Study of the crystal field and rare-earth magnetism in YF3: Yb3+ Текст научной статьи по специальности «Физика»

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aänetic Resonance in Solids

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Boris Malkin (KFU, Kazan) Alexander Shengelaya (Tbilisi State University, Tbilisi) Jörg Sichelschmidt (Max Planck Institute for Chemical Physics of Solids, Dresden) Haruhiko Suzuki (Kanazawa University, Kanazava) Murat Tagirov (KFU, Kazan) Dmitrii Tayurskii (KFU, Kazan) Valentine Zhikharev (KNRTU,

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Short cite this: Magn. Reson. Solids 19, 17205 (2017)

Study of the crystal field and rare-earth magnetism in YF3:Yb3+

A.V. Savinkov 1*, B.F. Gabbasov 1, O.A. Morozov 1, AG. Kiiamov 1, M.S. Tagirov 12 1 Institute of Physics, Kazan Federal University, Kremlevskaya 18, Kazan 420008, Russia 2 Institute of Perspective Research, TAS, L. Bulachnaya 36a, Kazan 420111, Russia *E-mail: Andrey.Savinkov@gmail.com (Received November 10, 2017; revised December 9, 2017; accepted December 11, 2017)

The electron paramagnetic resonance spectra (X-band, f ~ 9.42 GHz) of Yb3+ ions have been measured at temperature 15 K in YF3:Yb3+ single crystals. The principal values of the g-tensors, gb = g1 = 1.67, g2 = 2.42, g3 = 5.41, and directions n1 = [0,1, 0], n2 = [+ srn(54.8°), 0, cos(54.8°)], n3 = [+ sin(35.2°), 0, cos(35.2°)] of the corresponding principal axes for the Yb3+ ions which replace

Y3+ ions at two magnetically nonequivalent sites with the local Cs symmetry in the orthorhombic crystal lattice have been obtained from analysis of the angular dependences of the spectra taken in the static magnetic fields lying in the crystallographic (bc) and (ac) planes. Experimental data are interpreted in the frameworks of the crystal field theory. Using the obtained set of crystal field parameters for Yb3+ ions in the YF3 host related to the crystallographic system of coordinates, we can reproduce satisfactorily the crystal field energies of Yb3+ ions determined earlier from optical measurements.

PACS: 71.70.Ch, 71.70.Ej.

Keywords: crystal field parameters, exchange charge model, EPR, trifluorides

1. Introduction

The rare-earth trifluorides RF3 and rare-earth doped YF3:Re3+ (R is rare-earth ion) yttrium trifluoride have been studied in the past as a model system for testing theories of rare-earth magnetism in insulators (see, for example, Ref. [1-5]) and because of their numerous applications as promising host materials for solid laser and scintillator technology. In recent years interest in the study of rare-earth trifluorides has returned thanks to advances in the fabrication of nanoparticles of pure rare-earth fluorides RF3 and rare-earth ions doped nanoparticles as well [6-10]. The great interest appeared due to potential applications of the nanosized materials in high resolution displaying, electroluminescent devices and markers for biomolecules.

In present study we report the results of systematic studies of crystal field and low temperature magnetic properties of Yb3+ ion in diluted YF3:Yb3+ single crystals. Angular dependences of the electron paramagnetic resonance (EPR) spectrum of Yb3+ ion in YF3 host have been measured in YF3:Yb3+ single crystals which were rotated around the crystallographic a- and b-axes so that the static magnetic field was applied as B ± a, and B ± b respectively. Measured angular dependences of EPR spectrum and known from the literature spectrum of electronic energies of Yb3+ ion in YF3 host [11] have been analyzed in the framework of the crystal field theory. The set of crystal field parameters has been calculated using the semi-phenomenological exchange charge model [12] and then corrected by comparing results of calculations with the experimental data. Obtained set of the crystal field parameters reproduces satisfactorily the angular dependences of Yb3+ EPR spectrum, components of g-tensor and Stark energies of Yb3+ ion in YF3 host.

2. Experimental details

Two YF3:Yb3+ (0.5%) single crystals were grown from commercial powders of YF3 (99.99%) and YbF3 (99.99%) in carbon crucibles in high vacuum (less than 10-4 mbar) by temperature gradient technique. All YF3:Yb3+ samples were oriented using the X-ray diffraction pattern with the accuracy of ±3°. The samples were oriented so that angular dependences of EPR spectra were measured in the static magnetic field directed as B ± a and B ±b, i.e. perpendicular to the crystallographic axes a and b of orthorhombic crystal structure of the YF3.

Study of the crystal field and rare-earth magnetism in YF3:Yb3+

The EPR spectra of YF3:Yb3+ single crystals were measured with the X-band (~9.42 GHz) Bruker ESP300 spectrometer. The standard ER4102ST rectangular cavity with the TE102 mode was used. The studies were performed at 15 K, and the sample temperature was controlled using an Oxford Instruments ESR9 liquid helium flow system.

