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62ISSN 2072-5981 doi: 10.26907/mrsej
aänetic Resonance in Solids
Electronic Journal
Volume 21 Issue 1 Paper No 19103 1-5 pages 2019
doi: 10.26907/mrsej-19103
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Yoshio Kitaoka (Osaka University,
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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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* In Kazan University the Electron Paramagnetic Resonance (EPR) was discovered by Zavoisky E.K. in 1944.
Short cite this: Magn. Reson. Solids 21, 19103 (2019)
doi: 10.26907/mrsej-19103
Anomalous 141Pr nuclear magnetic relaxation in PrF3 Van Vleck paramagnetf
A.S. Aleksandrov A.V. Egorov 1 2 *, S.L. Korableva M.S. Tagirov 1 2 1 Institute of Physics, Kazan Federal University, 420008 Kazan, Russian Federation 2 Institute of Applied Research, Tatarstan Academy of Sciences, 420111 Kazan, Russian Federation
*E-mail: alexander.egorov@kpfu.ru (Received December 18, 2018; accepted December 19, 2018; published January 30, 2019)
The magnetic nuclear spin-lattice relaxation has been studied in PrF3. It was found that 141Pr spin-lattice relaxation rate is untypically high for the Van Vleck insulator. According to all existing experimental data the only relaxation channel for enhanced nuclear moments at low temperatures is interaction with paramagnetic impurities and typical nuclear relaxation rate in rare earth Van Vleck paramagnets at liquid helium temperatures is 1 s-1. The measured value is 100 s-1. At the assumption that relaxation is caused by the strong 4f-4f cooperative interaction mediated by phonons [1], we measured 141Pr relaxation rates in a number of PrxLa1-xF3 samples and found that in diluted samples relaxation slows down to the usual for insulators values.
PACS: 75.10.Dg, 76.30.-v, 75.20.
Keywords: Van Vleck paramagnet, nuclear spin-lattice relaxation, enhanced NMR, pseudoquadrupole interaction, Davydow splitting, 4f-4f cooperative interaction.
1. Introduction
The properties of insulating rare earth Van Vleck paramagnets including spectral and relaxation parameters are most fully described in [2]. Hamiltonian of the rare earth ion with non-zero nuclear spin in crystals includes a number of terms
where the first term describes the interaction with the crystal electric field, the second is electron Zeeman interaction Hamiltonian, the third corresponds to hyperfine interaction, the fourth is nuclear Zeeman Hamiltonian, the last is nuclear quadrupole interaction term, gj is Lande factor, / is Bohr magneton, aj is hyperfine interaction constant, J is total electron moment operator, I is nuclear spin operator, yi is nuclear gyromagnetic ratio, h is Planck constant, H is magnetic field. Such an approach sometimes is called single ion model or static model, since no 4f-4f or electron-phonon interaction is taken in account. In case of non-Kramers ions ground state can be a singlet. In this case the system of such ions is called Van Vleck paramagnet. At the temperatures satisfying condition kT ■ A, where A is the energy of the nearest excited state, temperature independent magnetic (Van Vleck) susceptibility is observed. The nuclear magnetic resonance of Van Vleck ions nuclei is not observed at high temperatures due to the broadening caused by hyperfine interaction. At low temperatures this interaction leads to phenomenon known as enhanced nuclear magnetic resonance. Hyperfine interaction leads to enhancement of nuclear magnetic moments. The effective Hamiltonian, including only nuclear spin operators has the following form
where y a are the components of the effective gyromagnetic ratio. Usually the effective nuclear moments are highly anisotropic. The last terms are similar to the nuclear quadrupole Hamiltonian and
f This paper was selected at XX International Youth Scientific School "Actual problems of magnetic resonance and its application", Kazan, 24-29 September 2018. The MRSej Editors, Prof. M.S. Tagirov and Prof. V.A. Zhikharev, are responsible for the publication.
H = Hf + g J p HJ + a J JI - Yi h HI + H,
(1)
Hr =-h Y y H I + D I2 + ^I (I +1) + E (I2 -12),
I ^^ i a a a z q \ ' V x y /
a=x y z
(2)
predict the splitting of the energy levels in the absence of external magnetic field. Actually, they are completely defined by hyperfine interaction and do not depend on nuclear quadrupole moment. Therefore, this special interaction is called pseudoquadrupole. The parameters of the effective nuclear Hamiltonian can be calculated using second order perturbation theory:
Ya=YI + 2gJfiK/n, K= aJZ E -E , D = aj
i i \l2
g Ja n)\ (K+K \ (A..-AA
y
-A.
E = aJ
(3)
where Eg is the energy of the ground singlet, |n) are eigen functions of Hcef Hamiltonian. The very
last analysis of the crystal electric field parameters in PrF3 was performed for the full 4f 2 configuration (91 states) [3].
