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Investigations of dielectric Van Vleck paramagnets at high magnetic fields and low temperatures
Physica B 284}288 (2000) 1686}1687
Investigations of dielectric Van Vleck paramagnets at high magnetic "elds and low temperatures Dmitrii A. Tayurskii *, Murat S. Tagirov , Haruhiko Suzuki Physics Department, Kazan State University, Kremlevskaya str., 18, Kazan 420008, Russia Faculty of Science, Kanazawa University, Kakuma-machi, Kanazawa 920-11, Japan
Abstract The in#uence of high magnetic "elds on the magnetic properties of dielectric Van Vleck paramagnets is discussed. The dynamics of coupled electron}nuclear spin system is investigated at high magnetic "elds and low temperatures. 2000 Elsevier Science B.V. All rights reserved. Keywords: High magnetic "eld; Nuclear magnetic resonance; Van Vleck paramagnet
1. Introduction Among di!erent dielectric crystals of rare-earth (RE) compounds the so-called `Van Vleck paramagnetsa form a special class. These substances have no magnetic moment in their ground electronic state, but their paramagnetic susceptibility strongly exceeds the diamagnetic one. Van Vleck paramagnetism takes place in crystals containing non-Kramers RE ions, for example, Tm>. The isotope Tm (100% natural abundance) has a nuclear spin equal to so the compounds of this element possess both electronic and nuclear magnetism. The so-called `enhanceda nuclear magnetic resonance is the main method of investigation for the Van Vleck paramagnets (see, for example, Refs. [1,2]). Almost all investigations have been carried out at magnetic "elds where the Zeeman energy of an ion can be considered as a perturbation. In Ref. [3], we proposed that dielectric Van Vleck paramagnets at high magnetic "elds (above 5 T) could be used for the nuclear dynamic polarization. In Ref. [4], the high-frequency electron paramagnetic resonance and resonant far-infrared absorption were observed for the "rst time at high magnetic "elds in thulium ethylsulphate Tm(C H SO ) ) 9H O(TmES) crystals. These
* Corresponding author. E-mail address: [email protected] (D.A. Tayurskii)
investigations showed that new, essential information about Van Vleck paramagnets can be obtained at high magnetic "elds. It is natural to expect that at high magnetic "elds the dynamics of the nuclear spin system will also exhibit new features. Foremost it is connected with the drastic change of ion wave functions due to the applied high magnetic "eld. In the present work we consider the electron}nuclear spin system of Tm> ion in TmES.
2. Electron}nuclear states at high magnetic 5elds Owing to its ground multiplet of H manifold, the system under consideration can be described by the e!ective Hamiltonian H"H #H #H #H , (1) 8 8 where H represents the in#uence of electric crystal "eld (the explicit form for it can be found in Ref. [1]), H and 8 H stand for the electron and nuclear Zeeman interac8 tions, respectively, H describes the hyper"ne interac tion. The e!ects of electron}phonon interaction are not taken into account here for simplicity. The numerical procedure of diagonalization of the Hamiltonian (1) allows us to "nd all magnetic quantities for Tm> ions in TmES crystal in the dependence on the strength of the applied magnetic "eld and the orientation of this "eld with respect to crystallographic axes (angle h).
0921-4526/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 2 9 0 2 - 6
D.A. Tayurskii et al. / Physica B 284}288 (2000) 1686}1687
Fig. 1. Magnetic "eld dependence of the transition frequencies between the lowest electron}nuclear sublevels of the ground multiplet (magnetic "eld is perpendicular to the c-axis of crystal).
1687
(1) are made of complicated a mixture of electronic and nuclear wave functions, and we cannot consider, for example, nuclear sublevels of the electron ground singlet as it has been done at low magnetic "elds [1]. It is more natural to consider the coupled electron}nuclear sublevels of the ground multiplet. Our calculations show that the frequencies of the transitions between two lowest electron}nuclear states, which are only populated at low temperatures, belong to the range close to conventional electron paramagnetic resonance frequencies (see Fig. 1). But the probabilities of the transitions between these levels are determined by matrix elements of the nuclear spin operator and we could observe resonant absorption in the parallel orientation of a magnetic "eld as well as in the perpendicular orientation. Moreover, the angular dependence of the transition frequencies and the magnetic moments of ions exhibit essentially non-linear and non-monotonic behavior at high magnetic "elds (see Fig. 2).
Acknowledgements The work was supported by Russian Foundation for Basic Research (the project 99-02-17536).
References Fig. 2. Angular dependence of the transition frequencies in a magnetic "eld of 15 T.
Here we should note that the usual terms, such as `paramagnetic shifta, `e!ective gyromagnetic ratioa, etc., are not applicable at high magnetic "elds. Our calculations show that the eigenfunctions of Hamiltonian
[1] L.K. Aminov, B.Z. Malkin, M.A. Teplov, in: K.A. Gschneidner, Jr., LeRoy Eyring (Eds.), Handbook on the Physics and Chemistry of Rare Earths, Vol. 22, Elsevier, Amsterdam, 1996 (Chapter 150). [2] A. Abragam, B. Bleaney, Proc. Roy. Soc. London A 387 (1983) 221. [3] M.S. Tagirov, D.A. Tayurskii, JETP Lett. 61 (1995) 672. [4] H.P. Moll, J. van Tol, P. Wyder, M.S. Tagirov, D.A. Tayurskii, Phys. Rev. Lett. 77 (1996) 3459.
