EPR, ENDOR and optical spectroscopy of Yb3+ ion in KZnF3 single crystals

Journal of Physics and Chemistry of Solids 77 (2015) 157–163

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EPR, ENDOR and optical spectroscopy of Yb3 þ ion in KZnF3 single crystals M.L. Falin a,n, K.I. Gerasimov a,b, V.A. Latypov a, A.M. Leushin b, S. Schweizer c, J.-M. Spaeth d a

Kazan Zavoisky Physical-Technical Institute, 420029 Kazan, Russian Federation Kazan (Volga Region) Federal University, 420008 Kazan, Russian Federation c South Westphalia University of Applied Sciences, Department of Electrical Engineering, 59494 Soest, Germany d University of Paderborn, Department of Physics, 33098 Paderborn, Germany b

art ic l e i nf o

a b s t r a c t

Article history: Received 1 August 2014 Received in revised form 30 September 2014 Accepted 6 October 2014 Available online 30 October 2014

The paramagnetic center of tetragonal symmetry formed by the Yb3 þ ion in the KZnF3 crystal has been studied using methods of EPR, ENDOR and optical spectroscopy. The location of the impurity ion and the structural model of the complex differing from the model of the Yb3 þ center in KMgF3 have been established. The empirical scheme of the energy levels of the Yb3 þ ion has been found. The parameters of its interaction with the crystal electrostatic field and the hyperfine interaction with ligands of the nearest environment have been determined. The parameters of the crystal field were used for the analysis of the distortions of the crystal lattice in the vicinity of Yb3 þ . The parameters of the transferred hyperfine interaction have been calculated for the distances between Yb3 þ and F  ions of the nearest environment obtained taking into account the found distortions. They are in good agreement with the experimental values. & Published by Elsevier Ltd.

Keywords: D. Crystal structure D. Electron paramagnetic resonance (EPR) D. Magnetic properties D. Optical properties

1. Introduction The composition of crystals of double fluorides (Ме+Ме2 +F −3 ) with the perovskite-type structure is more complicated than that of, e.g., widely used matrices of the homologous series of fluorite (Me2 +F2−). The high cubic symmetry and a wide variety of physicochemical properties make the study of impurity crystals of double fluorides interesting both from the theoretical and practical point of view. Using rare-earth (RE) elements as probes makes perovskites useful subjects for studying the behavior of RE ions located in two different positions in the crystal: either in the а-type sites in the environment of the octahedron of six fluorine ions or in b-type sites in the coordination of the same 12 ligands. However, the introduction of trivalent RE ions in perovskite structures is hampered, on the one hand, by the considerable difference of sizes of RE ions and lattice cations, and on the other hand, by the ion valence of the substitution. In [1] we presented the results of the detailed study of the tetragonal paramagnetic center of the Yb3 þ ion in the KMgF3 crystal using electron paramagnetic resonance (EPR), electronnuclear double resonance (ENDOR) and optical spectroscopy. These results showed conclusively that the tetragonal center is n

Corresponding author. Fax: þ 7 843 272 50 75. E-mail address: [email protected] (M.L. Falin).

http://dx.doi.org/10.1016/j.jpcs.2014.10.005 0022-3697/& Published by Elsevier Ltd.

formed during the incorporation of Yb3 þ in the octahedral positions of Mg2 þ ions, and not as a result of substituting univalent K þ ions surrounded by 12 fluorine ions, as it was supposed earlier in [2,3]. The excessive positive charge is compensated by the nonmagnetic oxygen ion O2  , which substitutes one of fluorine ions in the octahedron of the nearest environment of the Yb3 þ ion. One could expect that a similar center would exist in the KZnF3 crystal, the structural parameters of which (aoKZnF3 ¼ 0.4040 nm) almost KMgF

3 ¼0.3987 nm). coincide with those of the KMgF3 crystal (ao However, this is not the case in reality. It was found that the tetragonal symmetry center of the Yb3 þ ion in KZnF3 is formed only upon doping with YbF3 fluoride and metal lithium. In this work we present the results of the experimental and theoretical study of such Yb3 þ ion centers in the KZnF3 crystal using methods of EPR, ENDOR and optical spectroscopy.

