Correlation of EMR and optical spectroscopy data for Cr3+ and Mn2+ ions doped into yttrium aluminum borate YAl3(BO3)4 crystal – Extracting low symmetry aspects

Optical Materials 46 (2015) 254–259

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Correlation of EMR and optical spectroscopy data for Cr3+ and Mn2+ ions doped into yttrium aluminum borate YAl3(BO3)4 crystal – Extracting low symmetry aspects Czesław Rudowicz a,1, Paweł Gnutek a, Muhammed Açıkgöz b,⇑ a b

Institute of Physics, West Pomeranian University of Technology, Al. Piastów 17, 70-310 Szczecin, Poland _ Turkey Faculty of Arts and Sciences, Bahcesehir University, Besßiktasß, 34353 Istanbul,

a r t i c l e

i n f o

Article history: Received 18 November 2014 Received in revised form 31 March 2015 Accepted 13 April 2015 Available online 5 May 2015 Keywords: Electron magnetic resonance (EMR) Optical spectroscopy Zero-field splitting Crystal field Low symmetry aspects Cr3+ and Mn2+ ions in YAl3(BO3)4

a b s t r a c t In this study, the crystal field analysis for Cr3+ and Mn2+ ions doped into yttrium aluminum borate YAl3(BO3)4, for short YAB, crystal has been carried out to complement earlier study of the zero-field splitting (ZFS) parameters (ZFSPs). This analysis utilizes data on the distortion models obtained from analysis of the ZFSPs obtained experimentally by EMR for Cr3+ and Mn2+ ions at the Y3+ and Al3+ sites in YAB. This approach enables to verify and enhance reliability of the ZFSP modeling based on superposition model (SPM) analysis and the distortion models predicted previously. Subsequently, modeling of the crystal field parameters (CFPs) based on SPM analysis is carried out for Cr3+ and Mn2+ ions located at possible cation sites in YAB. The SPM predicted CFP values serve as input for the Crystal Field Analysis (CFA) package to calculate the CF energy levels. The predicted physical ZFS of the ground spin state, i.e. the 4A2 state for Cr3+ ion and the 6S state Mn2+ ions, enable calculation of the theoretical ZFSP values, D and D & (a–F), respectively, using the microscopic spin Hamiltonian (MSH) module in the CFA package. In this way, data on the distortions around the Cr3+ centers in YAB (and to a certain extent also for Mn2+ centers) obtained using the ZFSP data from EMR measurements may be correlated with data on the CF energy levels measured by optical spectroscopy. This modeling approach uncovers certain incompatibilities in the existing data for Cr3+:YAB, which call for reanalysis of the previous assignments of the energy levels observed in optical spectra and more accurate experimental data. Ó 2015 Elsevier B.V. All rights reserved.

1. Introduction Yttrium aluminum borate YAl3(BO3)4 (YAB) crystals doped with rare-earth (RE) ions have been extensively used as technologically important materials [1–6]. Since in laser applications dopant ions may result in different laser wavelengths, YAB crystals doped with transition metal (TM) ions have also been investigated. Electron magnetic resonance (EMR, alternatively called EPR) spectroscopy was employed to study Mn2+ [7] and Cr3+ [8] doped YAB single crystal to determine the spin Hamiltonian parameters at room temperature. Analysis of the crystal structure data and the available EMR spectra has revealed considerable low symmetry features. These findings indicate an approximated nature of the previous interpretation of EMR spectra and necessitate their reconsideration taking into account low symmetry aspects. ⇑ Corresponding author. Tel.: +90 212 3810307; fax: +90 212 3810300. E-mail addresses: [email protected] (C. Rudowicz), [email protected]. tr (M. Açıkgöz). 1 Since 1 March 2015: Visiting Professor, Faculty of Chemistry, A. Mickiewicz University, Umultowska 89B, 61-614 Poznan, Poland. http://dx.doi.org/10.1016/j.optmat.2015.04.028 0925-3467/Ó 2015 Elsevier B.V. All rights reserved.

In the previous studies superposition model (SPM) analysis has been utilized for modeling the zero-field splitting parameters (ZFSPs), denoted by SPM/ZFSP, for Mn2+ [9] and Cr3+ [10] ions located at possible cation sites in YAB. The theoretically predicted ZFSPs corroborate the importance of low symmetry aspects. Comparison of the experimental ZFSP values obtained from EMR measurements with the theoretical ones enables analysis of the structural distortions induced by dopant ions at the Y3+ and Al3+ sites. This analysis indicates that the ZFSPs for the six-coordinated Mn2+ and Cr3+ centers are well described by a structural model for the Y3+ and Al3+ sites incorporating the angular distortions of the surrounding oxygen ligands. The results obtained from SPM/ZFSP analysis [9,10] support the earlier findings [7,8] that Mn2+ and Cr3+ ions substitute for Al3+ ions in YAl3(BO3)4. It would be useful to complement the ZFSP modeling for Mn2+ and Cr3+ doped in YAB [9,10] by additional consideration of available optical spectroscopy data [8,11–14]. Subsequently, to utilize these data, calculations of the crystal field parameters (CFPs) and the CF energy levels are carried out. The present extension of the studies [9,10] enables correlation of EMR and optical spectroscopy data as well as verification and possible enhancement of reliability

