Phase transitions in the ferroelectric crystals †CH
3
NH
3
‡
5
Bi
2
Cl
11
and †CH
3
NH
3
‡
5
Bi
2
Br
11
studied by the nonlinear dielectric effect
P. Szklarz,
1
M. Galązka,
2
P. Zieliński,
2,3
and G. Bator
1,
*
1
Faculty of Chemistry, University of Wroclaw, Joliot-Curie 14, 50-383 Wroclaw, Poland
2
The H. Niewodniczański Institute of Nuclear Physics PAS, Radzikowskiego 152, PL-31-342 Kraków, Poland
3
Cracow University of Technology, Institute of Physics, ul. Podchorążych 1, 30-084 Kraków, Poland
Received 23 February 2006; revised manuscript received 19 July 2006; published 13 November 2006
The real part of the complex electric permittivity at low frequencies and at several biasing fields between 0
and 5 10
5
V/m has been measured in ferroelectric crystals CH
3
NH
3
5
Bi
2
Cl
11
MAPCB and
CH
3
NH
3
5
Bi
2
Br
11
MAPBB in the temperature range covering the temperature of the ferroelectric phase
transitions. Comparative measurements for the known triglycine sulphate NH
2
CH
2
COOH
3
H
2
SO
4
crystal
have been used as a test of the validity and of possible errors in the determination of the ferroelectric equation
of state by the method applied. The estimates of the critical parameters T
C
, , and then have been evaluated
for MAPCB and MAPBB on the basis of the Widom-Griffiths scaling hypothesis. Complementary pyroelectric
measurements of the spontaneous polarization providing the critical exponent are in accordance with the
parameters obtained.
DOI: 10.1103/PhysRevB.74.184111 PACS numbers: 77.22.-d, 75.40.Gb, 72.20.Ht
I. INTRODUCTION
Measurement of the electric susceptibility in a biasing
constant field is sometimes called nonlinear dielectric effect
NDE.
1,2
It is a convenient method of studying ferroelectric
phase transitions, especially those of second order. The ap-
plication of the biasing electric field then allows one to scan
the region of the critical point in a two-dimensional
temperature-field space. Generally, the temperature depen-
dence of the electric susceptibility measured in this way has
the form of an asymmetric bell-like curve with a maximum
which shifts towards higher temperatures with increasing bi-
asing field. Far below and far above the phase transition
region the curves tend to constant values corresponding to
the low- and high-temperature limit susceptibilities, respec-
tively. Consequently, such curves are concave—i.e., have
negative second derivative close to the maximum—and
convex—i.e., have positive second derivative in the low- and
high-temperature limits. Thus, there are at least two points of
vanishing second derivative on every such curve, one below
or to the left to and one above or to the right to the
maximum. The points are called inflection points. It has been
shown by the present authors
3,4
that for materials obeying the
scaling-invariant equation of state there are in fact from one
to three inflection points below the maximum depending on
the values of the critical exponents and . In particular
there is always an inflection point exactly at the critical tem-
perature for the classical mean-field exponents =1 and
=
1
2
.
What precedes the susceptibility is meant to be the static
one. In practice, however, only ac data are available in most
cases. Then, the low-frequency limit—i.e., that far below the
normal dielectric absorption peak—of the real part of the
complex electric susceptibility can be taken into account.
Rigorously it is impossible to come too closely to the critical
point because the dielectric absorption peak moves towards
zero frequency when the critical point is approached. The
effect is known as critical slowing down, which corresponds
to the relaxation time going to infinity. As a consequence,
any experimental frequency becomes too large to be consid-
ered as the static limit. Moreover, the thermal conductivity
tends to zero at the critical point so that the time needed to
attain the thermal equilibrium after supplying a portion of
heat to the system becomes infinite. Therefore, any experi-
mental rate of changes of temperature is too rapid close
enough to the critical point. No physical quantity measured
in such conditions then corresponds to the thermal equilib-
rium. Related to the zero of thermal conductivity is also the
phenomenon of passing from isothermal to adiabatic
susceptibility.
5
The use of a biasing field, which drives the system out of
the critical point, allows one to evade all the described ef-
fects of the critical slowing down. Staying at a distance from
the critical point in the temperature-field plane makes the
dielectric absorption peak always lie at a finite frequency.
Then, the low-frequency limit of the real susceptibility is, at
least in principle, always possible to attain. The present pa-
per deals with such a low-frequency electric susceptibility.
We use the frequency independence of the real part of the
susceptibility as a test of staying at the low-frequency limit
because this corresponds to the practically vertical part of the
Cole-Cole plot.
6
As described in Sec. III and in Refs. 7–13
the analysis of the data obtained in the NDE allows one to
determine, through so-called scaling invariants, all the pa-
rameters of the equation of state compatible with the scaling
hypothesis. Such an analysis has been done for the known
ferroelectrics TGS, TGSe, GPI, and DMAGaS.
7,8,11
In the present work the scaling equations of state are
established for the CH
3
NH
3
5
Bi
2
Cl
11
MAPCB and
CH
3
NH
3
5
Bi
2
Br
11
MAPBB crystals. These are relatively
new materials belonging to the familiy of halogenoanti-
monates III and halogenobismuthates IIIRef. 14 or imi-
dazolium tetrafluoroborate Ref. 15. Particularly interesting
are the recently synthesised methylammonium salts MAPCB
Ref. 16 and MAPBB Ref. 17. Both of them show qua-
sirigid anionic sublattices and orientationally disordered cat-
PHYSICAL REVIEW B 74, 184111 2006
1098-0121/2006/7418/1841117 ©2006 The American Physical Society 184111-1