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11Scientific Notes of Taurida National V. I. Vernadsky University
Series : Physics and Mathematics Sciences. Volume 27 (66). 2014. No. 2. P. 86-91
UDK 537.9
ANGULAR DEPENDENCE OF EPR LINE INTENSITIES OBSERVED IN
NICKEL-DOPED GaBO3
Seleznyova K.X1, Strugatsky M.1, Yagupov S.1, Kliava J.2
1Taurida National V. I. Vernadsky University, 4 Vernadsky Ave., Simferopol 295007, Crimea, Russia 2LOMA, UMR 5798 Université de Bordeaux-CNRS, 33405 Talence cedex, France E-mail: kira sel.ez.nyova@mail.ru
In experimental EPR studies of single crystals, the question of intensities of different resonance lines is usually considered as secondary. Meanwhile, in studying the EPR of Ni-doped GaBO3 we have observed a drastic change in intensity of several lines when the microwave magnetic field was rotated with respect of the crystal axes. A theoretical consideration of the corresponding perturbation operator allows to adequately account for this phenomenon. Keywords: EPR transition intensity, gallium borate.
PACS: 76.30.Fc
INTRODUCTION
The electron paramagnetic resonance (EPR) is observed in the conditions where the ground state of a paramagnetic ion is split by an applied magnetizing field B, and the energy difference between different split levels is matched by energy quanta of the microwave field B1. Usually, B is much stronger than B1, therefore the latter does not
affect the positions of different spectral lines but it is directly responsible for their intensities. Meanwhile, in the analysis of single crystal EPR spectra, the issue of relative intensities of different features is usually considered as secondary in comparison with that of the resonance fields.
Recently, we have studied the EPR of GaBO3 single crystals doped with iron and nickel [1]. In the latter case, we have found a striking dependence in intensity of certain lines; almost disappearing at some orientations. Is has seemed interesting to provide a theoretical analysis of this dependence and compare it with the experimental findings.
THEORY
Electronic transitions between the energy levels corresponding to different projections of the effective electron spin S are induced by the magnetic component of the electromagnetic wave interacting with the electron magnetic moment whose components are:
(ßgSl =ßY gS, i = X, y, z (1)
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where x, y and z are local symmetry axes (coinciding in our case with main crystallographic directions xc, yc, zc), J3 is the Bohr magneton and gt are components of the electron g tensor g supposed to be diagonal. The transition intensity Wpq between a couple of levels p and q is proportional to the square of modulus of the matrix element [2]
uPq = P(p\B g s\q). (2)
Usually, in EPR conditions Br ^ B, so, we choose B and Bx respective directions along zt and yl axes of the laboratory frame xl, yl, zl. The relation between the laboratory and the crystallographic frame is described by the following rotation matrix [3]:
A =
- cos^ cos3cos^-sin^sin^ - sin^ cos3cos^ + cos^sin^ sin3cos^
- cos^ cos3sin^ + sin^ cos^ - sin^cos3sin^-cos^ cos^ sin3sin^
cos ^ sin 3 sin ^ sin 3 cos 3
A
(3)
Where 3,p,n-yare Euler angles, see Fig. 1. One can see that in the xc,yc,zc frame 3 and p are spherical angles of B , and describes the orientation of B1 in the plane perpendicular to B .
Fig. 1. Definition of Euler angles between the crystallographic frame and the laboratory frame.
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The unit vectors of B and Bj in the crystallographic frame are given, respectively, by the third and the second columns of the l matrix, viz.:
C sin 3 cos ^ f- sin^ cos 3 cos (p + cos sin (p^
-sin^cos3sin^-cos^cos^ . (4) sin sin 3
l
sin 3 sin Ç cos 3
and lx =
Thus, the matrix element (2) can be expressed as follows:
P„ =ßB,{p\1j s\q) .
with / defined in Eq. (4).