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of the ZFSP modeling based on SPM analysis and the predicted distortion models. The calculations utilize data on the distortion models [9,10] obtained from the analysis of the experimental ZFSP values obtained from EMR measurements for Cr3+ and Mn2+ ions at the Y3+ and Al3+ sites in YAB [7,8]. Subsequently, the CFPs are also modeled for Cr3+ and Mn2+ ions located at possible cation sites in YAB utilizing the SPM analysis. To consider low symmetry aspects and assess the relative strength of the trigonal and lower symmetry crystal fields as well as their effects on the ZFSPs, both the trigonal and monoclinic CFPs are calculated. The so-obtained CFP values serve as input for the Crystal Field Analysis (CFA) package [15] to calculate the CF energy levels. In this way, data on the distortions around the Cr3+ centers in YAB (and to a certain extent also for Mn2+ centers) obtained using the CF energy levels measured by optical spectroscopy [8,11–14] may be correlated with that obtained using the ZFSP data from EMR measurements [7,8]. However, it turns out that optical spectroscopy data available for Mn2+:YAB are not sufficient to enable adequate correlation. Major difficulty in interpretation of EMR and optical spectroscopy data for Mn ions in YAB appears to be due to the existence of different valence states, namely, 2+, 3+, and 4+. Deeper analysis of the available optical spectra of Mn:YAB [13] suggests that Mn4+ ions are also observed by optical spectroscopy. Hence, similar CF calculations may be also carried out for Mn4+ ions in YAB. In view of the most recent EMR study [16] of Cr3+ ions in the Van Vleck paramagnet EuAl3(BO3)4, a comparative analysis of the ZFSPs for Cr3+:YAl3(BO3)4 and Cr3+:EuAl3(BO3)4 is also warranted. Doubts arise concerning the SPM/CFP methodology used in [16] to explain the values of the 4 A2 splitting, i.e. the ZFS of Cr3+ ions, since only final results were provided, whereas details of computations have been omitted therein. These aspects are also considered in this study. 2. Theoretical framework – CF Hamiltonian and SPM analysis For the sake of brevity, the theoretical framework is only recapped, whereas for references and details the readers may consult pertinent papers cited below. The general CF Hamiltonian is represented as [10,17]:

HCF ¼

X

X   Aqk r k Oqk ðLx ; Ly ; Lz Þ ¼ Bkq C kq ðh; uÞ;

ð1Þ

where the first and second form is given in the extended Stevens operator (ESO) notation and the Wybourne notation, respectively. The general SPM expressions for the CFPs in the ESO notation are employed [10,17]: n   X Aqk r k ¼ Ak ðRi ÞK qk ðhi ; ui Þ;

ð2Þ

i¼1

where (Ri, hi, ui) are the polar coordinates of the i-th ligand. The distance dependence of the intrinsic parameters Ak ’s for a given metal– ligand MLn complex is assumed in the form of a power-law with adjustable power-law exponents tk:

Ak ðRi Þ ¼ Ak ðR0 Þ

 t k R0 ; Ri

ð3Þ

where R0 is the reference distance, Ri are the ligand bond lengths while hi and ui angular positions of O2 ligands in a given cluster. In general, for SPM calculations, the nearest neighbor oxygen ligands are only considered. Internally in the SPM/CFP computer program the calculations of CFPs are carried out in the Stevens notation (Aqk ) and then converted to the Wybourne notation (Bkq) using the conversion factors [10]. For SPM/CFP calculations, the ligand bond lengths (Ri) and the angular positions (hi and ui) of the six (nearest neighbor) O2 ligands around the transition ion in YAB must be determined in a well specified axis system [9,10]. The so-obtained CFP values serve as input for the CFA package [15] to calculate the CF energy levels. The following relations between respective parameters are utilized: (i) the fourth-rank intrinsic parameter for octahedral sites and the cubic CF parameter Dq: A4 ðR0 Þ ¼ 34 DqðR0 Þ, and (ii) the second- and fourth-rank intrinsic parameters: A2 ðR0 Þ=A4 ðR0 Þ  9—12 with a middle value equal to 10.8 proved to be suitable for several ion-host systems [9,10]. The power-law exponents are chosen as t2 = 3 and t4 = 5, which are the values most commonly used in many studies. Also, the approximation R0  Ravg, where Ravg is the average sum of the ligand bond lengths: R(Ri)/6, is adopted for each cation site. 3. Results and discussion for Cr3+ ions in YAB Recently new crystallographic and optical spectroscopy data have just become available [18] for Cr3+ ions in YAB with a high doping concentration: YAl2.79Cr0.21(BO3)4. These data support the substitution of Cr3+ ions in Al3+ sites, which exhibited slightly modified environment as compared with the undistorted pure host sites. The polar coordinates (Ri, hi, ui) of the i-th ligand extracted from the crystal structure data for both pure YAB and YAl2.79Cr0.21(BO3)4 [18] are given in Table 1. At first glance, it seems that the symmetry of the cation sites in YAl2.79Cr0.21(BO3)4 is closer to orthorhombic than that in the pure YAB crystal. The CFPs Bkq calculated using SPM and the structural data (Table 1) are listed in Table 2 for the Al site occupied by Cr3+ ions in YAB and YAl2.79Cr0.21(BO3)4. It appears that the calculated CFPs reflect monoclinic symmetry expected for Cr3+ ions at Al3+ sites from crystallographic data [18]. Note that all, i.e. triclinic-like, CFPs were calculated, whereas only the non-zero, i.e. monoclinic CFPs, are listed. Comparison of the CFP set predicted for Cr:YAB with the Cr3+ concentration of 0.2% [12], i.e. for YAl2.994 Cr0.006(BO3)4, with that for YAl2.79Cr0.21(BO3)4 [18] indicates significant differences, except for the 4th-rank CFPs: B40, B42, and B43. The reason for this outcome may be ascribed to rather high content of chromium ions in [18] as compared with that used in other optical and EMR studies. Note that different distortions around Cr3+ ions may be expected for different concentrations, thus affecting the respective CFPs. The CFPs in Table 2 enable calculations of the CF energy levels for Cr3+ in YAB using the CFA package [15,19]. Then the results may be compared with the experimental data for Cr3+ in YAB at room temperature [12,20,21]. This includes the optical absorption and luminescence spectra [21] and the optical absorption spectra

