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81ISSN 2072-5981 doi: 10.26907/mrsej
aänetic Resonance in Solids
Electronic Journal
Volume 21 Issue 2 Paper No 19204 1-7 pages 2019
doi: 10.26907/mrsej-19204
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Established and published by Kazan University Endorsed by International Society of Magnetic Resonance (ISMAR) Registered by Russian Federation Committee on Press (#015140),
August 2, 1996 First Issue appeared on July 25, 1997
© Kazan Federal University (KFU)*
"Magnetic Resonance in Solids. Electronic Journal" (MRSey) is a
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Editors
Vadim Atsarkin (Institute of Radio Engineering and Electronics, Moscow) Yurij Bunkov (CNRS, Grenoble) Mikhail Eremin (KFU, Kazan) David Fushman (University of Maryland, College Park) Hugo Keller (University of Zürich,
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Yoshio Kitaoka (Osaka University,
Osaka)
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,
Kazan)
* In Kazan University the Electron Paramagnetic Resonance (EPR) was discovered by Zavoisky E.K. in 1944.
Short cite this: Magn. Reson. Solids 21, 19204 (2019)
doi: 10.26907/mrsej-19204
High frequency EPR spectroscopy of Er3+ ions in LiYF4 and LiLuF4:
a case study of crystal fields
G.S. Shakurov1*, S.L. Korableva2, B.Z. Malkin2
1 Zavoisky Physical-Technical Institute, FRC Kazan Scientific Center of RAS, Sibirsky trakt 10/7, Kazan 420029, Russia
2 Kazan Federal University, Kremlevskaya 18, Kazan 420008, Russia
*E-mail: [email protected]
(Received April 11, 2019; accepted May 7, 2019; published May 16, 2019)
We report the electronic paramagnetic resonance (EPR) studies on single crystals of L1RF4 (R = Y and Lu) doped with Er3+ ions in the frequency range of 37-1040 GHz at the liquid helium temperature. Resonance transitions between the Zeeman sublevels of three lower crystal-field Kramers doublets of Er3+ ions in magnetic fields up to 1 Tesla are registered. A prominent anisotropy of the EPR spectra in magnetic fields lying in the ab-plane of the tetragonal crystal lattice is revealed. The revised set of free-ion and crystal-field parameters for LiYF4:Er3+ and the new one for LiLuF4:Er3+ allow us to reproduce successfully the measured frequency and angular dependences of the resonant magnetic fields.
PACS: 71.70.Ej,75.10.Dg, 76.30.Kg.
Keywords: crystal field parameters, g-factors, magnetic anisotropy, optical spectra. 1. Introduction
The rare-earth doped crystals of double fluorides LiRF4 (R = Y, Lu) are well known model systems in condensed matter physics which are used for different applications in quantum electronics. Additional attention to these compounds was stimulated recently by their applications as quantum memory optical elements. In this case, the detailed information about energies and wave functions of crystal-field states of rare-earth ions is necessary. Traditionally such information about the ground state is obtained from standard electronic paramagnetic resonance (EPR) measurements at low temperatures. To study excited states, one has to work at enhanced temperatures. However, the temperature increasing induces quick relaxation processes and additional broadening of spectral lines that prevents observation of EPR signals. Direct studies of excited states are possible by making use of tunable high frequency EPR technique that allows us to observe resonance transitions from the ground state to excited states at external magnetic fields. In the present work, we carried out high frequency EPR measurements in LiYF4 and LiLuF4 single crystals doped with the trivalent erbium ions.
Rare-earth ions substitute for yttrium or lutetium ions in LiRF4 (R = Y, Lu) crystals at sites with local S4 symmetry. The ground multiplet 4l15/2 of an Er3+ ion is split in the tetragonal crystal field to eight Kramers doublets with the wave functions transforming accordingly to irreducible representations r56 or r78 of the S4 point symmetry group. Crystal-field energies of the ground and several excited multiplets of the Er3+ ground electronic configuration 4fn have been extensively studied by optical spectroscopy [1-3]. In particular, the measured gaps A1 = E(r718)) - E(r56)) and A 2 = E (rf^) - E (r506)) between the ground ^ doublet and the first (r 7)) and the second (r^) excited doublets are represented in Table 1 below. The results of EPR studies of impurity Er3+ ions in LiYF4 and LiLuF4 crystals (the measured g-factors of the ground and the first excited doublets and the spin-lattice relaxation times) were published in Refs. [4-8]. The most detailed measurements of spectral characteristics of impurity 166Er and 167Er isotopes in the LiYF4 single crystal accompanied by a comprehensive analysis of the data obtained with making use of the high-resolution magneto-optical spectroscopy were published recently in Ref. [9]. However, we found remarkable differences between some results of our measurements and preliminary calculations where we used crystal-field parameters available from literature.