The crystal structure of PrF3 and isomorphous to it LaF3, CeF3 and NdF3 compounds has a space group D34d (P3cl) [4, 5]. The rare earth site symmetry is C2. The ground multiplet 3H4 of the Pr3+ non-Kramers (4f 2-configuration) in crystal electric field (CEF) of low symmetry splits into 9 singlets. The set of CEF parameters for REF3 crystals based on comparison with experimental data was proposed in [6]. The 141Pr isotope has 100% natural abundance, spin I = 5/2, and gyromagnetic ratio Y/2n = 12.1 MHz/T. The 141Pr NMR spectra are well described by Hamiltonian (2) with the following parameters D/h = 4.31(1) MHz, E/h = 0.30(1) MHz, yj2n = 33.2(2) MHz/T, yyj2n =
32.4(2) MHz/T, yj 2n = 100.3(2) MHz/T [7, 8]. In zero magnetic field nuclear energy levels are split into three doublets. There are two allowed transitions with a frequencies of 9.063(3) MHz and 17.083 MHz [9]. Effective nuclear Hamiltonian parameters for the diluted system Pr:LaF3 were also obtained using rf-optical double resonance technique D/h = 4.185(1) MHz, E/h = 0.146(1) MHz, yj2n= 49.8(4) MHz/T, yyj2n = 25.3(3) MHz/T, yj2n = 101.6(3) MHz/T. The frequencies of the
transition are 8.5 MHz and 16.7 MHz [10]. Magnetic relaxation in such multilevel system is not exponential. The solution of kinetic equations for nuclear quadrupole resonance in case of I = 5/2 and n - 0 can be used for 141Pr pseudoquadrupole resonance [11]. In this case magnetization recovery function contains two weighted exponents. The weights are different for different transitions and depend on asymmetry parameter. The equivalent asymmetry parameters for the Hamiltonian (2) n = 3E/D are 0.21 for PrF3, and 0.1 for Pr:LaF3.
Nuclear spin-lattice relaxation in insulating Van Vleck compounds at low temperatures has the same nature as in diamagnetic insulators i.e. via paramagnetic centers which are always present in small amount in all rare earth compounds. Van Vleck paramagnets having effective magnetic moments intermediate between nuclear and electronic were used for adiabatic cooling as it was proposed in [12]. Insulators were never used for that purpose since spin-lattice relaxation is very slow. Intermetallic compounds such as PrCu6 were successfully used for that purpose since they have additional Korringa relaxation channel [13]. At higher temperatures the nuclear relaxation is driven by thermally excited states of 4f-ions and the temperature dependence of relaxation rate has a factor exp(-A/kT). 141Pr spin-lattice relaxation in PrF3 is anomalously fast at low temperatures. We measured T1= 5 ms for ±1/2 ±3/2 transition in a number of PrF3 powders at 4.2 K [9], and 7 ms for 141Pr NMR in PrF3 powder at the frequency of 6.65 MHz at 1.5 K [14].
2. Experimental
A number of single crystals PrxLa1-xF3 (x = 1, 0.2, 0.1, 0.05, 0.01) were grown using Bridgman-Stockbarger method. ESR measurements have shown that total content of paramagnetic impurities (Er3+, Dy3+, Nd3+, Gd3+) never exceeds 0.01% of the host rare earth ion. We used home-built NMR/NQR pulse spectrometer. All the measurements were provided using nuclear spin-echo technique. The three pulse sequence was used for the measurements of longitudinal nuclear
magnetization recovery: nj2 -1 -n/2 -t -n. The first saturating pulse is followed by two pulses producing Hahn echo. In case of uniform (single exponent) relaxation of the nuclear magnetization the data should be fitted by the function S(t) = S(<x>)[1 -exp(-t/T|)], where S(<x>) is the intensity of unsaturated echo, and T is relaxation time. The energy levels of 141Pr(I = 5/2) in all the samples under the study are the three doublets and the recovery curves contain two exponents. Their weights depend on transition: ±1/2 -o-±3/2 or ±3/2 -o-±5/2 and asymmetry of pseudoqudrupole interaction.
In order to follow the changes in recovery curves we used the function S (t) = S (<x>) 1 - exp (-t/T^
N < 1. In this case T equals to the time at which magnetization recovers to S(<x>) (1 - e) value.
