0:68 for the undistorted LiNbO3 lattice.

(3) The CF energy levels have been calculated, taking into account for the first time the SS and SOO interactions as well as the C3 LSE induced by the angle j; and assigned according to the observed optical spectra (see Table 2). Although the average contributions to the energy levels from the SS and SOO interactions as well as the LSE for Ni2þ : LiNbO3 crystals are only 1.81, 5.36, and 2:06 cm1 ; respectively, they become appreciable for certain terms, e.g., for some of the 3 Eð3 PÞ states the energy level shifts due to the SOO interaction reach the value of about 31 cm1 : (4) Since the distortion angle jðD0:68 Þ for LiNbO3 : Ni2þ is rather small, the contributions to the SH parameters arising from the LSE induced by the C3 symmetry are also small.

4. Summary

Acknowledgements

The CFA/MSH package recently developed by us [29] enables to study not only the CF energy levels and wave functions but also the MSH parameters as functions of the CF parameters (B20 ; B40 ; and B43 ) for 3d2 and 3d8 ions at trigonal type I ðC3v ; D3 ; D3d Þ and type II ðC3 ; C3h Þ symmetry sites. In this paper we utilized the CFA/MSH package to study the spectroscopic properties of Ni2þ ions in LiNbO3 crystals. We have taken into account for the first time the SS and SOO interactions and the low symmetry effects arising from the additional CF terms ImðB43 Þa0 induced by the angle j for C3 symmetry, which have been omitted in earlier works [19,22–25]. A good overall agreement between the theoretical and experimental values of the CF energy levels as well as the ZFS parameter D and the g-factors has been obtained. The general conclusions, which can be drawn from the present results, may be summarized as follows: (1) The ZFS parameter D for LiNbO3 :Ni2þ is mostly induced by the SO interaction, whereas the combined (SS+SOO) contributions are also appreciable and shall be considered in detailed investigations involving the lattice distortions and structural disorder. (2) The contributions to gjj ; g> ; and Dg from the SS and SOO interactions are very small.

The authors would like to thank the Editor, Prof. Frank de Boer, for his help in resolving technical issues concerning the early version of this paper. This work has been partially supported by the Education Committee Natural Science Foundation of Shaanxi Province (Project No. 02JK045) and by Baoji University of Arts and Science Key Research Grant as well as the City University of Hong Kong Research Grant (Project No. 7001099).

Table 3 The percentage contributions to the SH parameters for Ni2þ ions at C3 symmetry sites in LiNbO3 arising from the SO, SS, and SOO interactions Parameters

gSO (%)

gSS (%)

gSOO (%)

D gjj g> Dg

90.4 99.76 99.79 97.96

3.9 0.004 0.005 0

5.7 0.24 0.20 2.04

Calculated using the formula: (a) gSO ¼ fSO =fSOþSSþSOO ; (b) gSS ¼ ðfSOþSS  fSO Þ=fSOþSSþSOO ; (c) gSOO ¼ ðfSOþSOO  fSO Þ= fSOþSSþSOO :

References [1] M.N. Armerise, C. Canali, M. de Sario, E. Zanoni, Mater. Chem. Phys. 9 (1993) 267. [2] A. Torchia, O.M. Matos, P. Vaveliuk, J.O. Tocho, J. Phys.: Condens. Matter 13 (2001) 6577. [3] L.F. Johnson, A.A. Ballman, J. Appl. Phys. 40 (1969) 297. [4] G. Corradi, I.M. Zaritskii, A. Hofstaetter, K. Polg!ar, L.G. Rakitina, Phys. Rev. B 58 (1998) 8329. . [5] O. Thiemann, H. Donnerberg, M. Wohlecke, O.F. Schirmer, Phys. Rev. B 49 (1994) 5845. [6] G.M. Salley, S.A. Basun, A.A. Kaplyanskii, R.S. Meltzer, K. Polg!ar, U. Happek, J. Lumin. 87–89 (2000) 1133. [7] Y.M. Chang, T.H. Yeom, Y.Y. Yeung, C. Rudowicz, J. Phys.: Condens. Matter 5 (1994) 6221. [8] Z.Y. Yang, C. Rudowicz, J. Qin, Physica B 318 (2002) 188. ! [9] A. Kaminska, A. Suchocki, L. Arizmendi, D. Callejo, F. Jaque, Phys. Rev. B 62 (2000) 10802.

