Ferroelectric phase transition in lead germanate Pb₅Ge₃O₁₁ studied by ESR of Gd³⁺ probe
ESR spectra of Gd³⁺ probe have been studied in the range of ferroelectric phase transition TC=451 K in lead germanate Pb₅Ge₃O₁₁. Measurements of ESR line position have shown that local order parameter behaves in accordance with the mean field theory approach in a broad (∼150 K) temperature interval...
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Trubitsyn, M.P. Volnianskii, M.D. Ermakov, A.S. Linnik, V.G. 2017-06-13T12:43:03Z 2017-06-13T12:43:03Z 1999 Ferroelectric phase transition in lead germanate Pb₅Ge₃O₁₁ studied by ESR of Gd³⁺ probe / M.P. Trubitsyn, M.D. Volnianskii, A.S. Ermakov, V.G. Linnik // Condensed Matter Physics. — 1999. — Т. 2, № 4(20). — С. 677-684. — Бібліогр.: 19 назв. — англ. 1607-324X DOI:10.5488/CMP.2.4.677 PACS: 77.80.B https://nasplib.isofts.kiev.ua/handle/123456789/121015 ESR spectra of Gd³⁺ probe have been studied in the range of ferroelectric phase transition TC=451 K in lead germanate Pb₅Ge₃O₁₁. Measurements of ESR line position have shown that local order parameter behaves in accordance with the mean field theory approach in a broad (∼150 K) temperature interval below TC. Anomalous line width broadening observed around TC can be associated with a quasi-elastic central peak component of excitation spectrum, observed earlier using a light scattering experiment and attributed to static symmetry-breaking defects. ЕПР спектри iонiв Gd³⁺ вивчалися в iнтервалi сегнетоелектричного фазового переходу Tc=451 К кристалiв германату свинцю Pb₅Ge₃O₁₁. На пiдставi вимiрювання температурних залежностей положення ЕПР лiнiй показано, що поведiнка локального параметра порядку в досить широкому iнтервалi (∼ 150 К) сегнетоелектричної фази погоджується з теорiєю середнього молекулярного поля. Аномальне розширення резонансних лiнiй, що спостерiгається навколо Tc, може бути зiставлене з вузьким квазi-пружним центральним пiком у спектрах комбiнацiйного розсiяння свiтла i пов’язане зi статичними дефектами кристалічної гратки. en Інститут фізики конденсованих систем НАН України Condensed Matter Physics Ferroelectric phase transition in lead germanate Pb₅Ge₃O₁₁ studied by ESR of Gd³⁺ probe Дослiдження методом ЕПР сегнетоелектричного фазового переходу у кристалах германату свинцю Pb₅Ge₃O₁₁:Gd³⁺ Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Ferroelectric phase transition in lead germanate Pb₅Ge₃O₁₁ studied by ESR of Gd³⁺ probe |
| spellingShingle |
Ferroelectric phase transition in lead germanate Pb₅Ge₃O₁₁ studied by ESR of Gd³⁺ probe Trubitsyn, M.P. Volnianskii, M.D. Ermakov, A.S. Linnik, V.G. |
| title_short |
Ferroelectric phase transition in lead germanate Pb₅Ge₃O₁₁ studied by ESR of Gd³⁺ probe |
| title_full |
Ferroelectric phase transition in lead germanate Pb₅Ge₃O₁₁ studied by ESR of Gd³⁺ probe |
| title_fullStr |
Ferroelectric phase transition in lead germanate Pb₅Ge₃O₁₁ studied by ESR of Gd³⁺ probe |
| title_full_unstemmed |
Ferroelectric phase transition in lead germanate Pb₅Ge₃O₁₁ studied by ESR of Gd³⁺ probe |
| title_sort |
ferroelectric phase transition in lead germanate pb₅ge₃o₁₁ studied by esr of gd³⁺ probe |
| author |
Trubitsyn, M.P. Volnianskii, M.D. Ermakov, A.S. Linnik, V.G. |
| author_facet |
Trubitsyn, M.P. Volnianskii, M.D. Ermakov, A.S. Linnik, V.G. |
| publishDate |
1999 |
| language |
English |
| container_title |
Condensed Matter Physics |
| publisher |
Інститут фізики конденсованих систем НАН України |
| format |
Article |
| title_alt |
Дослiдження методом ЕПР сегнетоелектричного фазового переходу у кристалах германату свинцю Pb₅Ge₃O₁₁:Gd³⁺ |
| description |
ESR spectra of Gd³⁺ probe have been studied in the range of ferroelectric phase transition TC=451 K in lead germanate Pb₅Ge₃O₁₁. Measurements of ESR line position have shown that local order parameter behaves
in accordance with the mean field theory approach in a broad (∼150 K)
temperature interval below TC. Anomalous line width broadening observed
around TC can be associated with a quasi-elastic central peak component
of excitation spectrum, observed earlier using a light scattering experiment
and attributed to static symmetry-breaking defects.