In the magnetic field directed along the c-axis, the EPR spectrum contains a group of lines (Figure 1) corresponding to Yb3+ ions with typical hyperfine structure of three stable isotopes 169Yb, 171Yb and 173Yb. The g-factor in this direction is gc = 4.635. Each magnetically nonequivalent Yb3+ center in the YF3 crystal cell gives a resonant line in EPR spectrum due to transitions between sublevels of the ground state doublet of 2F7/2 multiplet. Transitions between higher-lying energy levels aren't observed because the distance to the excited levels is too large in comparison with the quantum of the X-band EPR. Also, the excited levels are not populated at T = 15 K.

Angular dependences of Yb3+ EPR spectra, measured in YF3:Yb3+ single crystals for the magnetic field oriented in the (bc) and (ac) plane are represented in Figure 2(a) and (b) respectively. The principal values of g-tensor g1 = 1.67(1), g2 = 2.42(1), g3 = 5.41(1) and g-factors along the crystallographic axes ga = 3.68(1), gb = g1 = 1.67(1), gc = 4.63(1) have been obtained from the analysis of the angular dependences. Obtained in our experiment the principal values of the g-tensor are in a good agreement with the values obtained in Ref. [13]. The principal components g2 and g3 are in the crystallographic (ac) plane and the principal direction corresponding to g2 has an angle of 54.8° with the c-axis; the principal direction of g1 coincides with the b-axis of YF3:Yb3+ crystal lattice.

Angle, degree Angle, degree

Figure 2. Angular dependences of Yb3+ EPR spectra, measured (open circles) in YF3:Yb3+ single crystals for the magnetic field oriented in the a) bc- and b) ac-plane of YF3 crystal structure. Calculated angular dependences are shown by solid lines.

3. Discussion

The YF3:Yb3+ samples have an orthorhombic structure with the space group Pnma (DH) [14]. The parameters of the YF3 crystal cell are a = 0.63537(7) nm, b = 0.68545(7) nm, c = 0.43953(5) nm [15]. The unit cell contains four formula units. The coordinates of fluorine F1 ions in 4c positions and F2

B. mT

Figure 1. The EPR spectrum in YF3:Yb3+ at the temperature 15 K in the magnetic field B || c.

A.V. Savinkov, B.F. Gabbasov, O.A. Morozov et al. Table 1. Atomic coordinates of the ions in Pnma structure of YF3 [15].

Y F1 F2

u V u1 V1 U2 S2 V2

0.3673(4) 0.0591(5) 0.5227(5) 0.5910(8) 0.1652(4) 0.0643(3) 0.3755(5)

fluorine ions in 8d positions are determined by parameters u\, U2, S2, V1, V2 and equal ± (U1, 1/4, v1), ± (u - 1/2, 1/4, 1/2 - v1) for F1; ± (U2, S2, v2), ± (U2, 1/2 - S2, v2), ± (U2 - 1/2, S2, 1/2 - v2), ± (U2 - 1/2, 1/2 - S2, 1/2 - v2) for F2; the rare-earth ions in 4c positions with the point symmetry Cs have the coordinates ± (u, 1/4, v), ± (u - 1/2, 1/4, 1/2 - v). The parameters U1, v^ U2, S2, v2, u, v are represented in Table 1 in units of the YF3 lattice constants [15].

To describe the results of EPR measurements and the electronic energies of Yb3+ ion in YF3 host, we consider the effective Hamiltonian of a single Yb3+ ion, operating in the total basis of 14 wave functions of the electronic 4f 13 configuration, in the external magnetic field B:

H j = H0 + HCF, j - HZ, j , (1)

here H0 is the free ion Hamiltonian which includes only the spin-orbit interaction for Yb3+ ion with parameter j = 2912 cm-1. The electronic Zeeman energy is Hz,j = , where ^ = -juBI (ln + 2sn)

is the electronic magnetic moment of the Yb3+ ion. The Yb3+ ions in the sublattices j = 1, 2, 3 and 4 are magnetically equivalent in pairs. The crystal field Hamiltonian

hcf,j = I I Bk0)(l|Klil)• oq (2)

k= 2,4,6 q=0:k

is determined by a single set of15 crystal field parameters Bkq (1) (in the Cartesian system of

coordinates defined so that x || c, y || b and z || a), Oq are Stevens' equivalent operators, reduced matrix

elements (l || ak || l) are Stevens' coefficients.