(5)
EXPERIMENTS AND DISCUSSION
Nickel-doped GaBO3 crystals were prepared in the Crystal Growth Laboratory of the Taurida National University (Simferopol) [4]. They have rhombohedral calcite structure with the space group D3d [5]. The crystals having the shape of thin hexagonal plates,
have been studied by EPR with an X-band spectrometer in the Institut de Chimie de la Matière Condensée de Bordeaux (Pessac, France). The spectra have been measured in two different configurations (i) and (ii), see Fig. 2. In both configurations, B was in the basal plane (3 = 90°) and Bj was either parallel (i), y/ = 0° or perpendicular (ii), y/ = 90° to this plane.
Fig. 2. Two different orientations of the crystals: (i) Br ^ C3 and (ii) Br PC3. In both cases, B ^ Br and B ^ C3.
Fig. 3 compares the EPR spectra for both configurations. In the context of the present study, most interesting are two features - closely spaced doublets - at ca. 0.04 and 0.23 T.
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One can see that the intensities of these features in the cases (i) and (ii) are strikingly different.
(i)
-1-1-n-1-1-
0 0.2 0.4 0.6
s, T
Fig. 3. EPR spectra for B1 parallel, y = 0o (i) and perpendicular, ry = 90o (ii) to the basal plane of the crystal.
The exact values of the resonance fields for these features, respectively, 0.0396 and 0.0406 T for the low-field one and 0.2259 and 0.2286 T for the medium-field one, have been determined by diagonalizing the general spin Hamiltonian matrix for trigonal symmetry [6, 7]. The corresponding resonance intensities have been calculated as follows [8]:
wpq x V2p2A21(pIllx(g• s)x + ly (g-S)y + llz(g-S)z|q)|2 , (6)
where v is the frequency of microwave field and l1x,, l1 and l1z are direction cosines of
B1, see expression (4).
Fig. 4 shows calculated relative intensities of the resonance features in question. The transitions (a) and (b) occur between non-adjacent levels 1^3 and 1^4, respectively, and one can see that their intensities are much weaker that the intensities of transitions (c) and (d) between adjacent levels, 1^2 and 2^3, respectively. The intensities of (a) and (b)
transitions become particularly low in the vicinity of iy = 90o, resulting in "disappearance" of these features, in good accordance with the experimental results shown in Fig. 3.
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0 40 80 120 160
Angle v|i, degrees
Fig. 4. Transition intensities for low-field, 0.0406 (a) and 0.0396 T (b), and medium-field, 0.2286 (c) and 0.2259 T (d) resonance features vs. the angle .
CONCLUSIONS
We have observed an unusually pronounced dependence on the orientation of the
microwave field B1, of intensities of certain EPR lines of Ni3+ in gallium borate single
crystals. The results of the theoretical analysis of this dependence are in good agreement with the experimental observations and clearly show the importance of using correct expressions of intensities of the resonance transitions interpreting the experimental EPR spectra.
ACKNOWLEDGEMENTS
This work was partially supported by RFBR Grant № 14-42-01557.
References
1. K. Seleznyova, M. Strugatsky, S. Yagupov, N. Postivey, A. Artemenko and J. Kliava, Physica Status SolidiB 251, 1393 (2014).
2. A. Abragam and B. Bleaney, Electron Paramagnetic resonance of transition ions (Clarendon Press, Oxford, General editors W. Marshall and D. H. Wilkinson, 1970).
3. G. Korn and T. Korn, Mathematical handbook for scientists and engineers (2nd ed., McGraw-Hillbook, New York, 1968).
4. M. Strugatsky, S. Yagupov, N. Postivey, K. Seleznyova, E. Milyukova and V. Yagupov, Scientific Notes of Taurida National V. I. Vernadsky University, Ser. Physics and Mathematics Sciences 24(63), 169 (2011).
5. S. Yagupov, E. Maksimova, I. Nayhatsky, V. Yagupov, E. Milyukova, K. Seleznyova and M. Strugatsky, "Iron Borate Based Monocrystals for Research in Magneto-ordered State Physics", in Abstracts of
90
International Conference on Oxide Materials for Electronic Engineering, OMEE-2014 (Lviv, 2014), p. 207.
6. S. Al'tshuler and B. Kozyrev, Electron Paramagnetic resonance in compounds of transition elements (Wiley & Sons, New York-Toronto-Jerusalem-London, 2nd ed, 1974).