Table 1 The ligand bond lengths and angular positions of O2 ligands in the axis system: (xka⁄, ykb, zkc) suitable for Al-II sites in pure YAl3(BO3)4 and YAl2.79Cr0.21(BO3)4; for the definition of axes and distinction between the Al sites, see [10]. Ligands

O(1) O(2) O(3)

Pure YAB

YAl2.79Cr0.21(BO3)4

Ri (nm)

hi (°)

ui (°)

Ri (nm)

hi (°)

ui (°)

0.1915596 0.1956346 0.1881938

50.982 51.942 54.327

7.535 113.940 127.509

0.1924423 0.1926174 0.1936342

51.174 51.216 51.758

6.293 113.770 128.355

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Table 2 The CF parameters (in cm1) calculated using the data in Table 1 for Cr3+ ions at Al-II sites with C2 symmetry in nominally pure YAB and YAl2.79Cr0.21(BO3)4. Sample

B20

B21

B22

B40

B41

B42

B43

B44

YAB YAl2.79Cr0.21(BO3)4

8505.6 13394.4

255.9 451.5

384.1 1437.8

22759.8 24529.2

3019.9 241.6

1137.0 721.2

23113.1 23890.6

2548.9 298.5

Table 3 The CF energy levels (ELs) for Cr3+ ions at the Al3+ sites in YAB calculated using the CFP sets as indicated. The available experimental and theoretical energy levels are also listed. The values of the SOCP f are in (cm1). Irreps

Exp. [8]

Exp. [12]

Theor. [11]

Theor. [14]

(a) f: 220

(b) 0

(c) 0

(d) 0

Theoretical – this work (d) 140

(d) 180

(d) 220

(d) 140*

(d) 140**

(e) 140*

4

A2 ZFS

0 1.05

0

0 1.05

0

0

0

0 0.63

0 1.04

0 1.57

0 1.09

0 1.11

0 2.29

2

14,641 14,695

14,621 14,676

14641.2 14695.3

14,471 14,489

14,393 14,425

14,416 14,453

14,341 14,440

14,308 14,431

14,274 14,421

14,977 14,990

14,634 14,698

14,207 14,375

2

15,275 15,321 15,375

15245.7 15258.1 15748.8

15,112 15,129 15,677

14,833 15,091 15,499

14,824 15,125 15,537

14,837 15,128 15,536

14,845 15,129 15,535

14,855 15,130 15,534

15,314 15,607 15,935

14,956 15,253 15,575

15,004 15,045 16,282

4

(16,950)

16395.5 16432.4 16473.1 16517.4 17606.1 17613.1

16,439

13,396

14,551

16,451

14,949

16,239

17,254

15,554

16,889

14,538 14,606 16,247 16,252 16,894 16,897

14,531 14,624 16,251 16,260 16,897 16,902

14,524 14,641 16,257 16,270 16,902 16,909

14,508 14,544 16,249 16,259 16,888 16,892

14,441 14,538 16,246 16,253 16,885 16,888

14,477 14,560 14,640 14,674 17,398 17,405

21690.1 22767.8 22917.9

20,994 22,383 22,498

20,747 22,032 22,102

20,980 22,345 22,397

20,973 22,329 22,413

20,968 22,326 22,417

20,963 22,325 22,421

21,184 22,621 22,675

20,732 22,208 22,305

20,168 23,936 24,132

23554.0 23561.6 23959.6 23960.8 23970.7 23992.2

22,672

20,459

21,917

24,155

21,684

23,105

24,171

21,763

23,206

21,909 21,927 23,114 23,121 23,216 23,224

21,904 21,933 23,118 23,130 23,222 23,235

21,898 21,941 23,124 23,141 23,231 23,252

21,659 21,681 22,752 22,788 22,870 22,946

21,598 21,613 22,652 22,665 22,771 22,791

21,233 21,239 22,971 22,982 23,254 23,263

E T1

T2

2

20,846

4

(23,750)