2. Experimental results Samples KZnF3:Yb were grown using the Bridgman–Stockbarger method in graphite crucibles in fluorine atmosphere. Crystals were activated by introducing 0.5–1.5 wt% YbF3 in the charge with the addition of metallic lithium in specific cases. EPR and ENDOR experiments were carried out on modified X-band (9.5 GHz) ERS-231 (Germany) [4] and custom-built EPR/ENDOR X-band spectrometers (see, e.g., [5]) at the temperatures of 4.2 and

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Fig. 1. ENDOR spectrum of Yb3 þ (Ttet) in KZnF3 at Н || С4. The positions of the Larmor frequency of lithium and fluorine are denoted by arrows. H¼ 725 mT (g|| ¼ 0.922), T ¼ 4.2 K.

6–8 K, and optical spectra were measured on a home-built multifunctional optical spectrometer [6] at 2, 77 and 300 К. Three types of the paramagnetic center Yb3 þ located in the structurally non-equivalent positions were singled out in KZnF3:Yb3 þ (Tcub) of the cubic symmetry, Yb3 þ (Ttrig) consisting of four magnetically non-equivalent complexes of the trigonal symmetry, and Yb3 þ (Ttet) consisting of three magnetically non-equivalent complexes of the tetragonal symmetry. As it was noted above, Yb3 þ (Ttet) in KZnF3, in contrast to KMgF3 [1], is formed only, when metallic lithium is introduced into the charge. The ENDOR spectrum of Yb3 þ (Ttet) showed lines, which were identified as lines of fluorine and lithium ions (Fig. 1). The intensity of the ENDOR lines has the maximum value, when the constant magnetic field Н is directed along the main crystallographic directions of the crystal, and decreases considerably at the deviation from them. The angular dependence of the ENDOR spectra in the (001) plane was studied in order to exactly identify the ENDOR lines according to their belonging to certain F  and Li þ . Fig. 2 shows the plot of the angular dependence of these lines. It was established from the angular dependence of the ENDOR lines that Yb3 þ is in the center of a regular octahedron, i.e., substitutes Zn2 þ , and the local compensation of the additional positive charge is performed by the replacement of one of the Zn2 þ ions of the nearest environment by a lithium ion. The inset in Fig. 2 shows a fragment of the crystal lattice KZnF3 with positions of the interstitial ion and ion-compensator. The complex [YbF6]3  is characterized by the symmetry С4v and the absence of an inversion center. The local symmetry of F1,6 and Li þ ions is С4v,, and that of each of F2,3,4,5 ions is Cs. The spin Hamiltonian of the described system has the form:

/ = gβHS +

∑ (SA m(i) I(i) − gn(i)βnHI(i)),

(1)

i F

7Li

19 

7

(i) Am

where S¼ I ¼1/2, I ¼3/2, gn ¼5.525454 (2.1707) for F ( Li), is the five-component tensor of the transferred hyperfine interaction (THFI) for F2,3,4,5 and two-component tensor for F1,6 and Li, i labels the ligands, m labels the tensor components (1–5). Since the quadrupole moment of Li is small (Q ∼0) and the coupling between Li þ and Yb3 þ is mainly due to the dipole–dipole interaction, instead of six ENDOR lines (sum and difference ENDOR lithium lines) only two are observed. Expressions for the frequencies of the ENDOR transitions are similar to those, which were used in ENDOR experiments of the tetragonal Yb3 center in KMgF3 [1]. Experimental values of the THFI parameters are given in Table 1. The obtained THFI parameters are compared with the

Fig. 2. Angular dependence of ENDOR lines of fluorine and lithium ions for Yb3 þ (Ttet) in KZnF3 during the rotation of the magnetic field Н in the (001) plane. ν ¼9.355 GHz, Т ¼4.2 K. ● – experimental points; 1–6 – numbering of F  ions corresponding to the notations in the inset; calculated lines: solid and dashed (summary and difference ENDOR frequencies, respectively) on the basis of data in Table 1, dash-dotted – Larmor frequencies of 19F and 7Li nuclei. Inset – structural model of Yb3 þ (Ttet).