At the first approximation the parameters of the electrostatic interaction of open Yb3+ electronic 4f-shell with the ion charges in the YF3:Yb3+ crystal lattice can be evaluated corresponding to the point charge model:

B(pc)k = v e2qL(1 -at)(rk)(-1)qC-,yL) (3)

Bq I Dk+1 , (3)

L RL

where eqL is the charge of the ligand, L; 6L and are angles in a spherical coordinate system with the origin at the nucleus of the rare-earth ion; Rl is the distance from the rare-earth ion to the ligand L. The values of the moments of the spatial density of the Yb3+ 4f-electrons are < r2 ) = 0.613, < r4 ) = 0.960, <r6) = 3.104 a.u. [16]; Oknl are the shielding factors with values 02 = 0.588, 04 = 06 = 0 taken for Yb3+ ion.

In order to correct the electrostatic interaction for the spatial distribution of the ligand charges, we used the semi phenomenological exchange charge model [12]:

?(ec)k =12(2k +1) ^

L

B(r)k =z • RT • sn' (RL ), (4)

j 21 +1 Rr

where Sknl represents the bilinear forms of overlap integrals for the wave functions of the Yb3+ 4f-electrons, and the wave functions of the 2s, 2p-electrons of the ligand ions (F-):

Snl (Rl ) = Gs\sf |2 + Ga\ Sal |2 + G„yk\s:'\2 (5)

Here Sn =(nl0|200), S? =(nl0| 210) , S^ =(nl1|211 (n = 4, l = 3 are quantum numbers for

Study of the crystal field and rare-earth magnetism in YF3:Yb3+

4f-electrons), the coefficients 72 = 3/2, 74 = 1/3, y6 = -3/2 for 4f-electrons. Parameters of the model Gs. Ga and Gn, were taken for Yb3+ ions with values Gs = Ga = GM = 15.0.

Thus, the crystal field parameters for Yb3+ ions in YF3 crystal lattice were calculated as a sum:

ftk = B(pc)k

q ~ q

B

(ec)k

(6)

Calculated values of the crystal field parameters are shown in Table 2 (column "Calculated"). Final sets of crystal field parameters (see column "Adjusted" in Table 2) was obtained by varying the calculated values of Bqk to minimize the squared deviation of the theoretically obtained values of g-factor (Table 3) from defined in our EPR experiment; squared deviation of calculated values of the energy sublevels of Yb3+ ions in YF3 host from the appropriate measured values [11] (totally four known energies, see Table 4) were also minimized. The errors in the adjusted crystal field parameters (see values given in brackets, column "Adjusted" in Table 2) corresponds to such changes of each Bqk that give rise to deviation of the minimization result no more than 5% of the best minimized value.

Table 2. The crystal field parameters (in cm 1) of the Yb3+ ions in YF3 crystal lattice.

Table 3. Values of g-factor of Yb3+ ion in YF3 crystal lattice.

Bqk Calculated Adjusted

Bo2 94.7 114.9(1)

B12 749 667.1(1)

B22 -236 -329.8(1)

Bo4 -1.7 -23.1(1)

B14 -670 -381.8(2)

B24 -12.2 -19.8(1)

B34 275 154.5(4)

B44 90.5 53.7(2)

Bo6 -0.86 -9.48(4)

B16 -290 -287.5(3)

B26 -284 -171.0(2)

B36 -41.8 -22.2(9)

B46 -73.1 -50.7(3)

B56 -862 -705.1(8)

B66 248 233.3(9)

g-factor Measured Calculated

g1 1.67(1) 1.670

g2 2.42(1) 2.423

g3 5.41(1) 5.409

ga 3.68(1) 3.690

gb 1.67(1) 1.670

gc 4.63(1) 4.638

rable 4. Crystal field energies (in cm of Yb3+ ions in YF3.

Multiplet, 2S +1 t Lj Measured [11] Calculated

0 0

2F7/2 116 116 290 390

10230 10231

2F5/2 10367 10385

10587 10566

4. Conclusion

The angular dependences of the EPR spectrum of Yb3+ ion in YF3 host have been measured in YF3:Yb3+ single crystals which were rotated around the crystallographic a- and b-axes so that the static magnetic field was applied respectively in (bc) and (ac) plane of YF3:Yb3+ crystal structure. The set of crystal field parameters has been calculated using the semi-phenomenological exchange charge model and then corrected by comparing the results of calculations with the experimental data. Using obtained set of the crystal field parameters the angular dependences of Yb3+ EPR spectra and values of g-factors have been calculated and found in a good agreement with ones measured experimentally. Stark energies of Yb3+ ion in YF3 host have been also reproduced satisfactorily.

A.V. Savinkov, B.F. Gabbasov, O.A. Morozov et al

Acknowledgments

Authors are grateful to B.Z. Malkin for useful discussions. The work is performed according to the Russian Government Program of Competitive Growth of Kazan Federal University, partially supported by RFBR grant №15-02-06990_a.

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