Ising-type behaviour of critical properties in weak ferroelectric Li₂Ge₇O₁₅
The dielectric constant ε and electron spin resonance spectra of Mn²⁺ ions have been studied in the range of the ferroelectric phase transition in Li₂Ge₇O₁₅ single crystals. Analysis of the experimental data permits one to estimate the critical exponents of dielectric susceptibility γ ≅ 1.25,...
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Інститут фізики конденсованих систем НАН України
1999
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| Цитувати: | Ising-type behaviour of critical properties in weak ferroelectric Li₂Ge₇O₁₅ / A.Yu. Kudzin, M.D. Volnianskii, M.P. Trubitsyn, I.A. Bsoul // Condensed Matter Physics. — 1999. — Т. 2, № 1(17). — С. 149-154. — Бібліогр.: 10 назв. — англ. |
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irk-123456789-1199242017-06-11T03:02:48Z Ising-type behaviour of critical properties in weak ferroelectric Li₂Ge₇O₁₅ Kudzin, A.Yu. Volnianskii, M.D. Trubitsyn, M.P. Bsoul, I.A. The dielectric constant ε and electron spin resonance spectra of Mn²⁺ ions have been studied in the range of the ferroelectric phase transition in Li₂Ge₇O₁₅ single crystals. Analysis of the experimental data permits one to estimate the critical exponents of dielectric susceptibility γ ≅ 1.25, order parameter β ≅ 0.32 and correlation length ν ≅ 0.63. The values of the critical exponents determined in a fairly broad temperature interval around Tc, are consistent with the theoretical predictions of the Ising model with a one-component non-polar ordering coordinate. Дiелектрична проникнiсть ε та спектри ЕПР iонiв Mn²⁺ дослiдженi в околi сегнетоелектричного фазового переходу у кристалах Li₂Ge₇O₁₅. Аналiз експериментальних даних дозволив оцiнити критичнi iндекси дiелектричної сприйнятливостi γ ≅ 1.25, параметра порядку β ≅ 0.32 i кореляцiйної довжини ν ≅ 0.63. Величини критичних iндексiв, обчисленi у досить широкому iнтервалi температур поблизу Tc, узгоджуються з теоретичними показниками моделi Iзiнга для однокомпонентного неполярного параметра порядку . 1999 Article Ising-type behaviour of critical properties in weak ferroelectric Li₂Ge₇O₁₅ / A.Yu. Kudzin, M.D. Volnianskii, M.P. Trubitsyn, I.A. Bsoul // Condensed Matter Physics. — 1999. — Т. 2, № 1(17). — С. 149-154. — Бібліогр.: 10 назв. — англ. 1607-324X DOI:10.5488/CMP.2.1.149 PACS: 77.80.Bh http://dspace.nbuv.gov.ua/handle/123456789/119924 en Condensed Matter Physics Інститут фізики конденсованих систем НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
| language |
English |
| description |
The dielectric constant ε and electron spin resonance spectra of Mn²⁺
ions have been studied in the range of the ferroelectric phase transition in
Li₂Ge₇O₁₅ single crystals. Analysis of the experimental data permits one
to estimate the critical exponents of dielectric susceptibility γ ≅ 1.25, order parameter β ≅ 0.32 and correlation length ν ≅ 0.63. The values of the
critical exponents determined in a fairly broad temperature interval around
Tc, are consistent with the theoretical predictions of the Ising model with a
one-component non-polar ordering coordinate. |
| format |
Article |
| author |
Kudzin, A.Yu. Volnianskii, M.D. Trubitsyn, M.P. Bsoul, I.A. |
| spellingShingle |
Kudzin, A.Yu. Volnianskii, M.D. Trubitsyn, M.P. Bsoul, I.A. Ising-type behaviour of critical properties in weak ferroelectric Li₂Ge₇O₁₅ Condensed Matter Physics |
| author_facet |
Kudzin, A.Yu. Volnianskii, M.D. Trubitsyn, M.P. Bsoul, I.A. |
| author_sort |