The temperature dependence of 141Pr spinlattice relaxation in PrF3 for two pseudoquadrupole frequencies have been measured (Fig. 1). At low temperatures relaxation rate is unusually fast and displays no temperature dependence. At higher temperatures the relaxation is caused by hyperfine field fluctuations caused by thermal excitations of 4f-ion. Therefore experimental data have been fitted by the following function T~l=A+Bexp(-A/kT). We obtained A = 220(10) s-1, A = 96(3) cm-1, and A = 362(16) s-1, A =79(6) cm-1 at high and low frequencies respectively. The frequencies of the pseudoquadrupole transitions become slightly smaller with the temperature increase. We followed these changes and all the measurements were done at the maximal signal intensity.
In order to clarify the origin of the fast
10°
10
10*
10
0.0
Figure 1.
iLin * n i
Hili i i *
-i
0.3 0.4 0.5 0.6 0.7 1/T, K"1
141Pr nuclei spin-lattice relaxation rate dependence on inverse temperature in PrF3. Open blue circles correspond to the frequency of 9.06 MHz at 4.2 K, filled red circles present the values obtained at 7.08 MHz, solid lines are fitting curves.
relaxation at low temperature we measured 141Pr
spin-lattice relaxation times, as well as spectroscopic characteristics in the set of PrxLai-xF3 single crystals at the temperature of 4.2 K (Table 1). All the measurements were done at the higher frequency 141Pr pseudoquadrupole transition. This frequency systematically changes from 17.08 MHz in PrF3 to 16.7 MHz in diluted Pr:LaF3 compound, reflecting the changes in crystal electric field. The line width has the smallest values in the samples with a highest and lowest Pr content, i.e. having the most ordered crystal structure. Spin-spin relaxation time (T2) increases by a factor of 2, indicating the increasing of the mean distance between the 141Pr nuclei and reduction of this contribution into spinspin relaxation. The most striking changes occur with a spin-lattice relaxation constant, which value increased by a factor 120 with the x decrease from 1.0 to 0.05. This fact supports the hypothesis that
Table 1. x denotes Pr content in PrxLai-xF3 crystals, v is the frequency of the pseudoquadrupole resonance transition, Sv is the line width, T1 is spin-lattice relaxation time, T2 is spin-spin relaxation time.
x v, MHz Sv, MHz T1, s T2, mks
1.0 17.08(1) 0.134 0.010(1) 10.5(2)
0.2 16.53(2) 0.88 0.21(4) 14.0(6)
0.1 16.50(2) 0.48(4) 0.70(8) 16.3(4)
0.05 16.55(2) 0.28(2) 1.2(2) 18.6(2)
0.01 16.6(1) 0.11(1) - -
141Pr spin-lattice relaxation in PrF3 is driven by some cooperative 4f-4f electron excitations. 141Pr spin-lattice relaxation rate dependence on temperature in Pr0.05La0.95F3 is presented on Fig. 2. The A parameter value was estimated to be 55(3) cm-1.
We also studied the form of 141Pr magnetization recovery curves in PrF3 and Pr0.05La0.95F3 samples at the temperatures of 4.2 K and 7 K. The data is presented at Fig. 3. The stretched exponent
exp -(t/Tl)N was used in order to follow the changes of non-exponent relaxation. In case of PrF3
parameter N does not change within the precision of fitting procedure: N(7 K) = 0.34(4), and N (4.2 K) = 0.39(2), approving that the spectral density of magnetic fluctuations is the same for all the nuclei at both temperatures. The most diluted sample under the study Pr0.05La0.95F3 displays at lower temperature smaller N value: N(7 K) = 0.78(3), and N(4.2 K) = 0.59(2). This fact indicated that relaxation at lower temperature has a different origin and 141Pr nuclei relax via paramagnetic impurities.
106
10 104
CO 10J
10 101
10"
Ti Mill I » 1 »-1-1-!
10
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
<•-1
Figure 2.
1/T, K-
141Pr nuclei spin-lattice relaxation rate in PrF3 (filled red circles), and Pr0.05La0.95F3 (open green circles). The solid lines are fitting curves.
0 0.0 0.01
Figure 3. Normalized and scaled over T1 141Pr longitudinal magnetization recovery curves. The fitting functions are plotted as solid lines. Filled red circles correspond to PrF3, T = 4.2 K, fitting parameter N = 0.39(2). Open blue circles: PrF3, T = 7 K, N = 0.34(4). Filled green squares: Pr0.05La0.95F3, T = 4.2 K, N = 0.59(5). Open purple squares: Pr0.05La0.95F3, T = 7 K, N = 0.78(3).