ЕПР спектри iонiв Gd³⁺ вивчалися в iнтервалi сегнетоелектричного
фазового переходу Tc=451 К кристалiв германату свинцю Pb₅Ge₃O₁₁.
На пiдставi вимiрювання температурних залежностей положення
ЕПР лiнiй показано, що поведiнка локального параметра порядку в
досить широкому iнтервалi (∼ 150 К) сегнетоелектричної фази погоджується з теорiєю середнього молекулярного поля. Аномальне
розширення резонансних лiнiй, що спостерiгається навколо Tc, може
бути зiставлене з вузьким квазi-пружним центральним пiком у спектрах комбiнацiйного розсiяння свiтла i пов’язане зi статичними дефектами кристалічної гратки.
|
| issn |
1607-324X |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/121015 |
| citation_txt |
Ferroelectric phase transition in lead germanate Pb₅Ge₃O₁₁ studied by ESR of Gd³⁺ probe / M.P. Trubitsyn, M.D. Volnianskii, A.S. Ermakov, V.G. Linnik // Condensed Matter Physics. — 1999. — Т. 2, № 4(20). — С. 677-684. — Бібліогр.: 19 назв. — англ. |
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| first_indexed |
2025-11-24T09:58:57Z |
| last_indexed |
2025-11-24T09:58:57Z |
| _version_ |
1850454238795137024 |
| fulltext |
Condensed Matter Physics, 1999, Vol. 2, No. 4(20), pp. 677–684
Ferroelectric phase transition in lead
germanate Pb5Ge3O11 studied by ESR
of Gd3+ probe
M.P.Trubitsyn, M.D.Volnianskii, A.S.Ermakov, V.G.Linnik
Dnipropetrovsk State University, Department of Physics
13 Naukovyi Lane, Dnipropetrovsk, 320625 Ukraine
Received November 23, 1998
ESR spectra of Gd3+ probe have been studied in the range of ferroelec-
tric phase transition TC=451 K in lead germanate Pb5Ge3O11. Measure-
ments of ESR line position have shown that local order parameter behaves
in accordance with the mean field theory approach in a broad (∼150 K)
temperature interval below TC. Anomalous line width broadening observed
around TC can be associated with a quasi-elastic central peak component
of excitation spectrum, observed earlier using a light scattering experiment
and attributed to static symmetry-breaking defects.