T2

T1

(16,615)

(23,390)

(a) ELs calculated in [11] using the matched trigonal CFPs and f = 220 cm1. (b) ELs calculated in [14] using the monoclinic CFPs obtained by the ECM and neglecting the SOC (f = 0). (c) ELs calculated using the monoclinic CFPs best matched in [10] to the distortions predicted by SPM/ZFS modeling. (d) ELs calculated using the monoclinic CFPs in the first line in Table 2. (e) ELs calculated using the monoclinic CFPs in the second line in Table 2. * Additionally, the SS and SOO parameters are included: M0 = 0.2021, and M2 = 0.0159 (in cm1). ** As set (⁄) except Racah parameters: B = 674 and C = 3100 (in cm1).

measured in the wavelength range 300–900 nm [20]. It has been shown that the optical absorption bands near k = 420 nm and 590 nm, which are due to the transitions 4 A2 ! 4 T1 and 4 A2 ! 4 T2 , respectively, are dominant features [21]. Similar bands were observed at k = 425 nm and 595 nm [20]. From these features, Dq and Racah parameters B and C were calculated for YAB as: Dq = 1680, B = 672, and C = 3225 [21], whereas Dq = 1680, B = 672, and C = 3218 [20]; all in units of (cm1). The typical value of the Trees correction a [15] for Cr3+ ion is taken as 70 cm1. The experimental and theoretical CF energy levels for Cr3+ ion at Al3+ sites in YAB as well as the physical ZFS of the ground 4A2 spin state of Cr3+ ion are presented in Table 3 together with the results of the present calculations. The CF energy levels for Cr3+ ions, which become split in trigonal CF, are denoted using the cubic irreducible representations (irreps) as used for interpretation of optical spectroscopy data [8]. The results of previous theoretical energy level calculations require some comments. Zhang et al. [11] used diagonalization of the complete d3 energy matrix with the spin-orbit coupling (SOC) parameter (SOCP) f = 220 cm1. The authors [11] carried out the assignment of all the levels according to the eigenfunctions obtained from diagonalization. However, no eigenfunctions have been explicitly listed thus preventing comparison with the present results. Brik et al. [14] calculated the CFPs using the exchange

charge model (ECM) assuming trigonal CF approximation. The CF energy levels were calculated without including the SOC [14], thus the value of the ZFS of the ground 4A2 state could not be extracted. In the previous SPM/CFP calculations for Cr3+:YAB [10] we used Dq = 1530 cm1 as for Cr3+ ions in SrTiO3 crystal [22]. However, the resulting CFP values used as input for the CFA package yielded the values of the energy levels 4T2 and 4T1 lower than the experimental ones [8,12]. Additionally, the energy levels 4T2 and 4 T1 become split by lower symmetry CF terms and overlap with the energy levels arising from the multiplets 2T1 and 2T2, respectively. Importantly, Dominiak-Dzik et al. [12] obtained for Cr3+:YAB Dq = 1662 cm1. This Dq value is used in the present SPM/CFP calculations since it provides better compatibility of the energy levels arising from the multiplets 4T2 and 4T1 as well as 2T1 and 2T2, respectively. The best fitting to the experimental data on the temperature dependence of the luminescence lifetime, obtained in the framework of their model, yielded the SOCP value f = 140 cm1 [12]. Such small SOCP value may seem unphysical as compared with the free ion value that corresponds closer to f = 220 cm1 used in [11]. However, the authors [12] have found the magnitudes of all fitted parameters, including f = 140 cm1 as reasonable. The disparity between the SOCP values [11,12] presents a dilemma, which requires special consideration as discussed below.