parameters of cubic centers [7] in the following manner. It is ^ ^ ^ known that B = (h/g^β)A is a true tensor unlike A , and that any asymmetric second-rank tensor can be decomposed into a symmetric and asymmetric parts. Using corresponding transformations, from the symmetric part one can single out a part called in the following Bs = (1/3)(hA1/g⊥β + hA2 /g⊥β + hA3 /g∥β) which represents the isotropic (purely covalent regardless of the dipole– dipole interaction) contribution to the THFI. When comparing the Bs values from the three sets of F1, F6 and F2–5 with the corresponding Bs from the cubic center Yb3 þ (Table 1), it is seen that the parameters of F2–5 ions almost coincide with the purely covalent contribution (with distances due to the deformation) of Table 1 (i) (in MHz) and Bs (in 10  4 T) of the Experimental values of the THFI parameters Am Yb3 þ ion with the first fluorine shell and the Li ion in KZnF3. 1–6 – F  labels corresponding to the notations in the structural model of KZnF3 (Fig. 1). The results for the cubic Yb3 þ center in KZnF3 [7] are given for comparison.

Tetragonal 2–5

A1 A2 A3 A4 A5 Bs

Cubic 1

6

þ

F1–6

F

F

F

Li

29.80 (3) 3.63 (3) 16.42 (3) 0.9 (1) 0.9 (1) 6.53

47.05 (2)

34.53 (2)

0.730 (10)

29.030

36.64 (2)

30.52 (2)

 0.305 (10)

11.136

15.90

12.61

0.02

6.38

M.L. Falin et al. / Journal of Physics and Chemistry of Solids 77 (2015) 157–163

159

Table 2 Energy levels (in cm  1) and g-factors Ttet of Yb3 þ in KZnF3. J

Irrep and g-factor

Exp.

Theory

5/2

4

11196 10491 10348 1108 568 430 0 |0.922(2)| |3.481(5)|

11,190 10,502 10,359 1122 573 432 0  0.922  3.540

Γt7 Γt6 3 Γt7 2 Γt6 2 Γt7 1 Γt7 1 Γt6 3

7/2

g||(1Γt6) g⊥(1Γt6)

Fig. 3. Experimental and simulated (dashed line) EPR lines of Yb3 þ (Ttet) in KZnF3 at H || z, ν ¼ 9.355 GHz, T ¼ 4.2 K.

the cubic center, while ions F1 and F6 are subjected to the strong local deformation. Since the contribution of the covalency Bs for the Li þ ion is small, the main contribution to the THFI parameters is produced by the dipole–dipole interaction with Yb3 þ (Ad–d) þþ determined by the distance (RYb3–Li ). It follows from the experi3þ þ mental values that RYb–Li ¼0.415 nm is significantly larger than þþ RYb3–Li ¼ 0.404 nm in the non-deformed KZnF3 crystal. The correctness of the determination of the THFI parameters and the structural model of the complex is also confirmed by the good simulation of the transferred hyperfine structure in the spectrum of the Yb3 þ (III) EPR line at Н || z (Fig. 3). Fig. 4 shows the complex spectra of the luminescence excitation (I) and luminescence (II) observed in the near IR region of Yb3 þ in KZnF3. For the reliable identification of spectral lines belonging to Yb3 þ (Ttet) we used samples (a) containing Yb3 þ (Ttrig)

plus Yb3 þ (Tcub) and (b) containing Yb3 þ (Ttrig) plus Yb3 þ (Ttet). Arrows indicate lines belonging of the studied Yb3 þ (Ttet). The belonging of these lines to this center was established by comparing the observed spectra with luminescence and excitation spectra of Yb3 þ (Tcub) and Yb3 þ (Ttrig) in KZnF3 studied in [8]. It follows from the analysis of the spectra that the luminescence peaks denoted by numbers 2–4 in Fig. 4 are due to transitions from the low-lying Stark level of the excited multiplet 2F5/2 of the Yb3 þ ion to three Stark sublevels of the ground multiplet 2F7/2. Peaks denoted by numbers 4–6 in the excitation spectrum correspond to the transitions from the lowest of levels 2F7/2 to the Stark components of the multiplet 2F5/2. The numbering of the peaks corresponds to the number of transitions, which are shown in the empirical scheme of the energy levels of Yb3 þ (Ttet) (Fig. 4). Experimental values of the energy of levels and measured g-factors are given in Table 2.