Key words: ferroelectric phase transition, electron spin resonance
PACS: 77.80.B
1. Introduction
Lead germanate Pb5Ge3O11 (PGO) has been the subject of intensive experimen-
tal and theoretical studies since the discovery of the structural phase transition from
a high temperature paraelectric phase to a polar one at TC=451 K [1, 2]. The crystal
structure of PGO monocrystals, studied using neutron and X-ray diffraction [2–4],
in non-polar phase corresponds to C1
3h space group and on cooling below TC sponta-
neous polarisation emerges along the c-axis of the trigonal C 1
3 structure. The unit cell
of PGO contains three formulae units. The structural framework is constructed by
alternative layers perpendicular to the polar axis and consisting of single (GeO 4)
4−
and paired (Ge2O7)
6− germanium-oxygen tetrahedra connected by predominantly
covalent Pb-O bonds [4]. From the microscopic point of view the structural distor-
tions at the phase transition can be associated with tilt of (GeO4)
4− tetrahedra,
twist of (Ge2O7)
6− pyro- groups and displacements of Pb2+ ions [4]. Besides, the
resulting dipolar moment emerges mainly due to (Ge2O7)
6−-groups distortion and
Pb2+ ions displacements. Investigations of Raman [5, 6] and submillimetre spec-
tra [7] reveal the softening of a low-frequency optic phonon and give evidence in
c© M.P.Trubitsyn, M.D.Volnianskii, A.S.Ermakov, V.G.Linnik 677
M.P.Trubitsyn et al.
favour of a displacive character of ferroelectric phase transition in PGO crystals. On
approaching the transition point from ferrophase above ∼400 K, the soft phonon
becomes overdamped, critical dynamics slow down and gain pronounced relaxation
features peculiar to an order-disorder scheme of a structural phase transition. In
addition to the overdamped soft mode, the central peak emerges in the excitation
spectrum of lead germanate. Very refined light scattering experiment, performed in
[6], makes it possible to resolve the line shape of the central peak and observe a
weakly diverging, relatively broad (∼4 GHz) dynamic central component coexisting
with a very narrow (6 2 MHz) quasi-elastic central singularity. Although the mi-
croscopic reasons of the observed critical dynamics are not completely clear up to
now, it has been assumed that the soft phonon reflects the oscillator type motion
of Pb2+ ions whereas relaxation of (GeO4)
4− tetrahedra contributes to a dynamic
central peak. The quasi-elastic central component is presumably originated from the
frozen-in symmetry-breaking defects [6].
It is well known that magnetic resonance represents highly sensitive experimen-
tal techniques giving a unique information regarding static and dynamic phenomena
accompanying structural phase transitions [8, 9]. ESR spectra of Gd3+ ions in lead
germanate have been reported earlier [10–13]. It has been shown that Gd3+ ions pre-
dominantly occupy positions of trigonal point symmetry and substitute Pb 2+ hosts
in PGO lattice. Among the fifteen lead ions in the PGO unit cell, six structurally
nonequivalent ions are positioned on the third order axis [4]. Theoretical analysis of
the Gd3+ spectra, performed in [14] based on the point-charge approximation and
superposition model, allows us to assume that gadoliniummost probably substitutes
Pb(4) ions in accordance with the earlier conclusions [10]. Since the paramagnetic
probe preserves the local symmetry of the host, it may be suggested that the excess
charge introduced by the probe is compensated non-locally.
The attention in the papers [10–13] was focused mainly on the details of Gd3+
centers localization and possible mechanisms of the paramagnetic probe charge com-
pensation. It seems that additional valuable information can be derived by applying
the ESR techniques to the study of static and dynamic properties of PGO in the
range of ferroelectric phase transition.
2. Theoretical background
ESR spectra in the range of structural phase transition can be described by usual
spin- Hamiltonian (SH) formalism based on the perturbation theory
HFP = HPP +H ′. (1)
Here HPP represents hexagonal SH appropriate to C3h local symmetry of the probe
in paraelectric phase; H ′-“perturbing” SH which contains trigonal spin operators
and describes lowering of the Gd3+ local symmetry at the phase transition [15]
H ′ = b34O
3
4 + c34Ω
3
4. (2)
678
Ferroelectric phase transition in lead germanate
Parameters of “perturbing” SH H ′ are the functions of the correlated atomic dis-
tortions in the range of paramagnetic probe. Consequently near TC the resonance
fields can be expanded in powers of the time dependent local order parameter
η(t) = 〈η〉+ δη(t)
BR(t) = B0 + aη +
1
2
bη2 + ...