High frequency EPR spectroscopy of Er3+ ions in LiYF4 and LiLuF4: a case .study of crystal fields Table 1. Spectral characteristics of impurity Er3+ ions in LiYF4 and LiLuF4.
Spectral LiYF4 LiLuF4
characteristics Measured Calculated Measured Calculated
gii( r 50)) 3.137 [4] 3.197 3.096 [7] 3.19
gi( r (0)) 8.105 [4] 8.108 8.138 [7] 8.12
A: (GHz) 517 [1], 510 [8] 510 660 [2], 658* 656.65
gii( r 7s) 8.18 [5], 7.97 [1] 8.109 8.504 [7] 8.50
gi( r78) 4.43 [5] 4.57 4.302 [7] 4.28
A2 (GHz) 869 [1], 828* 828.6 1050 [2], 1023* 1023.8
gii( r(2)) 0.11 [1], 0.3* 0.19 - 0.20
gi( r(66)) 7.8* 7.93 7.9* 7.91
* present work. Absolute values of errors in the measured g-factors do not exceed 0.1. 2. Details of experiments and results
We measured EPR spectra within the frequency v range of 37-1040 GHz at 4.2 K in LiYF4:Er (0.025%) and LiLuF4:Er (0.1%) single crystals grown by Bridgeman-Stockbarger method. The spectra were taken with the wide-band homemade spectrometer equipped by backward wave generators [10] in external magnetic fields up to 1 T. Apart from EPR signals corresponding to intra-doublet transitions, we observed inter-doublet transitions from the Zeeman sublevels of the ground doublet to sublevels of the first and the second excited doublets. Shapes of EPR signals measured at different frequencies in the spectra of LiREVEr^ (R = Y, Lu) are shown in Figure 1.
Let us number the lower six energy levels of Er3+ ion in the external magnetic field in ascending order of energy by indices from 1 to 6. The spectral lines corresponding to intra-doublet transitions (see Figure 1a) have a well resolved hyperfine structure (HFS) due to signals from 167Er isotope (natural abundance of 22.9%, nuclear spin I = 7/2). Spectral lines corresponding to 2^3 transitions (Figure 1b) have only partly resolved HFS. It should be noted that the inter-doublet transitions, as compared with the intra-doublet ones, are additionally broadened and have additional fine structure (also observed earlier in Ref. [8]) due to isotopic disorder in the lithium sublattices (crystal-field splittings depend on the relative number of 6Li+ and 7Li+ ions with natural abundances of 7 and 93%, respectively, in the nearest surroundings of an Er3+ ion).
The observed EPR signals in LiLuF4 corresponding to the 1^6 transitions in the magnetic field B||c (not shown) have weak intensities because of small power of backward wave generators and weak detector (n-InSb) sensitivity at THz frequencies. The measured angular and frequency-field dependences for the inter-doublet transitions in LiLuF4:Er3+ are shown in Figures 2 and 3. The output power of the backward generator depends strongly on frequency, and in the measurements of the
6.8 6.9 7.0 7.1 7.2 7.3 7.4 7.5 5.4 5.6 5.8 6.0 6.2 6.4 2.8 3.0 3.2 3.4
B (kG) B (kG) B (kG)
Figure 1. EPR signals in the spectra of LiLuF^Er^ (a - 1-^-2 transition, v= 82 GHz, b - 2-^-3 transition, v= 603 GHz) and LiYF^Er^ (c - 1^6 transition, v= 849 GHz). Bic.
6.7 ■ 6.6' 6.5'
6.4' 63
M 6.3.
cq
6.2 ■ 6.1 • 6.0 5.9
B||c
Blc
-1—
-50
—I—
50
—I—
100
—I—
150
200 250
0(degrees)
Figure 2. Measured (symbols) and calculated (solid line) angular dependences of the resonant magnetic field in LiLuF4:Er3+ for the 2-^-3 transitions at the frequency 603 GHz (0 is the angle between the magnetic field B and the c-axis in the {010} plane).