3. Analysis of the crystal field parameters and estimate of local distortions of the crystal lattice 3.1. Determination of the crystal field potential To interpret the experimental optical and EPR spectra due to the transitions between states of the term 2F of the configuration 4f13, we composed an energy matrix, comprising the spin–orbit

Fig. 4. Luminescence excitation (I) and luminescence (II) spectra of KZnF3: YbF3 (a) and KZnF3:YbF3:Li (b) samples at Т ¼ 2 and 77 K. Lines corresponding to Yb3 þ (Ttet) are denoted by arrows. The numbering of peaks corresponds to the numbering of transitions in the scheme of energy levels shown in the inset.

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interaction Hso of the Yb3 þ ion and its interaction with the crystal field Hcr. the Hamiltonian of the interaction between the Yb3 þ ion and the crystal field of tetragonal symmetry was written in the conventional form

Hcr(C4v) = B20O20 + B40O40 + B44O44 + B60O60 + B64O64 ,

Table 4 Energy levels (in cm  1) and g-factors of Yb3 þ Tcub in KMgF3 and KZnF3. J

Irrep and g-factor

5/2

levant radial 〈r k〉 and Oqk = ∑i Oqk (θi, φi) Stevens operators depending on the polar coordinates θi, φi of the i-th electron paramagnetic ion [9]. Radius-vectors of electrons of the configuration 4f13 are determined with respect to the cubic crystal axes X, Y, Z (see inset in Fig. 2). The theoretical energy levels and wave functions were determined for the diagonalization of the matrix of the Hamiltonian Hso þHcr. The values of the g-factors of the spin Hamiltonian βH g S′, where H is the intensity of the magnetic field, and S′ is the operator of the effective spin S′ ¼1/2 of the Yb3 þ ion were calculated with the wave functions of the Kramers ground state doublet. Then seven theoretical quantities (two g-factors and five values of the energy differences) were used for the leastsquare approximation (similar to the procedure described in [10]) of the corresponding experimental values in order to find the best values of g-factors, crystal field parameters and spin–orbit interaction. The theoretical values of the energy levels and g-factors along with the transformation properties of the corresponding states are presented in Table 2. The values of the crystal field and spin–orbit interaction parameters found from the experimental energy levels are given in Table 3 (Ttet-exp.). Theoretical positions of the energy levels nearly coincide with the experimental values, and the g-factors are described well. The crystal field parameters indicate that the crystal field of Ttet, as expected, is weak in comparison with the strong field of oxygen Ttet in the KMgF3 crystal [1]. It is also possible to state that a rather weak distortion of the cubic symmetry field takes place during the formation of Ttet in KZnF3 that is directly seen from the comparison of the crystal field parameters of Ttet and Tcub in Table 3. It should be noted that the given crystal field parameters of the cubic Yb3 þ center somewhat differ from the values of parameters [8], since the interpretation of the luminescence lines was specified and new positions of the energy levels were calculated, which along with the experimental values are presented in Table 4. For comparison it also shows data for the isomorphous KMgF3 crystal. New crystal field parameters of cubic Yb3 þ centers for both bases are given in Table 4. The weak distortion of the cubic symmetry field is also indicated by the slight splitting of the cubic quartet levels as the symmetry of the system decreases. This can be seen directly from the scheme of energy levels shown in Fig. 4. The wave functions of cubic states are mixed during the formation of functions of Kramers doublets of the tetragonal center. In particular, the wave function of the low-lying Kramers doublet 1Гt6 has the form

|1Гt6 ±

=±

7 0.8788| 2

±

1 ) 2

±

7 0.4770| 2

∓

7 ) 2

+

5 0.0090| 2

±

1 ), 2

(3)

where the first number in the states |J MJ) is the total moment of the multiplet, and the second number is its projection on the z axis Table 3 Spin–orbit interaction (ξ) and crystal field (Bkq ) parameters (in cm  1) Ttet and Tcub of