= B0 + a〈η〉+
1
2
b〈η2〉+
[
aδη +
1
2
b(η2 − 〈η2〉)
]
. (3)
Here B0 represents the line position above TC. Expansion coefficients a, b are deter-
mined by secular and non-secular matrix elements of SH H ′ correspondingly. Hence
parameters a, b depend on the probe site and magnetic field direction with respect
to the crystallographic axes. It can be shown that if the local symmetry, accounting
for the external magnetic field effect, contains elements destroyed at the phase tran-
sition, all odd terms in expansion (3) should vanish. As it has been shown in [10,
11], on cooling below TC the local symmetry of Gd3+ probe reduces from hexagonal
C3h to trigonal C3 point group, i.e. the mirror plane perpendicular to polar axis van-
ishes in ferroelectric phase. It means, that applying external magnetic field B along
or perpendicular to c-axis, one can provide quadratic coupling of resonance fields
with the local order parameter (a=0). For general orientation of B, the linear term
in expansion (3) becomes non-zero and both terms - linear and quadratic should
contribute to resonance fields.
3. Experimental results and discussion
300 400 500
400
450 3
2
1
TC
B
R
(m
T
)
T (K)
Figure 1. Temperature depen-
dencies of line positions MS =
−5/2β − 7/2 (1), −1/2β − 3/2
(2), −3/2β − 5/2 (3). B ‖ c.
PGO monocrystals were grown from the
melts by Czhokhralskii method with addition of
Gd2O3 (0.01 wt. percent). The samples studied
were cut off as parallelepipeds of 3x3x3 mm3 typ-
ical dimensions with edges parallel to crystal-
lographic axes. ESR spectra were registered by
conventional X-band spectrometer. The temper-
ature of the samples was regulated by nitrogen
gas flow cryostat.
ESR spectrum of Gd3+ in ground state
(4f 7,8 S7/2), consisting of seven fine structure
components ∆MS = ±1, was registered. In para-
electric phase the angular variations of spectra
reveal C3h local symmetry of active probe site
with a third order axis parallel to a unique polar
axis c. On cooling below TC for general orien-
tations of external magnetic field B the outer
fine structure lines MS = ±1/2β±3/2;±3/2β±
5/2;±5/2β ± 7/2 split into doublets in accor-
dance with the reducing of the local symmetry
679
M.P.Trubitsyn et al.
to C3 group [16] and the emerging of 1800 domains with antiparallel direction of
spontaneous polarization. The symmetry of ESR spectra and SH parameters un-
doubtedly show that Gd3+ centers studied in this work have got the same nature as
the ones investigated earlier in [10, 11].
300 400 500
380
400
TC-T (K)
∆B
R
2 (m
T
2 )
T (K)
B
R
(m
T
)
0 100
0
100
Figure 2. Line position of MS =
−5/2β7/2 at ∠B, c = 44
0,B⊥b
in the range of TC=451 K. In
the insert: line splitting squared
∆B2 vs (TC − T ).
Temperature dependencies of positionsBR(T )
of three high field ESR lines MS = −1/2β −
3/2;−3/2β−5/2;−5/2β−7/2, measured at ori-
entation B ‖ c, are plotted in figure 1. It can
be seen that in the paraelectric phase, reso-
nance lines linearly shift to high field side due
to the lattice contraction effect. Below TC, line
positions change their behaviour. Experimental
points deviate from dashed lines extrapolating to
ferroelectric phase the thermal drift of line po-
sition B0 above TC. In accordance with simple
theoretical description briefly given above, the
static part of expansion (3) determines the shift
of the line position induced by the local order
parameter. For main orientation B ‖ c the lin-
ear term in (3) is forbidden by symmetry. So,
the experimental data, represented in figure 1,
can be described by
BR = B0 +
1
2
b〈η〉2, (4)
with accounting of the B0 thermal drift above TC
and ignoring negligible fluctuation contributions,
i.e. assuming 〈η2〉 = 〈η〉2. It is clear, that devi-
ation of experimental points from dashed lines
(figure 1) results from the contribution of the local order parameter squared with
negative parameter b < 0 (4). From figure 1 it can be seen that experimental de-
pendencies can be satisfactorily described by the straight lines [B0(T )− BR(T )] ∼
〈η〉2 ∼ (TC − T ) in accordance with the mean field theory approach.