C. Rudowicz et al. / Optical Materials 46 (2015) 254–259

Wells et al. [8] obtained the ZFS of the ground 4A2 state as 1.0 cm1. Therefore, in order to verify this finding, the SOCP value f = 140 cm1 [12] was initially adopted, however, then a smaller ZFS value of 0.63 cm1 was obtained. Therefore, we take into account also other effects, i.e. the spin–spin (SS) and spin-other-orbit (SOO) interactions [19]. Using the respective SS (=SOO) parameters [23]: M0 = 0.2021 and M2 = 0.0159 (in cm1) we obtain the ground 4A2 state splitting equal to 1.08 cm1, which is close to the experimental value of 1.05 cm1 [8]. Note that the theoretical value was obtained independently by SPM/CFP modeling utilizing data on the distortion models obtained from analysis of the experimental ZFSPs. Hence, this result verifies and enhances reliability of the SPM/ZFSP modeling based on approximation of site symmetry [10] as well as the resulting local structural distortions around the Cr3+ centers in YAB. However, the unsatisfactory agreement between the experimental and theoretical data on the CF energy levels poses another dilemma. We have attempted to solve these dilemmas by numerous additional calculations aimed at finding the trends in the simulated values with the change of adjustable parameter values. In view of the above dilemmas, in order to test the feasibility of obtaining simultaneously a satisfactory agreement between the experimental and theoretical data obtained by optical absorption and EMR techniques, three SOCP values: f = 140 [12], 180 (middle value), and 220 [11] (in cm1) have been used in the present results calculations. The values of other adjustable parameters, namely, Racah parameters B and C and the Trees correction a and the parameters M0 and M2, have been varied in reasonable ranges. It turns out that variation of M0 and M2 has little effect on the CF energy levels and is omitted from further considerations. The results for selected combinations of parameter values are summarized in Table 3 and depicted in Fig. 1. The outcomes of the present efforts to find simultaneous agreement are discussed below. The results in Table 3 indicate that the value f = 220 cm1, which has apparently yielded perfect agreement between the experimental and theoretical ZFS value in [11] (see Table 3), seems rather too large since it yields the ZFS of 1.57 cm1. Note that in the present calculations (see Table 3), not only the SOC, with f = 140 cm1 [12], but the SOO and SS interactions are also included. The differences between the results in Table 3 and those in [14] are due to taking into account only the SOC therein. Importantly, the fact that the SOCP value f = 140 cm1 obtained first from optical measurements [12] provides also a good agreement between the experimental EMR measurements and the theoretically predicted ZFSPs data, lends support to the assertion that such small f value may still be physically acceptable. Hence, independent justification for the observed covalency reduction in the SOCP value may be sought, which is beyond the scope of this paper. Furthermore, the CF energy levels for Cr3+ ions in YAl2.79Cr0.21(BO3)4 are also calculated utilizing the crystallographic data [18]. This enables comparison of the latter results with several experimental observations and theoretical calculations for Cr3+:YAB. Notably, for YAl2.79Cr0.21(BO3)4 the splitting of the ground 4A2 state equals to 2.26 cm1 (see Table 3) is obtained, which is larger than the results for Cr3+:YAB. This outcome may be attributed to effect of very high content of chromium ions in the structure of YAl2.79Cr0.21(BO3)4. Independent measurements by EMR techniques would be required to verify this assertion. The variation (see Fig. 1) of the energy levels for Cr3+:YAB in the range of applicable SOCP values with the Trees correction a = 0 and 70 (in cm1) indicates what follows. Both values of a yield nearly identical physical ZFS of the ground 4A2 spin state. The difference between the two spin states of 4A2 increases from 0.008 cm1 for f = 50 cm1 to only 0.023 cm1 for f = 250 cm1. Hence both a values yield nearly identical curves represented by one curve Fig. 1a.

257

The results for the next four excited CF states indicate that a reversal of the sequence of levels 2E2 and 4T2 occur in between the two values of a = 0 and 70 cm1 (see Fig. 1b and c, respectively). Table 3 indicates also overlap and mixing of the energy levels arising from 2 E2 and 4T2 states. Moreover, for a = 70 cm1 the crossing of the two levels arising from the 2E level split in monoclinic CF is observed for f equal to about 125 cm1. Due to the large step in these calculations, Df = 50 cm1, graphically, this crossing is represented as a ‘repulsion’ of the two levels in Fig. 1c. Next we have varied Racah parameters B and C in the range (in cm1): 580–780 and 3000–3400, respectively. As indicated in Table 3, much better agreement between the experimental and theoretical values of (a) the ZFS of the state 4A2 and (b) the two 2 E energy levels has been obtained for B = 674 and C = 3100 (in cm1). The latter values only slightly differ from those reported

Fig. 1. The variation of the energy levels for Cr3+:YAB in the range of applicable SOCP values with the Trees correction a = 0 and 70 (cm1): (a) the physical ZFS of the ground 4A2 spin state – both a values yield nearly identical curves, (b and c) the next four excited CF states with a = 0 and 70, respectively (for explanations, see text).

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C. Rudowicz et al. / Optical Materials 46 (2015) 254–259

Table 4 The CFPs Bkq (in 104 cm1) for Mn2+ ions at Y and Al sites in YAl3(BO3)4 calculated by SPM utilizing the structural parameters: (a) for undistorted host and (b) corresponding to 0 the distortion parameters DR and Dh obtained by direct matching of the theoretical and experimental ZFSP b2 [9]. CFPs:

B20

(a) Y3+ site (b) Y3+ site [A] (a) Al3+ in Al-II site (a) Al-II site: approx. D3 (1) (b) Al-II site: approx. D3(1) [A]

696.7 10024.6 6191.3 6277.6 8008.3

B21

186.2

B22

B40

279.5

6836.3 12968.1 18412.1 18482.3 18725.7

B41

1221.8

B42

B43

B44

920.0

3362.0 5236.0 18697.9 18765.1 18581.6

1031.0

[A] – using the set A of model parameters [9]. (1) – using the symmetry increase from C2 in pure YAB to approximate D3 denoted as (1) in [9].

