ESR investigations of incommensurate Rb₂ZnCl₄:Mn²⁺
ESR spectra of Mn²⁺ probe have been studied in incommensurate rubidium zinc chloride monocrystals. It has been shown that temperature dependence of the resonance fields of ESR fine transition MS=3/2↔5/2 can be satisfactorily described based on the simple “local” model. ESR line position data confirm...
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Інститут фізики конденсованих систем НАН України
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| Cite this: | ESR investigations of incommensurate Rb₂ZnCl₄:Mn²⁺ / M.P. Trubitsyn // Condensed Matter Physics. — 1999. — Т. 2, № 4(20). — С. 671-676. — Бібліогр.: 13 назв. — англ. |
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nasplib_isofts_kiev_ua-123456789-1210132025-02-10T00:36:26Z ESR investigations of incommensurate Rb₂ZnCl₄:Mn²⁺ ЕПР дослiдження несумiрних кристалiв Rb₂ZnCl₄:Mn²⁺ Trubitsyn, M.P. ESR spectra of Mn²⁺ probe have been studied in incommensurate rubidium zinc chloride monocrystals. It has been shown that temperature dependence of the resonance fields of ESR fine transition MS=3/2↔5/2 can be satisfactorily described based on the simple “local” model. ESR line position data confirm non-classical character of the Rb₂ZnCl₄ critical properties, corresponding to 3D XY Heizenberg model. Проведено вивчення ЕПР спектрiв Mn²⁺ у несумiрнiй фазi монокристалiв тетрахлорцинкату рубiдiю. Показано, що температурна поведiнка резонансних полiв електронного переходу MS=3/2↔5/2 може бути описана в рамках простої “локальної” моделi. Температурнi залежностi положення резонансних лiнiй пiдтверджують некласичний характер властивостей Rb₂ZnCl₄ вiдповiдний до 3D XY моделi Гейзенберга. 1999 Article ESR investigations of incommensurate Rb₂ZnCl₄:Mn²⁺ / M.P. Trubitsyn // Condensed Matter Physics. — 1999. — Т. 2, № 4(20). — С. 671-676. — Бібліогр.: 13 назв. — англ. 1607-324X DOI:10.5488/CMP.2.4.671 PACS: 77.80.B https://nasplib.isofts.kiev.ua/handle/123456789/121013 en Condensed Matter Physics application/pdf Інститут фізики конденсованих систем НАН України |
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ESR spectra of Mn²⁺ probe have been studied in incommensurate rubidium zinc chloride monocrystals. It has been shown that temperature dependence of the resonance fields of ESR fine transition MS=3/2↔5/2 can
be satisfactorily described based on the simple “local” model. ESR line
position data confirm non-classical character of the Rb₂ZnCl₄ critical properties, corresponding to 3D XY Heizenberg model. |
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Trubitsyn, M.P. |
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Trubitsyn, M.P. ESR investigations of incommensurate Rb₂ZnCl₄:Mn²⁺ Condensed Matter Physics |
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Trubitsyn, M.P. |
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Trubitsyn, M.P. |
| title |
ESR investigations of incommensurate Rb₂ZnCl₄:Mn²⁺ |
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ESR investigations of incommensurate Rb₂ZnCl₄:Mn²⁺ |
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ESR investigations of incommensurate Rb₂ZnCl₄:Mn²⁺ |
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ESR investigations of incommensurate Rb₂ZnCl₄:Mn²⁺ |
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ESR investigations of incommensurate Rb₂ZnCl₄:Mn²⁺ |
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esr investigations of incommensurate rb₂zncl₄:mn²⁺ |
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Інститут фізики конденсованих систем НАН України |
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1999 |
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ESR investigations of incommensurate Rb₂ZnCl₄:Mn²⁺ / M.P. Trubitsyn // Condensed Matter Physics. — 1999. — Т. 2, № 4(20). — С. 671-676. — Бібліогр.: 13 назв. — англ. |
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Condensed Matter Physics |
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AT trubitsynmp esrinvestigationsofincommensuraterb2zncl4mn2 AT trubitsynmp eprdoslidžennânesumirnihkristalivrb2zncl4mn2 |
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2025-12-02T05:37:23Z |
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1850373669024432128 |
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Condensed Matter Physics, 1999, Vol. 2, No. 4(20), pp. 671–676
ESR investigations of incommensurate
Rb2ZnCl4:Mn2+
M.P.Trubitsyn
Dnipropetrovsk State University, Department of Physics
13 Naukovyi Lane, 320625 Dnipropetrovsk, Ukraine
Received October 15, 1998
ESR spectra of Mn2+ probe have been studied in incommensurate rubid-
ium zinc chloride monocrystals. It has been shown that temperature de-
pendence of the resonance fields of ESR fine transition MS=3/2↔5/2 can
be satisfactorily described based on the simple “local” model. ESR line
position data confirm non-classical character of the Rb2ZnCl4 critical prop-
erties, corresponding to 3D XY Heizenberg model.