Investigations of dielectric Van Vleck paramagnets at high magnetic "elds and low temperatures Dmitrii A. Tayurskii *, Murat S. Tagirov , Haruhiko Suzuki Physics Department, Kazan State University, Kremlevskaya str., 18, Kazan 420008, Russia Faculty of Science, Kanazawa University, Kakuma-machi, Kanazawa 920-11, Japan
Abstract The in#uence of high magnetic "elds on the magnetic properties of dielectric Van Vleck paramagnets is discussed. The dynamics of coupled electron}nuclear spin system is investigated at high magnetic "elds and low temperatures. 2000 Elsevier Science B.V. All rights reserved. Keywords: High magnetic "eld; Nuclear magnetic resonance; Van Vleck paramagnet
1. Introduction Among di!erent dielectric crystals of rare-earth (RE) compounds the so-called `Van Vleck paramagnetsa form a special class. These substances have no magnetic moment in their ground electronic state, but their paramagnetic susceptibility strongly exceeds the diamagnetic one. Van Vleck paramagnetism takes place in crystals containing non-Kramers RE ions, for example, Tm>. The isotope Tm (100% natural abundance) has a nuclear spin equal to so the compounds of this element possess both electronic and nuclear magnetism. The so-called `enhanceda nuclear magnetic resonance is the main method of investigation for the Van Vleck paramagnets (see, for example, Refs. [1,2]). Almost all investigations have been carried out at magnetic "elds where the Zeeman energy of an ion can be considered as a perturbation. In Ref. [3], we proposed that dielectric Van Vleck paramagnets at high magnetic "elds (above 5 T) could be used for the nuclear dynamic polarization. In Ref. [4], the high-frequency electron paramagnetic resonance and resonant far-infrared absorption were observed for the "rst time at high magnetic "elds in thulium ethylsulphate Tm(C H SO ) ) 9H O(TmES) crystals. These
* Corresponding author. E-mail address: [email protected] (D.A. Tayurskii)
investigations showed that new, essential information about Van Vleck paramagnets can be obtained at high magnetic "elds. It is natural to expect that at high magnetic "elds the dynamics of the nuclear spin system will also exhibit new features. Foremost it is connected with the drastic change of ion wave functions due to the applied high magnetic "eld. In the present work we consider the electron}nuclear spin system of Tm> ion in TmES.
2. Electron}nuclear states at high magnetic 5elds Owing to its ground multiplet of H manifold, the system under consideration can be described by the e!ective Hamiltonian H"H #H #H #H , (1) 8 8 where H represents the in#uence of electric crystal "eld (the explicit form for it can be found in Ref. [1]), H and 8 H stand for the electron and nuclear Zeeman interac8 tions, respectively, H describes the hyper"ne interac tion. The e!ects of electron}phonon interaction are not taken into account here for simplicity. The numerical procedure of diagonalization of the Hamiltonian (1) allows us to "nd all magnetic quantities for Tm> ions in TmES crystal in the dependence on the strength of the applied magnetic "eld and the orientation of this "eld with respect to crystallographic axes (angle h).
0921-4526/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 2 9 0 2 - 6
D.A. Tayurskii et al. / Physica B 284}288 (2000) 1686}1687
Fig. 1. Magnetic "eld dependence of the transition frequencies between the lowest electron}nuclear sublevels of the ground multiplet (magnetic "eld is perpendicular to the c-axis of crystal).
1687
(1) are made of complicated a mixture of electronic and nuclear wave functions, and we cannot consider, for example, nuclear sublevels of the electron ground singlet as it has been done at low magnetic "elds [1]. It is more natural to consider the coupled electron}nuclear sublevels of the ground multiplet. Our calculations show that the frequencies of the transitions between two lowest electron}nuclear states, which are only populated at low temperatures, belong to the range close to conventional electron paramagnetic resonance frequencies (see Fig. 1). But the probabilities of the transitions between these levels are determined by matrix elements of the nuclear spin operator and we could observe resonant absorption in the parallel orientation of a magnetic "eld as well as in the perpendicular orientation. Moreover, the angular dependence of the transition frequencies and the magnetic moments of ions exhibit essentially non-linear and non-monotonic behavior at high magnetic "elds (see Fig. 2).
Acknowledgements The work was supported by Russian Foundation for Basic Research (the project 99-02-17536).
References Fig. 2. Angular dependence of the transition frequencies in a magnetic "eld of 15 T.
Here we should note that the usual terms, such as `paramagnetic shifta, `e!ective gyromagnetic ratioa, etc., are not applicable at high magnetic "elds. Our calculations show that the eigenfunctions of Hamiltonian
[1] L.K. Aminov, B.Z. Malkin, M.A. Teplov, in: K.A. Gschneidner, Jr., LeRoy Eyring (Eds.), Handbook on the Physics and Chemistry of Rare Earths, Vol. 22, Elsevier, Amsterdam, 1996 (Chapter 150). [2] A. Abragam, B. Bleaney, Proc. Roy. Soc. London A 387 (1983) 221. [3] M.S. Tagirov, D.A. Tayurskii, JETP Lett. 61 (1995) 672. [4] H.P. Moll, J. van Tol, P. Wyder, M.S. Tagirov, D.A. Tayurskii, Phys. Rev. Lett. 77 (1996) 3459.