Table 5 The ZFSPs (in 104 cm1) calculated using the CFA/MSH package for Mn2+ ions at various sites in YAl3(BO3)4. 0

ZFSP: 3+

Y site Y3+ site [A] Al-II site: approx. D3(1) Al-II site: approx. D3(1) [A] Expt. values [7] a

0

b2 = D

b4 = 1/3(a  F)

173 1203 795 985 734.6

80 558 383 472 4.25a

Absolute value.

in [20,21], see above. Finally, we have attempted to increase the value of f from 140 cm1 but this has led to an increase in the values of both the ZFS and the 2E energies. Thus shifting the values of f closer to the free ion value of 220 cm1 appears to diminish the overall agreement for the crucial experimental data items (a) and (b). These findings have important implications for interpretation of the experimental energy levels and complicate their assignments. The predicted variation of the energy levels creates some ambiguities, which give rise to doubts if the reported assignments are unique and valid. Note that we consider not only the energy level values but also the associated wavefunctions as well as other relevant free-ion parameters. Interestingly, if the wavefunctions are not taken into account in the analysis, then the energy levels arranged sequentially with the increasing energy would agree better with other theoretical predictions [11,14]. The trends in the simulated values of the CF energy levels revealed in Table 3 and Fig. 1 do not allow for an ideal Table 6 The energy levels (in cm1) calculated using the CFA package for Mn2+ ions at various sites in YAl3(BO3)4. Y3+ site

Y3+ site [A]

Al-II site: approx. D3(1)

Al-II site: approx. D3(1) [A]

0 0.0745 0.1117

0 0.5197 0.7774

0 0.3504 0.5152

0 0.4330 0.6380

21,087 21,095 21,100 21,112 22,280 22,284

17,989 18,125 18,243 18,352 19,118 19,134

12,799 12,879 12,884 12,981 13,067 13,133

12,636 12,703 12,719 12,848 12,949 13,029

23,216 23,226 23,229 23,240 23,240 23,247

19,953 19,975 22,630 22,641 22,652 22,668

14,985 15,454 15,517 16,807 16,843 18,229

14,844 15,275 15,448 16,400 16,450 18,343

23,369 23,394 23,409 23,429 23,462 23,463

23,199 23,235 23,260 23,283 23,457 23,461

18,241 18,250 18,261 23,272 23,302 23,305

18,350 18,355 18,361 23,142 23,181 23,197

simultaneous agreement between the experimental and theoretical values for the available experimental data items, while adopting a rather larger value of the SOCP f, which would correspond to a lower covalency reduction. Importantly, fairly good matching for (a) the ZFS of the state 4A2 and (b) the two 2E energy levels, obtained by EMR techniques and optical absorption, respectively, has been achieved for f = 140 cm1 as compared with the free ion f = 220 cm1. This seems a reasonable compromise, which enables to reconcile the data obtained by optical absorption and EMR techniques. Nevertheless, the results of the present modeling approach reveal certain incompatibilities in the existing data for Cr3+:YAB. This calls for reanalysis of the previous assignments of the energy levels observed in optical spectra. It may be envisaged that future more accurate experimental data could help resolving the problems encountered in the present modeling. Finally, we remark that the quality of the available experimental data does not allow for a detailed consideration of the low symmetry aspects in optical spectra. Moreover, the origin of the broad lines visible in optical spectra corresponding to the multiplets 4T2 and 4T1 (indicated by brackets in Table 3) requires explanation. In this case only the middle point of overlapping lines was determined, whereas separate CF energy levels could not be resolved. This makes the presumed sequence of the energy levels uncertain. In general, such broad lines may be due to a number of factors, discussion of which is beyond the scope of this paper. 4. Results and discussion for Mn2+ ions in YAB Following the same procedure applied for Cr3+ ion in Section 3, we have also considered SPM analysis of the CFPs for Mn2+ ions at the cation sites in YAB structure. In order to correlate the experimental data from optical spectroscopy with those from EMR, we have also calculated CFPs utilizing data on the predicted positions of ligands that form the nearest surrounding of Mn2+ at Y and Al sites, which yielded the best matching of the theoretical and experimental values of the axial ZFSP D. As input for SPM/CFP calculations and CFA analysis we adopt the following values. The cubic CF parameter Dq = 950 cm1 was taken as an average value for two different concentrations of Mn2+ ions in MgGa2O4 in octahedral sites [24]. In a similar way as in [24], in the present case we take the average values of the Racah parameters B and C = 4B as well as the Trees correction a for the two concentrations of Mn2+ ions in YAB as: B = 722, C (=4B) = 3088, and a = 90 (in cm1). The SOC parameter is taken as f = 320 cm1 [25], the SS (SOO) ones as (in cm1): M0 = 0.2205 and M2 = 0.0160 [23], whereas R0 = 0.20224 nm, which is equal to the Mg–O distance in MgGa2O4 [24]. The calculated values of the CFPs (Bkq) in the Wybourne notation are listed in Table 4 for Y and Al sites, which may be potentially occupied by Mn2+ ions in YAB. Next, the ZFSPs for the Mn2+ ions at the Y and Al sites in YAl3(BO3)4 have been calculated using the MSH module in the CFA package [15,19]. Since only two ZFSPs can be resolved from the available two ZFS transitions for Mn2+ (S = 5/2) ions, an