Yb3 þ in KZnF3. Parameter

ξ

B20

B40

B44

B60

B64

Ttet-exp. Ttet-theory(A) Ttet-theory(B) Tcub-exp. Tcub-exp. (KMgF3)

2894

199

311 191 310 330 330.5

1768 1752 1767 1650

19 57 20 4.8 11.0

 193  207  194  101

2930 2900

0 0

KZnF3 аo ¼ 4.040 Å

Exp.

Theory

Exp.

Theory

10,414

10,414

10,407

10,407

(2) 11,166

2 − Γ7 2 − Γ8 1 − Γ7 1 − Γ8 Γ6−

where the crystal field parameters Bqk ≡ Aqk〈r k〉 incorporate the re-

1 ) 2

KMgF3 аo ¼ 3.974 Å

7/2

g(Γ6−)

11,163

1105

1105

1092

1092

473

473

432

432

0 |2.584|

0  2.667

0 |2.582|

0  2.667

of the center. If these functions are presented in the form of a linear combination of cubic states [11] 1

1

1

1

|1Гt6 ± 2 ) = 0.9791|Γ6− ± 2 ) + 0.2029|1Γ8− ± 2 ) + 0.0090|2 Γ8− ± 2 ), (4) then we see that the admixture of the cubic functions of the excited levels by the tetragonal crystal field to the functions of the ground state doublet Γ6− is rather small. The domination of the contribution of the functions of the cubic doublet Γ6− in this state, which is the ground state energy level of the octahedral center with cubic symmetry, is also confirmed by ENDOR indicating that the Yb3 þ ion in the studied Ttet is in the octahedral position of the KZnF3 crystal. 3.2. Structure of Ttet It can be seen in Table 3 that the experimental crystal field parameters of Ttet and Tcub of the Yb3 þ ion in KZnF3 differ only slightly. Due to the fact that the crystal field acting on the paramagnetic ion is mainly determined by the direct and exchange interaction between the Yb3 þ ion and the nearest F  ions, it is possible to assume that no considerable change of the positions of ligands occur during the formation Ttet with respect to the positions, which they occupied in the center Tcub. The studies of ligand ENDOR indicated (see Table 1) that only the F  ions located near the axis connecting the ion-compensator (Li þ ) and the Yb3 ion shift noticeably, and the distances from Yb3 to each of four F  ions located symmetrically in the plane perpendicular to the axis of the center almost do not differ from those in the center of cubic symmetry. To estimate quantitatively the lattice distortions near an impurity ion, we use the superposition model [12–15], which postulates that the crystal field parameters are a linear superposition of parameters due to each ligand. The resulting crystal field parameters are

Bkq =

∑ Kkq( Θi ,

Φi) B¯k(Ri),

i

(5)

Kkq(Θi ,

where Φi) are the coordination factors depending on the angular positions (defined by the spherical angles Θi and Φi) of all ions located at the distance Ri from the impurity ion (the most complete table of their expressions is given in [15]) and B¯k(Ri) are the “intrinsic” parameters depending on the ligand type. The dependence of the B¯k(Ri) parameters in the limited regions of distances is assumed as a power law:

⎛ R ⎞tk B¯ k(Ri) = B¯ k(R 0)⎜ 0 ⎟ , ⎝ Ri ⎠

(6)

in which tk are the power-law exponents, and B¯k(R0) is the intrinsic parameter of the model referring to the reference distance R0 usually taken equal to the sum of ionic radii of the magnetic ion and ligand.