1046
640
- 630
- 620
- 610
- 600
590
B (kG)
Figure 3. Measured (symbols) and calculated (solid lines) frequency-field dependences for transitions 1^6 (circles, Blc) and 2-^-3 (squares, the magnetic field direction is declined from the c-axis by 50 degrees) in LiLuF4:Er3+.
frequency-field dependences we selected the magnetic field orientations corresponding to the largest values of effective g-factors and the narrowest spectral lines to improve the signal to noise ratios.
The zero-field splittings (ZFS) Ai(LiLuF4) = 658±1 GHz and A2(LiLuF4) = 1023 GHz were determined by making use the linear extrapolations of the measured frequency-field dependences (see Figure 3). It should be noted that it was difficult to register EPR signals corresponding to transitions between the ground rdoublet and the second excited doublet rfor magnetic fields B| | c due to small effective g-factor, large line width and, correspondingly, small signal to noise ratio. The values of ZFS were additionally checked by comparing the measured and calculated angular dependences of resonant magnetic fields (see below).
The broad band EPR spectra of LiYF4:Er3+ crystals corresponding to resonance transitions from the ground r(06) doublet to the first excited r™ doublet have been studied earlier in Ref. [8]. The value of Ai(LiYF4) = 510 GHz has been found. In the present work, we fulfilled detailed measurements of the inter-doublet transitions from the ground doublet to the second excited r doublet. The frequency-field dependences for transitions 1^5, 2^5, 1^6 and 2^6 in the magnetic fields B||c and Blc are shown in Figure 4. The value of A2(LiYF4) = 828.6 ±1 GHz is obtained directly from measurements in zero magnetic field (see Figure 4). The obtained values of ZFS Ai and A2 agree satisfactorily with the
High frequency EPR spectroscopy of Er3+ ions in LiYF4 and LiLuFr. a case study of crystal fields
ones from optical spectroscopy data [1-3], however, the correction for the A2(LiLuF4) value (1023 GHz as compared with 1050 GHz [2]) is essential.
Though the measured frequency-field dependences are practically linear, the ascending and descending branches shown in Figure 4 propagate asymmetrically relative to the line A2 = 828 GHz. This asymmetry gives evidence for mutual repulsion of Zeeman sublevels of different crystal-field doublets. Note, the transitions 1^5 and 2^6 between the Zeeman sublevels with almost the same magnetic moments (compare g±( Г(0)) and g±( Г (2)) in Table 1) are not observed in the collinear constant and alternating magnetic fields B||B(0 normal to the c-axis.
Measurements in the magnetic field B±c while rotating the sample of LiLuF4:Er3+ around the c-axis revealed remarkable anisotropy of EPR spectra (see Figure 5a). For different directions of the magnetic field in the аб-plane, not only the intensity of EPR signal varies strongly (the mechanism of such a strong intensity variation remains unclear at present time), but the position of the spectral line (a value of the resonant magnetic field) varies as well. Note that the decrease of the signal intensity is accompanied by the increasing asymmetry of the line shape, this brings about an increasing error in the measured line position. The measured angular dependence of the resonant magnetic field in the аб-plane is shown in Figure 5b (a similar variation of resonance frequencies in the magnetic field rotating around the S4 symmetry axis in EPR spectra of LiYF4:Er3+ was marked earlier in Ref. [8]).
880
840
О
800
760
B (kG)
Figure 4. Resonance frequencies vs magnetic fields for the transitions from the ground r(6) doublet to the second excited r(6) doublet in LiYF^Er3^ Triangles and circles correspond to transitions in the magnetic fields Blc and B||c, respectively. The calculated dependences are represented by solid lines.
5.0
5.5
(a)
<p = -50o
B ||[100]
p = 50"
О
cq
6.281
6.276.266.256.246.236.226.21 -
(b)
7.0
100 -80 -60 -40 ' -20 ' 0 20 40 60 ' 80 100
6.0 6.5
B (kG) 9 (degrees)
Figure 5. (a) EPR signals in LiLuF^Er^ for magnetic fields B in the (ab) plane at the frequency 603 GHz.
(b) Angular dependence of the resonant magnetic field, p is the angle between the field and the a-axis.