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approximation is built into the CFA/MSH package, which automatically calculates the conventional ZFSPs [26,27], D and (a–F), for axial symmetry. The results are given in Table 5 for each case considered in CFP analysis. It can be seen that even for the set Al-II approx. D3 (1), which takes into account the ascent of the actual site symmetry for Al from monoclinic, C2, to the approximated trigonal symmetry, D3(1), we obtain the theoretical value of ZFSP D close to the experimental one. These results confirm that Mn2+ ions substitute at Al sites. While an acceptable agreement between D(theor) and D(exp) is obtained, the predicted values of the ZFSP 0

b4 = 1/3(a  F) [26,27] are about 90 times larger than the experimental value. However, an acceptable agreement between the experimental [7] and theoretical values of the 4th-rank ZFSPs was obtained in [9] only after reinterpretation of the experimental values [7], i.e. swapping a with F. The doubts concerning proper interpretation of the reported experimental values of a and F [7] indicate that a better analysis of EMR spectra is required in order to achieve more reliable matching of the theoretical and experimental 4th-rank ZFSPs. A few aspects require explanation. The module MSH in the CFA package [19] returns the positive values of D. However, on checking the ordering of the spin wavefunctions, it turns out that the lowest spin level corresponds to the dominant quantum number MS = ±5/2, next one MS = ±3/2, and the highest MS = ±1/2. Hence, as indicated in Table 5 the negative sign should be ascribed to D, which agrees with the experimentally determined sign [7]. Due to the approximated nature of the experimental EMR data [7] and limitations of the module MSH in the CFA package [19], detailed discussion of the low symmetry aspects in EMR spectra for Mn2+ ions in YAl3(BO3)4 is not feasible. Nevertheless, the results of SPM/CFP modeling indicate that the theoretically predicted CFPs corroborate the importance of low symmetry aspects for Mn2+ ions substituting at the Al-II sites. The energy levels calculated using the CFA package and the CFP values from Table 4 for Mn2+ ions at various sites in YAl3(BO3)4 are provided in Table 6. Since at present no corresponding experimental data are available in literature, we provide only a selected set of the lowest Mn2+ energy levels. The results in Table 6 may be useful when the pertinent data become available. 5. Conclusions The data on the distortion models obtained [9,10] from analysis of the zero-field splitting (ZFS) parameters (ZFSPs) obtained experimentally by EMR [7,8] for Cr3+ and Mn2+ ions at the Y3+ and Al3+ sites in yttrium aluminum borate YAl3(BO3)4 (YAB) have been utilized to calculate the respective crystal field parameters (CFPs) using superposition model (SPM) analysis. Hence, this study complements the earlier ZFSP modeling [9,10] based on SPM and the resulting distortion models. The present modeling of the CFPs based on SPM analysis utilizes the structural information obtained earlier from SPM/ZFSP modeling. In principle, the so-obtained CFPs could also be varied for better simultaneous matching of the two experimental and theoretical data items: (a) the ZFS of the state 4 A2 and (b) the two 2E energy levels. However, our main objective was to correlate the available EMR and optical spectroscopy data. This approach provides input parameters for the Crystal Field Analysis (CFA) package [15,19] to calculate the CF energy levels. The results are compared with available optical spectroscopy data [8,11–14] for Cr3+ and Mn2+ ions located at possible cation sites in YAB. By varying Racah parameters much better agreement between the experimental and theoretical values of (a) the ZFS of the state 4 A2 and (b) the two 2E energy levels has been obtained for