Naturally the line position should be more sensitive to a local order parameter
magnitude for general orientations of the external magnetic field, allowing non-zero
linear term in expansion (3). The experimental dependency of MS = −5/2β − 7/2
line position at ∠B, c = 44
0,B⊥b is presented in figure 2. Single ESR line slightly
shifts to high fields and below TC splits into two components, resulting from nonzero
value of the local order parameter ±〈η〉. In accordance with (3), positions of the
splitted components are given by
BR1,R2 = B0 ± a〈η〉+
1
2
b〈η〉2. (5)
From this expression it follows that the distance between components of
doublet is proportional to the first order of local order parameter
680
Ferroelectric phase transition in lead germanate
300 400 500
1
2
TC
δB
(
m
T
)
T (K)
2
1
Figure 3. Temperature depen-
dencies of line width MS =
−3/2β − 5/2 (1), −5/2β − 7/2
(2). B ‖ c.
300 400 500
2
4
T (K)
δB
(m
T
)
Figure 4. Anomalous line width
broadening. MS = −5/2β− 7/2,
∠B, c = 44
0,B⊥b.
∆B = BR1 − BR2 = 2a〈η〉.
In the vicinity of transition point 448÷451 K the
line splitting is masked by anomalous line width
broadening and line position determination de-
mands a more refine analysis of the spectral con-
tour. Excluding this temperature interval, least
square fitting of equation (5) to experimental da-
ta gives the value of transition point of 450.5 K.
Fitting the line splitting ∆B vs (TC − T ) in a
double logarithmic scale gives for TC the value
of 451.4 K. Hence TC=451 K can be accepted as
experimentally measured transition point with
± 0.5 K uncertainty. Squared line splitting ∆B 2
vs (TC−T ) is plotted in the insert to figure 2. It
is quite clear that experimental points well cor-
respond to the straight line up to (TC−T ) ∼ 150
K, confirming the classic behaviour of the local
order parameter 〈η〉 ∼ (TC − T )1/2.
Besides the line positions, width of ESR lines
demonstrates pronounced anomaly in the range
of TC. Temperature dependencies of peak to peak
line width for MS = −3/2β − 5/2;−5/2β − 7/2
at B ‖ c are presented in figure 3. Weak but
distinctly visible anomalies of line width can be
seen around TC. These anomalies result from the
local order parameter fluctuations and can be
described by the time dependent part of reso-
nance fields expansion (3). Since for the main
orientation B ‖ c, linear term in (3) is forbid-
den by symmetry, detected anomalies can be at-
tributed to the quadratic term originated from
two-phonon relaxation processes. Weakness of
line width increasing for B ‖ c does not make it
possible to analyze the anomalies quantitatively.
Temperature dependence of MS = −5/2β −
7/2 line width, measured at general orientation (∠B, c = 44
0,B⊥b), is depicted in
the figure 4. A well pronounced λ- shaped anomaly has been observed around TC.