7. C. A. Bates and R. S. Wardlaw, J. Phys. C: Solid State Phys. 12, 2133 (1979).
8. J. Kliava, EPR spectroscopy of disordered solids (Riga, Zinatne, 1988).
Селезньова К. Кутова залежшсть штенсивностей лшш ЕПР в GaBO3, легованому нжелем / К. Селезньова, М. Стругацький, С. Ягупов, Я. Клява // Вчеш записки Тавршського национального ушверситету iMeHi В. I. Вернадського. Серш : Фiзико-математичнi науки. - 2014. - Т. 27 (66), № 2. -С. 86-91.
В експериментальних дослвдженнях ЕПР монокристатв питання про штенсивност рiзних резонансних лiнiй, як правило, вважаеться вторинним. Проте, при ЕПР-дослiдженнях GaBO3, легованого Ni, ми спостершали рiзку змшу iнтенсивностi ряду лiнiй при обертанш мiкрохвильового магнiтного поля вiдносно криматчних осей. Теоретичний розгляд вiдповiдного оператора збурення дозволяе адекватно пояснити це явище.
KnwHoei слова: iнтенсивнiсть лшш ЕПР, борат галш.
Селезнева К. Угловая зависимость интенсивностей линий ЭПР в GaBO3, легированном никелем / К. Селезнева, М. Стругацкий, С. Ягупов, Я. Клява // Ученые записки Таврического национального университета имени В. И. Вернадского. Серия : Физико-математические науки. -2014. - Т. 27 (66), № 2. - С. 86-91.
В экспериментальных исследованиях ЭПР монокристаллов вопрос об интенсивностях различных резонансных линий, как правило, считается вторичным. Тем не менее, при ЭПР-исследованиях GaBO3, легированного Ni, мы наблюдали резкое изменение интенсивности ряда линий при вращении микроволнового магнитного поля относительно кристаллических осей. Теоретическое рассмотрение соответствующего оператора возмущения позволяет адекватно объяснить это явление. Ключевые слова: интенсивность линий ЭПР, борат галлия.
Список литературы
1. Electron paramagnetic resonance of Fe3+ in gallium borate: Superposition model analysis / K. Seleznyova, M. Strugatsky, S. Yagupov, et al. // Physica Status Solidi B. - 2014. - Vol. 251. -P. 1393.
2. Abragam A. Electron Paramagnetic Resonance of Transition Ions / A. Abragam and B. Bleaney ; ed. by W. Marshall and D. H. Wilkinson. - Oxford : Clarendon Press, 1970. - 944 p.
3. Korn G. Mathematical handbook for scientists and engineers / G. Korn and T. Korn. - New York : McGraw-Hillbook, 1968. - 1152 p.
4. Monocrystal system FexGa1-xBO3 for research in solid state physics / M. Strugatsky, S. Yagupov, N. Postivey, et al. // Scientific Notes of Taurida National V. I. Vernadsky University. - Series: Physics and Mathematics Sciences. - 2011. - Vol. 24(63), No 2. - P. 169.
5. Iron Borate Based Monocrystals for Research in Magneto-ordered State Physics / S. Yagupov, E. Maksimova, I. Nayhatsky, et al. // International Conference on Oxide Materials for Electronic Engineering (0MEE-2014) : Abstracts. - Lviv, 2014. - P. 207.
6. Al'tshuler S. Electron Paramagnetic resonance in compounds of transition elements / S. Al'tshuler and B. Kozyrev. - New York-Toronto-Jerusalem-London : Wiley & Sons, 1974. - 589 p.
7. Bates C. A. An analysis of EPR spectra from the Ni3+:AkO3 system / C. A. Bates and R. S. Wardlaw // J. Phys. C: Solid State Phys. - 1979. - Vol. 12. - P. 2133.
8. Клява Я. Г. ЭПР-спектроскопия неупорядоченных твердых тел / Я. Г. Клява. - Рига : Зинатне, 1988. - 320 c.
Received 03 September 2014.
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