Key words: incommensurate phase transition, electron spin resonance.
PACS: 77.80.B
1. Introduction
Rubidium zinc chloride Rb2ZnCl4 is one of the most intensively investigated com-
pounds with A2BX4 formulae [1]. Below Ti=303 K Rb2ZnCl4 undergoes the phase
transition from high temperature paraelectric phase (space group D16
2h – Pnam) to the
incommensurate phase with wave vector of structural modulation q i=(1/3-δ)a∗ di-
rected along a axis [2]. As it is well known a considerable progress in studying the in-
commensurate phases has been achieved by using radiospectroscopic techniques and
in particular via ESR of Mn2+ probe in Rb2ZnCl4 crystals [3]. Investigations of the
orientational diagrams of the ESR fine structure have shown that Mn2+ centers, sub-
stituting Zn2+ ions, are localized in chloride tetrahedra. Detection of the forbidden
hyperfine doublets (∆mJ = ± 1) on passing through paraelectric-incommensurate
phase transition unequivocally indicates that Mn2+ is an appropriate paramagnetic
probe and it is very sensitive to (ZnCl4) group rotations associated with incommen-
surate structural modulation [4].
The purpose of this paper is to present the results of ESR measurements per-
formed on the monocrystals Rb2ZnCl4 doped with Mn2+ probe. The samples studied
have been cut out from the monocrystals grown by Chokhralskii method. ESR spec-
tra have been measured on cooling run by using the conventional X-band spectrom-
eter. The temperature of the samples was regulated by means of a standard nitrogen
c© M.P.Trubitsyn 671
M.P.Trubitsyn
280 320
480
520
H
R (m
T)
T, K
1 10
1
10
∆H
(m
T)
∆ T, K
2β=0.80
Figure 1. Resonance fields of hyperfine line mJ=5/2, MS=3/2↔5/2 around Ti
at H || a. Solid lines are calculated using (2). In the insert: splitting between
singularities ∆H vs. ∆T = (Ti − T ) in a log-log scale.
gas flow cryostat providing the temperature stabilisation within 0.1 K during the
ESR spectrum recording.
2. Temperature dependence of Mn 2+ ESR spectra
It is well known that below Ti the single lines of magnetic resonance transform
into inhomogeneously broadened spectra restricted by edge singularity peaks [5]. The
singular line shape, having been observed in a number of incommensurate materials,
reflects the dependence of the ESR signal position at the phase of incommensurate
distortion. In the high temperature interval of incommensurate phase the plane
wave limit represents a reasonable approximation. If displacements of all neighbours
within the range of the probe are in phase then incommensurate distortion at the
given lattice site can be expressed in the simple “local” form U = ρ cosϕ(z) [5,6].
Here the amplitude ρ is assumed spatially independent whereas the phase ϕ varies
linearly along the modulation axis ϕ = q iz + ϕ0. According to neutron scattering
data [2], the phase shift between Cl− ions, forming (ZnCl4) tetrahedra, does not
exceed ∼ 20 just below Ti and further decreases on cooling. So, it may be expected,
that displacements of Mn2+ nearest neighbouring Cl− ions are nearly in phase and,
hence, “local” approximation [5,6] should be well adapted to the description of ESR
spectra in the temperature region adjoining Ti. In this case the resonance fields can
be expanded in powers of the local order parameter U
HR = H0 + aU +
1
2
bU2 + ... = H0 + A∆T β cosϕ+
1
2
B∆T 2β cos2 ϕ;
672
ESR investigations of incommensurate Rb2ZnCl4:Mn2+
∆T = (Ti − T ), ρ ∼ ∆T β , A ∼ a, B ∼ b. (1)
Here H0 corresponds to the line position in high temperature paraelectric phase.
Expansion parameters in (1) depend on the paramagnetic ion location in the unit
cell and on the direction of the external magnetic field H with respect to the crys-
tallographic axes. If H is applied along (or perpendicular to) the local symmetry
elements vanishing at the phase transition, the coefficients at linear term in (1)
should be equal to zero. In this case on cooling below Ti the single line splits into
the spectrum edged by two singularity peaks. Their positions are determined by
condition |dHR/dϕ| = 0 [5] and in accordance with (1) are given by
HQ1 = H0 (ϕ = ±π/2),
HQ2 = H0 +
1
2
B∆T 2β (ϕ = 0, π). (2)
So, HQ1 corresponds to the line position in paraelectric phase, whereas singularity
HQ2 shifts from H0 proportionally to the order parameter amplitude squared ρ2 ∼
∆T 2β. If the applied magnetic field destroys the symmetry elements vanishing at
Ti, the linear term in (1) is allowed by symmetry. In the case of dominant linear
contribution to the resonance fields two singularities are observed below T i at
HL1 = H0 − A∆T β +
1
2
B∆T 2β (ϕ = 0),
HL2 = H0 + A∆T β +
1
2
B∆T 2β (ϕ = π). (3)
It has to be noted that if A < |B|, the third singularity should appear at the
temperature independent position
HLQ = H0 −
A2
2B
.