M.L. Falin et al. / Journal of Physics and Chemistry of Solids 77 (2015) 157–163

The tk and B¯k (R0) values can be determined from the crystal field parameters of Tcub of the Yb3 þ ion in isomorphous KMgF3 and KZnF3 crystals given in Table 3, if one knows the equilibrium positions of ligands F  with respect to Yb3 þ . Information about the distances to the nearest neighbors can be obtained either empirically by measuring the transferred hyperfine structure parameters As and Ap and assuming that they also follow certain power laws analogous to (6), [16,17] or they can be calculated theoretically minimizing the energy of any lattice including the considered center as it was done in [18–21]. Because of the absence of the necessary data about the KZnF3:Yb3 þ crystal, we used the tk and B¯k (R0) values obtained in [22] during the analysis of the structure of tetragonal oxygen centers of the Yb3 þ ion in the KMgF3 crystal assuming that the same parameters can be applicable to the description of the interaction between Yb3 þ and F  ions as in the isomorphous KZnF3 crystal. We managed to obtain the theoretical values of the crystal field parameters close to the experimental ones in [22] with the following parameter values of the superposition model: t4 ¼7.95, B¯4 (R0)¼105.72 cm  1, t6 ¼49.83, B¯6 (R0)¼ 18.48 cm  1. For the distance R0 we used the value of 0.219 nm that is somewhat larger than the sum of ionic radii of the magnetic ion and ligand [23]. Fluorine ions 1, 2, 3, 4, 5 and 6 comprising the octahedron of the nearest environment of the Yb3 þ ion in the coordinate system of the cubic center occupy positions with coordinates: R1 ¼R2 ¼R3 ¼R4 ¼ R5 ¼R6 ¼ R, ϑ1 ¼ 0, ϑ2 ¼ ϑ3 ¼ ϑ4 ¼ ϑ5 ¼ π/2, ϑ6 ¼ π, ϕ2 ¼0, ϕ3 ¼ π/2, ϕ4 ¼ π, ϕ5 ¼3π/2. First let us assume that the Yb3 þ ion and four F2, F3, F4, and F5 ions remain in the same plane perpendicular to the axis of the center during the formation of Ttet, so that the angular coordinates of the ions do not change, and only the coordinates R1, R2, R3, R4, R5, R6 change with the distances R2, R3, R4 and R5 being equal due to the tetragonal symmetry of the center. Four- and six-order crystal field parameters in this model are described by the following system of equations: 3 B40 = B¯4(R1) + B¯4(R6) + 2 B¯4(R2)B44

=

35 ¯ B (R ) B 0 2 4 2 6

5 = B¯6(R1) + B¯6(R6) − 4 B¯6(R2)B64

=−

63 ¯ B (R ), 4 6 2

161

parameters we have the system

B40 = B¯4(R1) + B¯4(R6) + 4B¯4(R2)K40(ϑ2)B44 = 4B¯4(R2)K44(ϑ2)B60 = B¯6(R1) + B¯6(R6) + 4B¯6(R2)K60(ϑ2)B64 = 4B¯6(R2)K64(ϑ2),

(8)

the solution of which leads to the values R1 ¼0.2195 nm, R6 ¼0.2206 nm, R2 ¼0.2182 nm, ϑ2 ¼79.1° (Δϑ2 ¼  10.9°). It is necessary to note that all structural factors Kkq (ϑ2) are even functions of the angle ϑ2, therefore from the equations system (8) we obtain the second solution with the angle ϑ2 ¼ 100.9°, which leads not to a decrease but an increase of the angle ϑ2 by Δϑ2 ¼ 10.9°. This solution, however, should be excluded, because due to electrostatic forces it is of low probability that the axial F1 ion would move in the direction to the Li þ ion when the Li þ ion substituted the Zn2 þ ion. On the contrary, it would rather move away from it. (i) for Li þ , from This is also confirmed by the experimental values Am which follows that the Yb3 þ moves away from the ion-compensator. One should also notice that the distances R1 and R6 analytically enter equations of the system (8) in the same manner, therefore the obtained values R1 ¼0.2195 nm, R6 ¼0.2206 nm can be treated as R1 ¼0.2206 nm, R6 ¼0.2195 nm. However, when taking into account the transferred hyperfine structure, the first variant seems to be preferable. Comparing R1 and R6 values with the corresponding distance in the pure crystal (Rm ¼0.2020 nm), it is seen that in this deformation model the first axial F1 ion moves away from the Yb3 þ ion by 0.0175 nm, and the F6 ion by 0.0186 nm during the formation of the tetragonal center. Each of the planar ions moves away from the paramagnetic ion by 0.016 nm. The theoretical values of the crystal field parameters of the tetragonal centers (Ttet-theory (B)) obtained with these R1, R6, R2 and ϑ2 values are in good agreement with the experimental values Ttet-exp. (Table 3). The structure of Ttet established as a result of the performed analysis is given in Fig. 5, where the cross-section of the center in the plane coming through its axis and two planar fluorine ions F2 and F4 is shown. If one assumes that the plane of four planar F  ions and the Li þ ion do not shift with respect to the crystal environment during the formation of the tetragonal center, then for