Kudzin, A.Yu. |
| title |
Ising-type behaviour of critical properties in weak ferroelectric Li₂Ge₇O₁₅ |
| title_short |
Ising-type behaviour of critical properties in weak ferroelectric Li₂Ge₇O₁₅ |
| title_full |
Ising-type behaviour of critical properties in weak ferroelectric Li₂Ge₇O₁₅ |
| title_fullStr |
Ising-type behaviour of critical properties in weak ferroelectric Li₂Ge₇O₁₅ |
| title_full_unstemmed |
Ising-type behaviour of critical properties in weak ferroelectric Li₂Ge₇O₁₅ |
| title_sort |
ising-type behaviour of critical properties in weak ferroelectric li₂ge₇o₁₅ |
| publisher |
Інститут фізики конденсованих систем НАН України |
| publishDate |
1999 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/119924 |
| citation_txt |
Ising-type behaviour of critical properties in weak ferroelectric Li₂Ge₇O₁₅ / A.Yu. Kudzin, M.D. Volnianskii, M.P. Trubitsyn, I.A. Bsoul // Condensed Matter Physics. — 1999. — Т. 2, № 1(17). — С. 149-154. — Бібліогр.: 10 назв. — англ. |
| series |
Condensed Matter Physics |
| work_keys_str_mv |
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2025-07-08T16:55:08Z |
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2025-07-08T16:55:08Z |
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1837098555424112640 |
| fulltext |
Condensed Matter Physics, 1999, Vol. 2, No. 1(17), p. 149–154
Ising-type behaviour of critical
properties in weak ferroelectric
Li2Ge7O15
A.Yu.Kudzin, M.D.Volnianskii, M.P.Trubitsyn, I.A.Bsoul
Dnipropetrovsk State University,
13 Naukova Str., 320625 Dnipropetrovsk, Ukraine
Received January 20, 1998
The dielectric constant ε and electron spin resonance spectra of Mn2+
ions have been studied in the range of the ferroelectric phase transition in
Li2Ge7O15 single crystals. Analysis of the experimental data permits one
to estimate the critical exponents of dielectric susceptibility γ ∼= 1.25, or-
der parameter β ∼= 0.32 and correlation length ν ∼= 0.63. The values of the
critical exponents determined in a fairly broad temperature interval around
Tc, are consistent with the theoretical predictions of the Ising model with a
one-component non-polar ordering coordinate.
Key words: weak ferroelectric, dielectric constant, electron spin
resonance
PACS: 77.80.Bh
1. Introduction
In Li2Ge7O15 crystals, hereafter abbreviated as LGO, a second order transition
from the paraelectric phase (space group D14
2h) to the ferroelectric one (space group
C5
2ν) occurs at temperature Tc=283.5 K [1,2]. The phonon mode, becoming soft
on approaching Tc , was observed by the Raman scattering [3] and submillimeter
spectroscopy [4]. As it was emphasized in [4], the soft mode is characterized by
an extremely small effective charge and its contribution to the dielectric constant
anomaly does not exceed 10% of the magnitude of ε peak at Tc. Dielectric inves-
tigations, carried out in the 21 MHz ÷ 7 GHz frequency range [5], have revealed
that another mode of a relaxational type becomes dominant near the transition
point and gives the main contribution to ε anomaly. In accordance with X-Ray
data [1], the structure of LGO crystals is formed by (GeO4) and (GeO6) polyhedral
frameworks, whereas Li+ ions are positioned in structural channels. The neutron
diffraction study [6] allows one to associate the cooperative tilting motion of the
(GeO4) tetrahedrons with oscillator-type dynamics and shows that the motion of
c© A.Yu.Kudzin, M.D.Volnianskii, M.P.Trubitsyn, I.A.Bsoul 149
A.Yu.Kudzin et al.
Li+ ions along the channels direction has a relaxational nature.