The high field Mn2+ hyperfine sextuplet corresponding to electron transition
MS=3/2↔5/2 has been measured in the temperature range of Ti for the following
orientations of static magnetic field: i) H || a and ii) H deviated from a to c axis up
to 7◦. Above Ti the line position has been determined by simulation of the spectral
contour by convolution of lorentzian function with gaussian distribution. In the
incommensurate phase it was assumed that individual paramagnetic center gave the
lorentzian shaped signal, the position of which depends on the amplitude and phase
of incommensurate displacements according to (1).
The temperature dependence of the resonance fields of low field hyperfine com-
ponent (mJ=5/2) for orientation i)H || a is represented in figure 1. In high tempera-
ture phase the hyperfine line weakly shifts toward high fields. Below Ti=304.4 K the
single line splits into singularity spectrum. On cooling, high field singularity nearly
continues the thermal drift of line position in paraphase, whereas another singular-
ity considerably shifts to low fields. Since in the paraelectric phase (ab) represents
the mirror plane for paramagnetic centers point symmetry group, the linear term
673
M.P.Trubitsyn
280 300 320
440
480
H R (m
T)
T, K
1 10
1
10
∆T, K
∆H
(m
T)
β=0.34
Figure 2. Temperature dependence of resonance fields at the deviated orientation
6 H,a=7◦, H⊥b. Solid lines are calculated using (3). In the insert: ∆H vs. ∆T
in a double logarithmic scale.
in expansion (1) vanishes for the orientation considered. Hence quadratic coupling
between resonance fields and the order parameter is realized and line positions have
to be described by expressions (2). The distance between singularities according to
(2) equals ∆H = HQ2 − HQ1 = (B/2)∆T 2β. The singularity splitting ∆H versus
(Ti − T ) is represented in the insert to figure 1 in a double logarithmic scale. It can
be seen that for (Ti − T ) > 3.5 K the experimental behaviour corresponds to the
straight line with the mean slope of 0.80±0.01. The theoretical dependencies, cal-
culated using (2) and taking into account the H0 thermal drift, the estimated index
value 2β=0.80 and parameter B1=–3.28 mTK−2β (A1=0), are represented in figure 1
by solid lines. Following the arguments presented in [7,8], the deviation of calculated
curves from experimental dependencies observed around Ti may be ascribed to the
mean square fluctuations contributing to the line position.
For the deviated orientation ii) 6 H, a=7◦ the resonance fields measured in the
range of Ti are represented in the figure 2. In this case, the applied magnetic field
breaks the mirror plane (ab), the linear term in (1) is allowed by symmetry and
provides the dominant contribution to the resonance fields. The singularity split-
ting, in accordance with (3) equal to ∆H = HL2 − HL1 =2A∆T β, is plotted in
the insert to the figure 2 in a log-log scale. The experimental dependence can be
approximated by a straight line with the mean slope β=0.34±0.01. The solid lines
depicted in the figure 2 are calculated using (3) with parameters A2=10.86 mTK−β,
B2=–4.02 mTK−2β.
The data obtained and represented in figures 1,2 show that resonance fields of
the ESR fine sextuplet MS=3/2↔5/2 can be satisfactorily described by expansion
(1) based on the “local” approximation [5]. Nevertheless, the tendency of high field
674
ESR investigations of incommensurate Rb2ZnCl4:Mn2+
singularity temperature behaviour (figure 1) allows us to assume that at lower tem-
peratures “non-local” effects would become noticeable. One may suppose that super-
position of rotation and twist of chloride tetrahedra would result in “non-locality”
of interaction [9].
The order parameter critical index estimated from the linear singularity splitting
β=0.34 is consistent with the previous NMR [10] and ESR [11,12] data. This value is
very close to the theoretical exponent of 3D XY Heizenberg model. It is remarkable
that within the experimental accuracy the value of critical exponent determined
in the case of “quadratic” coupling (2β=0.80) noticeably exceeds the doubled β
value derived from linearly splitted singularity spectra. This departure qualitatively
agrees with NMR results [10] and may be attributed to the secondary order pa-
rameters having totally different character of critical behaviour in comparison with
the primary lattice distortion. As it has been pointed out in [13], the contribution
of the secondary order parameters can alter the values of critical indexes measured
experimentally.