(7)

from which it is possible to determine the distances R1, R2, R6 characterizing the structure of Ttet using the experimental Bkq values given in Table 3. Solving the system of Eq. (7), we find R1 ¼0.2279 nm, R6 ¼0.2279 nm, and R2 ¼0.2204 nm. In this model of Ttet the F1 and F6 ions are very strongly shifted by 0.026 nm in the directions away from the paramagnetic ion from the positions, which they occupied in the KZnF3 crystal, and the four planar ions are removed from the axis of the center by 0.018 nm. The interpretation of the crystal field parameters is bad (see Table 3, line “tetr. theor.(А)”). The theoretical value of the axial parameter B60 differs by approximately a factor of two and that of the parameter B40 by a factor of three compared to their experimental values. Therefore, further in the analysis of the structure of Ttet we dropped the requirement of the absence of the variation of the angular coordinates and assumed that the Yb3 þ ion may come out of the plane of four planar F2, F3, F4 and F5 ions rising or descending with respect to it. Such deformation of the center can be additionally characterized by the angle ϑ2 and the variation of this angle may, in principle, lead to a smaller change of the structure of the cubic center structure and may improve the description of all crystal field parameters. Instead of (7) now for the crystal field

Fig. 5. Structural model of Yb3 þ (Ttet) in KZnF3. Positions F  in the (100) plane. Dotted lines – positions F  in the undistorted crystal lattice. Solid lines – positions F  calculated within the superposition model.

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Table 5 Theoretical values of the THFI parameters An(i) (in MHz) for the first fluorine shell of Yb3 þ in KZnF3 (see text for details). (i) Am

Hd–d

H4f

H5d,6s

Hvh

Hodd

field

A1(1) = A⊥

12.64

23.04

5.12

2.94

1.2

A3(1) = A|| A1(6) = A⊥ A3(6) = A|| A1(2 − 5) A2(2 − 5) A3(2 − 5)

 5.76

45.54

 1.82

9.64

 8.66

12.44

16.38

 1.44

5.48

 0.14

 5.68

37.69

 2.13

9.41

 7.426

Hspin

polar

Total

Exper.