So, the physical properties of LGO crystals are characterized by a combination
of the features usually attributed to displacive and order-disorder types of struc-
tural phase transitions. It seems that previous attempts to describe the tempera-
ture behaviour of the LGO dielectric constant [7] and the central peak intensity
in hyper-Raman experiment [8] on the basis of the mean field approximation can
be specified.
This paper reports the results of the dielectric constant ε and ESR measure-
ments carried out in the range of the LGO phase transition.
2. Dielectric data
The studied LGO monocrystals were grown from the melt by the Chokhralsky
method. The samples used in dielectric experiments were prepared as the plates
of characteristic dimensions 10×6×1.6 mm3 with the polar axes c perpendicular
to the largest plane. The dielectric measurements were performed at 1 kHz in the
interval 273 ÷ 303 K at cooling. The temperature was changed with the rate ∼
0.2 K/min and controlled with the accuracy 0.02 K. The dielectric constant was
measured with a precision higher than 10−3.
The temperature behaviour ε(T) in the range of the transition point is rep-
resented in the insert to figure 1. The dielectric constant demonstrates a well-
pronounced λ-shaped anomaly and reaches its maximal value ∼300 at T∗ =
283.92 K. The magnitude and sharpness of the ε peak manifests a much better
quality of the investigated monocrystals in comparison with LGO samples studied
in [7]. Since the dielectric constant below Tc may be affected by such artifacts as
the domain walls motion, mobile imperfections effects etc., our attention is focused
on the analysis of the ε(T) behaviour in a paraelectric phase.
At first we try to describe the dependence ε(T) within the framework of the
Landau theory. The expression of the Curie-Weiss type
ε = ε0 +
C
(T − Tc)
, (1)
with three parameters – background ε0, Curie-Weiss constant C and transition
temperature Tc, is fitted by the least square method to the experimental data.
The calculations are performed in the interval T ∗ 6 T < 296 K since above 296 K
the dielectric constant varies very slowly and the real behaviour ε(T) is masked
by experimental precision. The fitting procedure yields the following values:
ε0 = 10.8; C = 3.5 K; Tc = 283.93 K
with the relative mean square error σ = 0.16. An attempt to take into account
the possible drift of the background dielectric constant and to represent it as
ε0 = ε′0 + pT does not decrease the σ value.
Further, the experimental data are fitted by the exponential expression
150
Critical properties in Li2Ge7O15
ε = ε0 + A(T − Tc)
−γ, (2)
including additional parameter γ. The values calculated in the interval T ∗ 6 T <
296 K are as follows:
ε0 = 11.0; A = 3.3 Kγ ; γ = 1.25; Tc = 283.90 K
with σ=5.8×10−2.
280 300
0
300
ε
T, K
0.1 1 10 100
0.1
1
10
100
γ = 1.25
ε-ε
0
T-T
C
, K
Figure 1. Dielectric constant (ε−ε0) ver-
sus (T − Tc) in a log-log scale (T > Tc).
In the insert: dependence ε(T ) around Tc
in an ordinary scale.
The obtained results clearly show
that an assumption of a non-classical
exponential behaviour (2) decreases the
mean square error σ in approximately
three times in comparison with the
classical Curie-Weiss expression (1).
Besides, the use of (2) gives a more
reliable value of the transition point,
whereas parameter Tc, obtained on the
basis of the Curie-Weiss law (1), is
higher than temperature T∗ of the di-
electric peak and hence slightly exceeds
the real transition point.
So, it may be concluded that ex-
ponential expression (2) with a non-
classical value of γ gives a better fit to
the experimental data than the Landau
theory. The temperature dependence of
(ε− ε0) versus (T − Tc), represented in
figure 1 in a log-log scale, satisfactorily
corresponds to a straight line with slope
γ ∼=1.25 in the interval considered.
It seems important to support the
conclusion about the non-classical be-
haviour of the dielectric constant in
LGO by alternative experimental techniques. In the next section we report some
results of the electron spin resonance investigations of the ferroelectric phase tran-
sition in LGO.