3. Conclusions
It has been shown that temperature behaviour of the Mn2+ electron transition
MS=3/2↔5/2 in high temperature interval of Rb2 Zn Cl4 incommensurate phase
can be satisfactorily described based on the simple “local” approximation [5]. In ac-
cordance with order parameter dimensionality (n=2) the determined value of critical
index β corresponds to 3D XY Heizenberg model. Non-coincidence of the critical
indexes obtained for the cases of linear and quadratic coupling of resonance fields
with the order parameter confirms a non-classical character of the rubidium zinc
chloride critical properties.
References
1. Scheleg A.U., Zaretskii V.V. List of incommensurate crystals. – In: Incommensurate
Phases in Dielectrics – Materials. Amsterdam, 1986, p. 367–402.
2. Gesi K., Iizumi M. Neutron scattering study on the incommensurate phases in fer-
roelectric Rb2ZnCl4 and K2ZnCl4. // Journ. Phys. Soc. Jap., 1979, vol. 46, No. 2,
p. 697–698.
3. Muller K.A., Fayet J.C. Structural phase transitions studied by electron spin res-
onance. – In: Structural Phase Transitions II (Ed. by K.A.Muller & H.Thomas),
Springer-Verlag-Berlin, 1991, vol. 45, p. 1–82.
4. Pezeril M., Emery J., Fayet J.C. EPR investigations of commensurate-incommensurate
structural phase transition through “forbidden” hyperfine lines. Application to
Rb2ZnCl4:Mn2+. // J.Physique Lett. (France), 1980, vol. 41, No. 21, p. L499–L502.
5. Blinc R. Magnetic resonance and relaxation in structurally incommensurate systems.
// Phys. Reports, 1981, vol. 79, No. 5, p. 331–398.
6. Blinc R., Seliger J., Zumer S. NMR in incommensurate systems: non-local effects. //
J.Phys.C: Solid State Phys., 1985, vol. 18, p. 2313–2330.
675
M.P.Trubitsyn
7. Kaziba A., Pezeril M., Emery J., Fayet J.C. Critical slowing-down and central peak
phenomena near Ti in Rb2ZnCl4:Mn2+ through E.P.R. measurements. // J. Physique
Lett. (France), 1985, vol. 46, p. L387–L393.
8. Trubitsyn M.P., Savchenko V.V. Fluctuations of incommensurate wave near
paraelectric-modulated phase transition in Rb2ZnCl4. // Ferroelectrics, 1992, vol. 134,
p. 259–264.
9. Emery J., Hubert S., Fayet J.C. Large phase fluctuations near Ti and phase pinning
in incommensurate ThBr4:Gd3+ through ESR measurements. // J. Physique Lett.
(France), 1984, vol. 45, p. L693–L700.
10. Walisch R., Perez-Mato J.M., Petersson J. NMR determination of the non-classical
critical exponents β and β̄ in incommensurate Rb2ZnCl4. // Phys. Rev B, 1989, vol. 40,
No. 16, p. 10747–10752.
11. Kaziba A., Fayet J.C. Phase and amplitude fluctuations near Ti in the incommensurate
phase of Rb2ZnCl4:Mn2+ through E.P.R. measurements. // J. Physique Lett.(France),
1986, vol. 47, p. L239–L248.
12. Horikx J.J., Arts A.F.M., de Wijn H.W. Order parameter in incommensurate
Rb2ZnCl4 studied by Mn2+ electron paramagnetic resonance. // Phys. Rev B, 1988,
vol. 37, No. 13, p. 7209–7214.
13. Cowley R.A., Bruce A.D. The theory of structurally incommensurate systems:
1. Disordered-incommensurate phase transition. // J. Phys.C: Solid State Phys., 1978,
vol. 11, p. 3577–3590.
ЕПР дослiдження несумiрних кристалiв
Rb2ZnCl4:Mn2+
М.П.Трубiцин
Днiпропетровський державний унiверситет, фiзичний факультет
320625 Днiпропетровськ, пров. Науковий, 13
Отримано 15 жовтня 1998 р.
Проведено вивчення ЕПР спектрiв Mn2+ у несумiрнiй фазi монокри-
сталiв тетрахлорцинкату рубiдiю. Показано, що температурна пове-
дiнка резонансних полiв електронного переходу MS=3/2↔5/2 може
бути описана в рамках простої “локальної” моделi. Температурнi за-
лежностi положення резонансних лiнiй пiдтверджують некласичний
характер властивостей Rb2ZnCl4 вiдповiдний до 3D XY моделi Гейзен-
берга.
Ключові слова: неспiвмiрний фазовий перехiд, електронний
парамагнiтний резонанс
PACS: 77.80.B
676
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