Line width δB increases from ∼ 2.0 mT at 523 K to ∼ 3.8 mT closely to transition
point. Anomalous line width broadening is accompanied by changes of line shape
and results exceptionally from increasing of the gaussian component [17]. It can be
seen that in ferroelectric phase both splitted components have got different widths
on cooling away from TC. As it has been shown above for general orientation chosen,
coupling between resonance fields and local order parameter (3) is dominated by a
681
M.P.Trubitsyn et al.
linear term. Critical contribution to the line width can be expressed through the
resonance line second moment
δB2
CR = 4(〈B2
R〉 − 〈BR〉
2) ∼ (a± b〈η〉)2
∑
q
〈δη2q〉. (6)
Since ESR measures the local properties of the probe, the sum in (6) gets over
fluctuations with all wave vectors within Brillouin zone. Hence, pronounced line
width broadening reflects the critical divergence of the order parameter susceptibil-
ity, connected with mean square fluctuations by fluctuation-dissipation theorem. As
it can be seen from the factor (a ± b〈η〉)2 before the sum in (6), different widths
of two splitted components below TC may arise from the second order term contri-
bution. Inhomogeneous gaussian character of line width broadening gives evidence
that order parameter fluctuations, contributing to line width anomalies, are slow in
comparison with the frequency analogue of the background non-critical ESR line
width ∼ 30 MHz.
4. Conclusions
Lead germanate undergoes ferroelectric phase transition with the emerging of
spontaneous polarization along the unique trigonal axis. Hence it belongs to the
universality class of the systems with one-component polar order parameter where
long-range dipole-dipole interactions predetermine applicability of mean field theory
around transition point [18]. In agreement with this assertion, ESR line position data
of Gd3+ probe demonstrate classic behaviour of the local order parameter in a broad
temperature interval of ferroelectric phase.
Anomalous line width broadening, observed for general orientations of exter-
nal magnetic field around TC, is determined by increasing of inhomogeneous gaus-
sian component. It may be concluded, that critical line width is contributed by
quasi-static order parameter fluctuations with frequencies less than ∼ 30 MHz. De-
tailed measurements of the Gd3+ line width anisotropy, performed recently in [19],
have shown that the main contribution to line width involve triclinic spin operators
(b12O
1
2+c12Ω
1
2) by contrast to trigonal symmetry of the “perturbing” SH H ′ (2), which
determines line splitting in ferroelectric phase. Authors of [19] have assumed that
triclinic anisotropy of the critical line width results from the non-local charge com-
pensators statistically positioned relative to the paramagnetic ion location. Perhaps
that anisotropy of line width is not necessarily to connect with non-local charge
compensators but it is quite sufficient to consider a possible influence of symmetry-
breaking defects of any sort. It seems that the observed features of ESR line width
broadening may be associated with a very narrow elastic central peak component,
detected in light scattering experiment [6] and presumably originated from frozen-in
symmetry-breaking defects. Obviously the range of influence of such defects becomes
infinitely large as the correlation length diverges on approaching TC and anisotropy
of ESR critical line width could be reduced.
682
Ferroelectric phase transition in lead germanate
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Дослiдження методом ЕПР сегнетоелектричного
фазового переходу у кристалах германату свинцю
Pb5Ge3O11:Gd3+
М.П.Трубiцин, М.Д.Волнянський, А.С.Ермаков, В.Г.Лiннiк
Днiпропетровський державний унiверситет, фiзичний факультет
320625 Днiпропетровськ, пров. Науковий, 13
Отримано 23 листопада 1998 р.
ЕПР спектри iонiв Gd3+ вивчалися в iнтервалi сегнетоелектричного
фазового переходуTc=451 К кристалiв германату свинцю Pb5Ge3O11.
На пiдставi вимiрювання температурних залежностей положення
ЕПР лiнiй показано, що поведiнка локального параметра порядку в
досить широкому iнтервалi (∼ 150 К) сегнетоелектричної фази по-
годжується з теорiєю середнього молекулярного поля. Аномальне
розширення резонансних лiнiй, що спостерiгається навколоTc, може
бути зiставлене з вузьким квазi-пружним центральним пiком у спек-
трах комбiнацiйного розсiяння свiтла i пов’язане зi статичними де-
фектами кристалічної гратки.
Ключові слова: сегнетоелектричний фазовий перехiд,
електронний парамагнiтний резонанс
PACS: 77.80.B
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