3. Radiospectroscopic data
The ESR spectra were studied in LGO monocrystals doped with Mn2+ (0.06%;
0.2% wt) ions. The samples were cut as 3×3×4 mm3 parallelepipeds with sides
parallel to the main crystallographic planes. The spectra were measured on a
conventional X-band spectrometer Radiopan SE/X 2547 equipped with a liquid
nitrogen gas flow system. The localization of paramagnetic ions in the LGO lattice
151
A.Yu.Kudzin et al.
was determined on the basis of angular dependencies of Mn2+ spectra. The data
reported earlier [9] give evidence that Mn2+ centers substitute Li+ ions in broad
channels of the LGO structure with non-local compensation of the excess charge of
the probe. It should be noted that the Mn2+ probe preserves the point symmetry
of the host ion and, hence, does not drastically perturb the surroundings. So, one
may hope, that ESR of manganese adequately reflects the critical properties of the
perfect LGO structure.
In an ESR experiment, the information about statical and dynamical phenom-
ena accompanying the structural phase transition can be obtained by measuring
the ESR line position, width and shape. As it was shown in [10], on approaching
Tc from above, the resonance lines of Mn2+ broaden and split into doublets in the
ferroelectric phase.
0.1 1 10
1
10
β = 0.32
∆H
, m
T
T
C
-T, K
0 5 10
0
100
∆H
2 , m
T
2
T
C
-T, K
Figure 2. ESR line splitting ∆H versus
(Tc − T ) in a log-log scale. In the insert:
dependence ∆H2(Tc−T ) demonstrating
deviation of the experimental behaviour
from the Landau theory.
The line splitting, observed below
Tc, results from the correlated atomic
distortions within a range of the para-
magnetic probe. The local shift of the
splitted resonance lines with temper-
ature variations in the ferrophase is
induced by the local order parameter
and, consequently, reflects its magni-
tude. It may be shown that the distance
∆H between splitted spectral compo-
nents is proportional to the local order
parameter ηloc. So, measuring ∆H(T)
allows one to investigate the tempera-
ture behaviour of ηloc. The dependence
of ∆H versus (Tc–T) is represented in
figure 2 in a log-log scale. It is quite
clear that the experimental behaviour
in the interval Tc − 10K 6 T < Tc may
be described by a straight line with the
mean slope β ∼=0.32, which apprecia-
bly differs from the classical value of
the order parameter critical exponent
0.5. The dependence ∆H2(Tc-T), repre-
sented in the insert to figure 2, demon-
strates that the local order parameter
behaviour significantly deviates from
the Landau theory predictions in the
low temperature vicinity of the transi-
tion point.
As it was mentioned above, the ESR lines anomalously broaden around Tc. The
analysis of ESR spectra transformation via the phase transition shows that line
width broadening is determined by inhomogeneous mechanisms and contributed by
152
Critical properties in Li2Ge7O15
the local order parameter fluctuations δηloc [10]. Simulating the experimental line
shape, we derived the critical contribution to the line width δHCR and separated
it from unessential background. The critical ESR line width dependence δHCR(T),
measured on approaching Tc from above, is represented in a double logarithmic
scale in figure 3. It can be seen that in the interval Tc + 1K 6 T 6 Tc + 20K the
experimental behaviour satisfactorily agrees with the exponential law δHCR ∼(T-
Tc)
−ν . The mean slope of the δHCR(T–Tc) dependence in this interval permits one
to estimate the critical index of the correlation length ν ∼= 0.63. In the narrow
interval ∼1K above Tc the dependence of the critical line width deviates from a
straight line and tends to saturation (figure 3). This deviation may be interpreted
as the result of partial suppression of local order parameter fluctuations by long-
range dipole-dipole interactions.