ARTICLE IN PRESS Z.-Y. Yang et al. / Physica B 348 (2004) 151–159 [10] M. Paul, M. Tabuchi, A.R. West, Chem. Mater. 9 (1997) 3206. [11] T.H. Yeom, S.H. Choh, Y.M. Chang, C. Rudowicz, Phys. Stat. Sol. B 185 (1994) 417. [12] V.K. Jain, Solid State Commun. 84 (1992) 669. [13] M.G. Zhao, M. Chiu, Phys. Rev. B 49 (1994) 12556. [14] T.H. Yeom, S.H. Choh, Y.M. Chang, C. Rudowicz, Phys. Stat. Sol. B 185 (1994) 407. ! J.A. Sanz, A. Kling, [15] B. Herreros, G. Lifante, F. Cusso, J.C. Soarer, M.F. da Silva, P.D. Townsend, P.J. Chandler, J. Phys.: Condens. Matter 10 (1998) 3275. [16] J.R. Pilbrow, Transition Ion Electron Paramagnetic Resonance, Clarendon Press, Oxford, 1990. [17] C. Rudowicz, Magn. Reson. Rev. 13 (1987) 1; C. Rudowicz, Magn. Reson. Rev. 13 (1988) 335. [18] C. Rudowicz, S.K. Misra, Appl. Spectrosc. Rev. 36 (2001) 11. [19] A.K. Petrosyan, A.A. Mirzakhanyan, Phys. Stat. Sol. B 133 (1986) 315. [20] L. Arizmendi, J.M. Cabrera, F. Agullo-lopez, Ferroelectrics 26 (1980) 823. [21] G.I. Malovichko, V.G. Gravero, S.N. Lukin, Fiz. Tverd. Tela. 28 (1987) 991 (Engl. Transl. Sov. Phys.-Solid State 28 (1986) 553). [22] K.W. Zhou, S.B. Zhao, P.F. Wu, J.K. Xie, Phys. Stat. Sol. B 162 (1990) 193. [23] Y. Li, J. Phys.: Condens. Matter 7 (1995) 4075. [24] C. Rudowicz, Y.Y. Yeung, Z.Y. Yang, J. Qin, J. Phys.: Condens. Matter 14 (2002) 5619. [25] H.M. Zhang, D.P. Ma, D. Liu, Acta Phys. Sinica 51 (2002) 1554. [26] Y.Y. Yeung, C. Rudowicz, Comput. Chem. 16 (1992) 207. [27] Y.Y. Yeung, C. Rudowicz, J. Comput. Phys. 109 (1993) 150. [28] Y.M. Chang, C. Rudowicz, Y.Y. Yeung, Comput. Phys. 8 (1994) 1994. [29] C. Rudowicz, Z.Y. Yang, Y.Y. Yeung, J. Qin, J. Phys. Chem. Solids 64 (2003) 1419. [30] M. Blume, R.E. Watson, Proc. R. Soc. (London) A 271 (1963) 565.

159

[31] B.G. Wybourne, Spectroscopic Properties of Rare Earth, Wiley, New York, 1965. [32] C. Rudowicz, Chem. Phys. 102 (1986) 437. [33] S. Sugano, Y. Tanabe, H. Kamimura, Multiplets of Transition-Metal Ions in Crystals, Academic Press, New York, 1970. [34] B.S. Tsukerblat, Group Theory in Chemistry and Spectroscopy, Academic Press, London, 1994. [35] S. Fraga, J. Karwowski, K.M.S. Saxena, Handbook of Atomic Data, Elsevier, Amsterdam, 1976. [36] C.A. Morrison, Crystal Fields for Transition-Metal Ions in Laser Host Materials, Springer, Berlin, 1992. [37] A.M. Glass, J. Chem. Phys. 50 (1969) 1501. [38] S.C. Abrahams, J.M. Reddy, J.L. Bernstein, J. Phys. Chem. Solids 27 (1966) 997. [39] S.C. Abrahams, W.C. Hamilton, J.M. Reddy, J. Phys. Chem. Solids 27 (1966) 1013. [40] C. Zaldo, C. Prieto, H. Dexpert, P. Fessler, J. Phys.: Condens. Matter 3 (1991) 4135. [41] I.W. Park, S.H. Chon, K.J. Song, J.N. Kim, J. Korean Phys. Soc. 26 (1993) 172. [42] J.N. Kim, H.L. Park, J. Korean Phys. Soc. 15 (1982) 122. [43] D.J. Newman, B. Ng (Eds.), Crystal Field Handbook, Cambridge University Press, Cambridge, 2000. [44] D.J. Newman, B. Ng, Rep. Prog. Phys. 52 (1989) 699. [45] Y.Y. Yeung, D.J. Newman, Phys. Rev. B 34 (1986) 2258. [46] C. Rudowicz, Phys. Rev. B 37 (1988) 27. [47] C. Rudowicz, J. Phys. C: Solid State Phys. 20 (1987) 6033. [48] W.L. Yu, M.G. Zhao, Phys. Rev. B 16 (1988) 9254. [49] D.J. Newman, D.C. Pryce, W.A. Runciman, Am. Mineral. 63 (1978) 1278. [50] Z.M. Li, W.L. Shuen, J. Phys. Chem. Solids 57 (1996) 1673. [51] A. Edgar, J. Phys. C 9 (1976) 4303. [52] Z.Y. Yang, J. Phys.: Condens. Matter 12 (2000) 4091. [53] Z.Y. Yang, C. Rudowicz, Y.Y. Yeung, J. Phys. Chem. Solids 64 (2003) 887. [54] L. Arizmendi, J.M. Cabrear, F. Agullo-lopez, Ferroelectrics 56 (1984) 79.