3. Discussion
Our data on 141Pr nuclear spin-lattice relaxation in PrxLai-*F3 single crystals at the temperatures when the
8
population of excited Pr3+ singlets becomes substantial obeys the following law T|-1 = ^ ai exp (-AjkT),
i=1
where At are the energies of excited levels, the relative values of factors ai are determined by the wave functions of the electron states [15]. It is hardly possible to determine contribution of each level from the relaxation data. Instead of it, one can fit the data using single exponent process, and the parameter A obtained from the fitting procedure should not be smaller than the energy of the lowest excited level. Three closest to the ground Pr3+ levels in PrF3 have the energies of 60, 69, and 134 cm-1 [6]. We obtained 96 and 79 cm-1 for the high and low frequency 141Pr transitions. The closest to the ground Pr3+ levels in Pr:LaF3 have the energies of 57, 76, and 136 cm-1 [16]. The fitting of the data in Pr0.05La0.95F3 sample gave the value of 55(3) cm-1. This facts support the validity of the proposed model of 141Pr relaxation at higher temperatures.
Let us turn to the low temperature region. There is a number of arguments that 141Pr relaxation in Van-Vleck paramagnet PrF3 cannot be explained by interaction with paramagnetic impurities. a) The relaxation rates are anomalously high. b) These rates are reproduced with high precision for the samples grown using very different starting chemical compounds. We measured the relaxation rate in the sample originally used for acoustic magnetic resonance in 1979 [8] and obtained the same values as for our crystals. c) 141Pr relaxation time in highly diluted Pr:LaF3 sample at the temperature of 2 K is about 1 s [10] i.e. 200 times longer than our data on PrF3.
The extensive studies of PrF3 crystals using Raman and infrared spectroscopy have been provided by M. Dahl et al. and outlined in [1]. Collective magnetic moments and Davydow splitting were observed. The total number of lines in exciton spectrum appeared to be 16 instead of 8. M. Dahl explains it by Davydow splitting. These effects result from Jahn-Teller type coupling of the 4f- and the phonon systems. The identification of the pure phonon and 4f-excitations (excitons) was provided using the studies of a mixed crystals LaxPr1-xF3. The electronic excitations gain intensity in PrF3 while phonons can be traced from LaF3 to PrF3. Our studies show that the 141Pr nuclear relaxation in PrF3 is driven by the hyperfine field fluctuations caused by 4f-excitations.
The possible explanation of 141Pr nuclear relaxation anomalous temperature dependence possibly can be explained by the narrowing of the lines in exciton spectrum with a temperature decrease, observed by the same authors [1].
4. Conclusion
The analysis of our experimental data supports the idea that 141Pr nuclear magnetic relaxation in insulating Van Vleck paramagnet PrF3 is governed by a strong phonon mediated 4f-4f excitations.
References
1. Dahl M. Z. Physik B 72, 87 (1988)
2. Aminov L.K., Malkin B.Z., Teplov M.A. in Handbook on the Physics and Chemistry of Rare Earths, V. 22, Ch. 150, P. 295-506 (ed. by K.A. Gschneider and L. Eyring), Elsevier, Amsterdam (1996)
3. Savinkov A.V., Irisov D. S., Malkin B.Z., Safiullin K.R., Suzuki H., Tagirov M.S., Tayurskii D.A. J. Phys.: Condens. Matter 18, 6337 (2006)
4. Anderson L.O., Johansson G. Z. Kristallogr. 127, 386 (1968)
5. Maximov B., Shultz H. Acta Crystallogr. 41, 88 (1985)
6. Morrison C.A., Leavitt R.P. J. Chem. Phys. 71, 2366 (1979)
7. Bolshakov I.G., Teplov M.A. Available from VINITI. 1274-1279 (1979)
8. Alt'shuler S.A., Duglav A.V., Khasanov A.Kh. JETP Lett. 29, 624 (1979)
9. Alakshin E.M., Aleksandrov A.S., Egorov A.V., Klochkov A.V., Korableva S.L., Tagirov M.S. JETP Letters 94, 240 (2011)
10. Reddy B.R., Erickson L.E. Phys. Rev. Lett. B 27, 5217 (1983)
11. Chepin J., Ross J. J. Phys.: Condens. Matter 3, 8103 (1991)
12. Al'tshuler S.A. Pis 'ma v Zh. Eksp. Teor. Fiz. 3, 177 (1966) (in Russian)
13. Andres K., Bucher E. J. Low. Temp. Phys. 9, 267 (1972)
14. Egorov A.V., Irisov D.S., Klochkov A.V., Kono K., Kuzmin V.V., Safiullin K.R., Tagirov M.S., Tayurskii D.A., Yudin A.N. J. Phys.: Conf. Series 150, 032019 (2009)
15. Aminov L.K., Teplov M.A. Sov. Phys. Usp. 28, 762 (1985) (Uspekhi Fizicheskih Nauk 147, 49 (1985), in Russian)
16. Feldmann K., Hennig K., Kaun L.P., Lippold B., Matthies S., Matz W., Savenko B.N., Welsch D. Phys. Status Solidi B 70, 71 (1975)