4. Conclusions
0.1 1 10
0.1
1
ν = 0.63
δH
, m
T
T-T
C
, K
Figure 3. Temperature dependence of
critical contribution to the ESR line
width in a log-log scale.
Investigations of the dielectric con-
stant and Mn2+ ESR spectra near the
ferroelectric phase transition in LGO
crystals allow one to determine the val-
ues of three critical indexes: the ex-
ponent of dielectric susceptibility γ ∼=
1.25, order parameter β ∼= 0.32 and cor-
relation length ν ∼= 0.63. It is remark-
able that the values of the critical ex-
ponents obtained in a fairly broad tem-
perature range of Tc via studying the
macroscopic and local properties are
consistent with each other and corre-
spond to the theoretical values given by
a three-dimensional Ising model with
a one-component non-polar ordering
coordinate. Obviously, an extremely
small soft mode effective charge pre-
determines the Ising-type behaviour of
the LGO critical properties. Dipole-
dipole interactions, mainly determining
critical phenomena in classical uniaxial
ferroelectrics, are no longer a decisive factor in LGO crystals. Consequently, order
parameter fluctuations are well pronounced in a broad interval around Tc and lead
to characteristic features peculiar to the order-disorder structural phase transition.
153
A.Yu.Kudzin et al.
References
1. Volenkle H., Wittman F., Nowotny H., Die kristallstruktur des lithiumhepttager-
manats Li2Ge7O15. // Monatsh. Chem., 1970, vol. 101, p. 46–56.
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transition of ortorombic Li2Ge7O15. // Z. Kristallogr., 1980, vol. 153, p. 329–337.
3. Wada M. Soft mode spectroscopic study of ferroelectric phase transition in
Li2Ge7O15. // Indian J. of Pure & Appl. Phys., 1988, vol. 26, No. 2, p. 68–71.
4. Volkov A., Kozlov G., Goncharov Yu. Observation of the soft polar mode in the
paraelectric phase in Li2Ge7O15. // Journ. Phys. Soc. Jap., 1985, vol. 54, No. 2,
p. 818–821.
5. Horioka M., Sawada A., Wada M. Dielectric critical slowing-down in ferroelectric
Li2Ge7O15. // Journ. Phys. Soc. Jap., 1989, vol. 58, No. 10, p. 3793–3797.
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Soc. Jap., 1983, vol. 52, No. 1, p. 193–199.
8. Morioka Y., Wada M., Sawada A. Hyper-Raman study of ferroelectric phase transition
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9. Trubitsyn M.P., Volnianskii M.D., Kudzin A.Yu. EPR of Mn2+ ions in lithium hep-
tagermanate crystals. // Kristallographia, 1991, vol. 36, No. 6, p. 1472–1476 (in Rus-
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10. Trubitsyn M.P., Volnianskii M.D., Kudzin A.Yu. EPR line width broadening near
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Iзінгівська поведінка критичних властивостей
слабкого сегнетоелектрика Li2Ge7O15
А.Ю.Кудзін, М.Д.Волнянський, М.П.Трубіцин, І.А.Бусоул
Дніпропетровський державний університет,
320625 Дніпропетровськ, пров. Науковий, 13
Отримано 20 січня 1998 р.
Дiелектрична проникнiсть ε та спектри ЕПР iонiв Mn2+ дослiдженi в
околi сегнетоелектричного фазового переходу у кристалах
Li2Ge7O15. Аналiз експериментальних даних дозволив оцiнити кри-
тичнi iндекси дiелектричної сприйнятливостi γ ≃ 1.25, параметра по-
рядку β ≃ 0.32 i кореляцiйної довжини ν ≃ 0.63. Величини критичних
iндексiв, обчисленi у досить широкому iнтервалi температур побли-
зу Tc, узгоджуються з теоретичними показниками моделi Iзiнга для
однокомпонентного неполярного параметра порядку .
Ключові слова: слабкий сегнетоелектрик, діелектрична константа,
електронний парамагнітний резонанс.
PACS: 77.80.Bh.
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