3. Discussion
As has been shown earlier [6], an external magnetic field mixes remarkably wave functions of crystal-field sublevels of the ground multiplet of impurity Er3+ ions in LiYF4, and one has to include nonlinear in magnetic field terms into the effective Spin-Hamiltonian when describing the EPR spectra corresponding to intra-doublet transitions. In the present work, to analyze the measured frequency-field and angular dependences, we consider the parameterized single-ion Hamiltonian operating in the total space of 364 states of the electronic 4fn configuration of an Er3+ ion:
H = H fi + H CF + Hz, (1)
where Hfi is the free-ion Hamiltonian written in the standard form [11],
Hfi = X Fk fk +<£lA + aL2 + pG(G2) + yG(R) + X Tktk + XMkmk + X Pkpk, (2)
k=2,4,6 n k=2,3,4,6,7,8 k=0,2,4 k=2,4,6
and the operator Hcf determines the crystal-field interaction. In the crystallographic system of coordinates, Hcf is written as follows
Hcf = X (BO0+BO0 + B;O;+b-;O-; + BO+BO+B-4O-4 ), (3)
n
here Op are linear combinations of single-electron spherical tensor operators that coincide with Stevens operators in the truncated space of states of a fixed angular momentum [12]. The operator Hz corresponds to the Zeeman energy:
Hz =X^e(kln + 2s n )B. (4)
n
The symbol En in (2)-(4) means summation over 4f electrons with angular and spin moments, ln and Sn, respectively, k = 0.99 is the orbital reduction factor. The matrix elements of operators L = Enln, S Ensn Enlnsn fk (the angular parts of the two-electron electrostatic interaction), mk, pk (spin-dependent magnetic and relativistic spin-other orbit interactions), tk (three-body electrostatic interactions) and Casimir operators G(G2) and G(R7) in the two-body electrostatic correlation terms in the basis of 364 Slater determinants of the electronic 4f 11 configuration were tabulated by M.V. Vanyunin [13]. Initial values of parameters in (2)-(4) were taken from Ref. [9]. The final set of parameters in the free-ion Hamiltonian (2) (in units of cm-1) for Er ions in LiYF4 (F2 = 96829, F4= 68001, F6 = 54342, a = 17.1, p = -582.1, у = 1800, P2 = 594, P4 = 297, P6 = 60, T 2 = 451,
T3 = 61, T4= 100, T6= -245, T7 =305, T8= 160, M0 = 3.86, M2 = 2.16, M4 = 1.2, and the spinorbit coupling constant ^ = 2366) as well as the crystal-field parameters (see Table 2) were determined from the fitting procedure by making use of numerical diagonalization of the Hamiltonian (1) for fixed values and directions of the magnetic field B and the subsequent comparison of the measured resonance frequencies with the calculated frequencies of corresponding quantum transitions. The lattice constants of LiLuF4 (a = 0.5146 nm, c = 1.05886 nm [14]) are slightly less than the ones of LiYF4 (a = 0.5164 nm, c = 1.0741 nm [15]), and to describe the EPR spectra of Er3+ ions in LiLuF4, it was necessary not only to enlarge the crystal-field parameters (see Table 2), but to slightly diminish parameters F2 and a of the free-ion Hamiltonian (2) as well (for LiLuF4, F2 = 96629 cm l, a = 16.9 cm
The g-factors for the Kramers doublets Г (note, the g-tensor has diagonal elements only in the case of local S4 symmetry) were simulated using the corresponding eigen-functions of the Hamiltonian (1) in zero magnetic field | Г + and | Г -):
g±(Г) = 2|(Г+14 + 2Sx |Г ->|, g|| (Г) = 2|(Г+14 + 2SZ |Г+)|.
The calculated g-factors (see Table 1) as well as the crystal-field splittings of the ground and several excited multiplets (see Table 3) of impurity Er3+ ions in LiYF4 and LiLuF4 agree satisfactorily with our experimental data and the available optical data.
High frequency EPR spectroscopy of Er3+ ions in LiYF4 and LiLuF4: a case .study of crystal fields Table 2. Crystal-field parameters Bkp (cm-1).
k LiYF 4:Er3+ LiLuF4:R3+
p [9] Present work R = Ho [8] R = Er Present work
2 0 190 189 188.4 199.0
4 0 -80 -80.1 -80.5 -80.35
4 4 -760.8 -750.3 -640.2 -762.95
4 -4 -679.4 -678.8 -623.6 -690.38
6 0 -2.3 -3.2 -3.5 -3.39
6 4 -363 -378.32 -379.0 -406.82
6 -4 -222 -215.9 -230.3 -214.05
Table 3. Crystal-field energies (cm 1) of the ground and excited multiplet sublevels of Er3+ ions.