2.61

47.38

47.05

 2.54

36.44

36.64

1.43

34.16

34.53

 1.59

30.29

30.52 29.80

11.89

27.59

 29.02

23.88

0

 4.15

30.19

 23.76

5.82

14.31

4.75

0

2.72

3.85

3.63

3.52

6.96

6.01

0

1.78

15.97

16.10

 2.3

the displacement (δ0) of the Yb3 þ ion with respect to the plane we will have δ0 ¼R2sin(Δϑ2) ¼  0.0413 nm taking into account the results of Table 3, tetr.theor.(B). For the distance of the planar F  ions (Rp) from the axis of the center we find Rp ¼R2cos(Δϑ2)¼ 0.2143 nm. For the displacement δp of planar ions from the axis of the center we have δp ¼Rp  Rm ¼0.0123 nm. The displacement δ1 of the axial F1− ion is determined by δ1 ¼R1  Rm þ δ0 ¼ 0.0237 nm, and for the displacement δ6 of the axial F −6 ion we find δ6 ¼Rm  R6 þ δ0 ¼  0.0599 nm. (i) was The theoretical calculation of the THFI parameters Am carried out taking into account all bonding mechanisms developed in [1,24–28] for the RE ion-fluorine couplings. The distance between Yb3 þ and F(1), F(6) and F(2–5) has been taken from the deformation model above. The considerable increase in the covalent bond with the axial F1 and F6 ions can be explained by the rather large change of the wavefunction of the tetragonal Yb3 þ from the cubic case. The overlap integrals were evaluated with Hartree– Fock wave functions of Yb3 þ [29] and F  [30]. The electron transfer energies, the radial 5s-, 5d-functions and 5d-, 6s-, 6pfunctions, the 4f–5d and 4f–6s interaction parameters necessary for the calculations were taken from [31–33], respectively. The mixing of the F  1s- and 2s- shells was taken into account as well. The reduced matrix elements W(1k)j and V(j) for Yb3 þ were calculated in [31]. The values of the covalency parameters γ providing the best convergence of the experimental and theoretical values are the following: for F(1), γ4fs ¼ 0.015, γ4fs ¼  0.06, γ4fπ ¼ 0.07, γ5ds ¼0.09, γ5ds ¼  0.04, γ5dπ ¼0.05; for F6, γ4fs ¼0.016, γ4fs ¼ 0.07, γ4fπ ¼0.05, γ5ds ¼0.03, γ5ds ¼  0.1, γ5dπ ¼0.7; for F2–5, γ4fs ¼0.003, γ4fs ¼  0.07, γ4fπ ¼0.06, γ5ds ¼ 0.16, γ5ds ¼  0.3, γ5dπ ¼0.4. The covalency parameters for 6s and 6p shells were taken to be equal to γ5d. The radial integrals were taken to be the same as in the work [34]. The 4f–5d interaction parameters G1, G3 and G5 were taken from [35] for Yb3 þ and the 4f–6s interaction parameter G3 ¼ 2359 cm  1 from [36]. Table 5 presents the numerical contributions obtained from the various mechanisms of the Yb3 þ fluorine interaction which were included. These are: the dipole–dipole contribution including multipole corrections (Hd–d); the effect of overlap and covalency (H4f); the processes of electron transfer into the empty 5d and 6s shell (H5d,6s); the effects of mixing of the 4f and 5d states by the field of the virtual hole on the fluorine atom (Hvh) and by the odd crystal field (Hodd field); the sum of the effects of spin polarization of the 5s and 5p shells (H5s-5d, H5s-6s, H5p-6p)–(Hspin polar). The sum of all these contributions and the experimental values of the corresponding THFI are given in the last two columns of this table. As can be seen in Table 5, (i) the theoretical approximation of the THFI parameters Am is quite satisfactory (the calculation for the parameters A4(2 − 5) and

A5(2 − 5) was not carried out because of the smallness of these constants).

4. Conclusions The study performed in this work made it possible to prove reliably that Ttet of the Yb3 þ ion in the KZnF3 crystal is a complex, in which the paramagnetic ion occupies the position of the Zn2 þ ion surrounded by the octahedron of six fluorine ions, and the excess charge is compensated by an additional lithium ion. The fact that in the isomorphous KMgF3 crystal the same Yb3 þ forms a tetragonal center of a different structure indicates the complexity of the physicochemical properties with respect to the complex formation in such matrices. From the application point of view further detailed studies are required. Our semi-empirical theoretical interpretation of the experimental data yields a satisfactory agreement.

Acknowledgments This study was supported by the Grant NSh-4653.2014.2 and the Russian Foundation for Basic Research (Project no. 13-0297031r_Volga region_a). One of the authors (MLF) gratefully acknowledges the Deutscher Akademischer Austauschdienst (DAAD) grant. This study of author (AML) was supported by the Kazan (Volga Region) Federal University (ND 02, VD 0210, Theme no. 021000086 “Budget 14-86”). We are grateful to R.Yu. Abdulsabirov and S.L. Korableva (Kazan Federal University, Kazan, Russian Federation) for the crystal growth and D. Lovy (University of Geneva, Geneva, Switzerland) for spectra simulations.

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