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B = 674 and C = 3100 (in cm1). However, this agreement has been achieved for the SOCP f = 140 cm1 and not for values closer to the free ion f = 220 cm1. This seems a reasonable compromise reconciling the data obtained by optical absorption and EMR techniques. Nevertheless, the present results reveal certain incompatibilities in the existing data for Cr3+:YAB, thus calling for reanalysis of the previous assignments of the energy levels observed in optical spectra and more accurate experimental data. The physical ZFS of the ground spin state, i.e. the 4A2 state for Cr3+ ion and the 6S state Mn2+ ions has also been predicted due to SPM/CFP modeling using the microscopic spin Hamiltonian (MSH) module in the CFA package. This has enabled theoretical calculations of the ZFSPs, D and D & (a–F), for Cr:YAB and Mn:YAB, respectively. Usage of the data on the distortions around the Cr3+ centers in YAB (and to a certain extent also for Mn2+ centers) obtained using the ZFSP data from EMR measurements have enabled correlation with data on the CF energy levels measured by optical spectroscopy. The results support the earlier finding [8] that Cr3+ ions substitute for Al3+ ions in YAB, whereas the nature of the substitution of Mn2+ ions for Al3+ ions in YAB is less firmly confirmed. The present analysis of EMR and optical spectroscopy data indicates that Mn2+ and Cr3+ ions substitute for Al3+ at sites exhibiting low local symmetry, i.e. monoclinic C2. The correlation of EMR and optical spectroscopy data has proved useful for verification and enhancement of reliability of the ZFSP values and the distortion models predicted based on SPM analysis. References [1] J.T. Lin, Laser Optron. (1990) 34–40. [2] D. Jaque, J. Capmany, J.G. Sole, Phys. Lett. 75 (1999) 325–327. [3] N.I. Leonyuk, E.V. Koporulina, V.V. Maltsev, O.V. Pilipenko, M.D. Melekhova, A.V. Mokhov, Opt. Mater. 26 (2004) 443–447. [4] I.T. Bodnar, V.V. Filippov, N.V. Kuleshov, N.I. Leonyuk, V.V. Mal’tsev, O.V. Pilipenko, Inorg. Mater. 44 (2008) 863–865. [5] H. Liu, X. Chen, L.X. Huang, X. Xu, G. Zhang, N. Ye, Mater. Res. Innov. 15 (2011) 140–144. [6] A. Majchrowski, I.V. Kityk, Ferroelectr. Lett. 29 (2002) 31–36. [7] A.M. Vorotynov, G.A. Petrakovskii, Ya.G. Shiyan, L.N. Bezmaternykh, V.E. Temerov, A.F. Bovina, P. Aleshkevych, Phys. Solid State 49 (2007) 463–466. [8] J.P.R. Wells, M. Yamaga, T.P.J. Han, M. Honda, J. Phys.: Condens. Matter 15 (2003) 539–547. [9] M. Acikgoz, P. Gnutek, Opt. Mater. 36 (2014) 1311–1318. [10] M. Acikgoz, P. Gnutek, C. Rudowicz, Opt. Mater. 36 (2014) 1342–1349. [11] J.P. Zhang, G. Chen, H.B. Zhou, Commun. Theor. Phys. (Beijing, China) 45 (2006) 1121–1125. [12] G. Dominiak-Dzik, W. Ryba-Romanowski, M. Grinberg, E. Beregi, L. Kovacs, J. Phys.: Condens. Matter 14 (2002) 5229–5237. [13] A.S. Aleksandrovsky, I.A. Gudim, A.S. Krylov, V.L. Temerov, Phys. Solid State 49 (2007) 1695–1699. [14] M.G. Brik, A. Majchrowski, L. Jaroszewicz, A. Wojciechowski, I.V. Kityk, Phil. Mag. 90 (2010) 4569–4578. [15] Y.Y. Yeung, C. Rudowicz, Comput. Chem. 16 (1992) 207–216. [16] A.D. Prokhorov, E.E. Zubov, A.A. Prokhorov, L.F. Chernush, R. Minyakaev, V.P. Dyakonov, H. Szymczak, Phys. Status Solidi B 250 (2013) 1331–1338. [17] C. Rudowicz, P. Gnutek, J. Phys.: Condens. Matter 22 (2010) 045501 (11 pp). [18] P. Liu, J. Liu, X. Zheng, H. Luo, X. Li, Z. Yao, X. Yu, X. Shi, B. Hou, Y. Xia, J. Mater. Chem. C2 (2014) 5769–5777. [19] P. Gnutek, Z.-Y. Yang, C. Rudowicz, J. Phys.: Condens. Matter 21 (2009) 455402 (11 pp). [20] G. Wang, H.G. Gallagher, T.P.J. Han, B. Henderson, J. Cryst. Growth 153 (1995) 169–174. [21] G. Wang, H.G. Gallagher, T.P.J. Han, B. Henderson, J. Cryst. Growth 163 (1996) 272–278. [22] L. Rimai, T. Deutsch, B.D. Silverman, Phys. Rev. 133 (1964) A1123–A1133. [23] S. Fraga, J. Karwowski, K.M.S. Saxena, Handbook of Atomic Data, Elsevier Scientific Publishing company, Amsterdam–Oxford–New York, 1976. [24] G.K.B. Costa, S.S. Pedro, I.C.S. Carvalho, L.P. Sosman, Opt. Mater. 31 (2009) 1620–1627. [25] A. Mehra, P. Venkateswarlu, Phys. Rev. Lett. 19 (1967) 145–146. [26] C. Rudowicz, Magn. Reson. Rev. 13 (1987) 1–89. Erratum:C. Rudowicz, Magn. Res. Rev. 13 (1987) 335. [27] C. Rudowicz, S.K. Misra, Appl. Spectrosc. Rev. 36 (2001) 11–63.