Doublet LiYF4 LiLuF4
symmetry Experiment Theory Experiment [2] Theory
4115/2 T56 0 [3] 0 0 0
T78 17 [3] 17 22 21.9
T56 27.6 [3] 27.6 35 34.1
T78 56 [3] 58.5 58 64.8
T78 252±2 [1] 245.8 262 257.0
T78 291 ±6 [1] 288.7 300 304.3
T56 320±3 [1] 316.4 335 330.5
T56 347±3 [1] 344.8 368 363.0
4113/2 T78 6534.3 [3] 6536.5 6545 6544.0
T56 6538.3 [3] 6539.4 6548 6546.6
T56 6578.6 [3] 6579.4 6587 6587.1
T78 6672.5 [3] 6667.5 6684 6677.6
T56 6696.0 [3] 6697.9 6715 6711.3
T78 6724.0 [3] 6719.2 6735 6730.5
T56 6738.3 [3] 6737.0 6750 6750.3
4F9/2 T78 15314 [16] 15309 15300 15300
T56 15333 [16] 15334 15327 15327
T78 15349 [16] 15348 15345 15342
T78 15425 [16] 15419 15420 15414
T56 15477 [16] 15474 15450 15471
We obtain also an overall good agreement between the calculated and measured frequency-field dependences (see Figures 3 and 4). Differences between the calculated and measured values (up to 60 G) of resonant magnetic fields in the {010} plane for the 2^3 transitions (Figure 2) are caused, at least partly, by slightly under-estimated values of gi-factors of the ground and the first excited doublets of Er3+ ions in LiLuF4; we have also to remember about intrinsic drawbacks of the single-electron crystal-field approach that neglects correlated two-particle terms in Hcf and shifts of the crystal-field levels induced by the electron-phonon interaction.
In the case of local S4 symmetry, the angular dependence of the Zeeman energy of any state of a paramagnetic ion in the external magnetic field B lying in the ab-plane is described by a four-petal regular rosette. Correspondingly, a frequency of a transition between any two Zeeman sublevels i and j of Kramers doublets is given by the expression
Vji (p) = jB) + bjB cos[4(p - (Pji)] (5)
where p is the angle between the magnetic field and the a-axis, and functions aj(B) contain differences of zero-field and Zeeman energies of the considered sublevels. From numerical simulations of the frequencies of the 2^-3 transitions in LiLuF4:Er3+ for different directions of the magnetic field B = 6.25 kG in the a6-plane, we obtained the following angular dependence of the resonant magnetic field at the frequency of 603 GHz: B(p) = 6.25 - 0.0218cos[4(p-10.8°)] (kG). This function matches successfully the experimental data (see Figure 5). Larger absolute values of the measured differences B(pp - 6.25 kG in the regions of p—30° and p~ +100° are most likely caused by a deviation of the rotation axis from the c-axis.
The obtained corrected set of crystal-field parameters for impurity Er3+ ions in LiYF4 allowed us to reproduce successfully not only the studied in the present work spectral characteristics of the three lower crystal-field sublevels of the ground multiplet 4Ii5/2, but the measured earlier in Ref. [9] g-factors of the two lower sublevels of the first excited 4Ii3/2 multiplet and the lowest sublevel of the %/2 multiplet as well (see Table 4).
Table 4. g-factors of the excited states of Er3+ ions in LiYF4.
Energy of the crystal-field doublet (cm-1) gl g||
Measured [9] Calculated Measured [9] Calculated
4l9/2 T78 12361 2.94 3.00 3.72 3.64
4l13/2 T56 6538.3 5.94 5.92 1.30 1.44
4l13/2 T78 6534.3 7.32 7.33 1.52 1.53
4. Summary
The obtained sets of crystal-field parameters, the revised one for LiYF4:Er3+ and the new one for LiLuF4:Er3+, can be used for predictions of spectral characteristics of the studied compounds that are necessary for its applications in quantum and optoelectronics.
Acknowledgements
The authors are grateful to V.A. Shustov for X-ray diffraction measurements and orientation of the samples. References
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