Dynamics of nanoscale polar regions and critical behavior of the uniaxial relaxor
Sr
0.61
Ba
0.39
Nb
2
O
6
:Co
J. Banys,
1
J. Macutkevic,
1
R. Grigalaitis,
1
and W. Kleemann
2,
*
1
Faculty of Physics, Vilnius University, Sauletekio 9, 10222 Vilnius, Lithuania
2
Angewandte Physik, Universität Duisburg-Essen, D-47048 Duisburg, Germany
Received 23 January 2005; published 12 July 2005
The complex dielectric susceptibility of Sr
0.61
Ba
0.39
Nb
2
O
6
: Co has been measured at frequencies 10
1
f
10
9
Hz and temperatures 300 T 400 K before and after poling. The high-frequency relaxation peak
observed above the ferroelectric phase transition temperature, T
c
348 K, is analyzed in terms of distribution
functions of the relaxation time, g, using Tikhonov regularization. It reveals the criticality of the largest
relaxation time in agreement with activated dynamic scaling of the three-dimensional random-field Ising
model. Differences of zero-field- and field-cooled g are discussed.
DOI: 10.1103/PhysRevB.72.024106 PACS numbers: 77.22.Ch, 64.70.Pf, 77.80.-e, 77.84.Dy
I. INTRODUCTION
Solving the relaxor enigma is still one of the most chal-
lenging problems in the physics of ferroelectrics. Ever since
the discovery of the archetypical relaxor material
PbMg
1/3
Nb
2/3
O
3
PMN,
1
the origin of its key features—i
huge frequency dispersion of the dielectric susceptibility in
the Curie range above the transition temperature T
c
, ii non-
ergodic behavior at low temperatures T T
c
, and iii virtu-
ally no symmetry breaking after zero-field cooling ZFC to
below T
c
—has been discussed controversially. Very probably
and in accordance with long-standing propositions of Cross
and co-workers
2,3
the appearance of fluctuating polar precur-
sor clusters polar nanoregions at temperatures T T
c
has to
be considered as the primary signature of relaxor behavior.
4
Indeed, it appears plausible that polar nanoregions with a
wide size distribution are at the heart of the observed giant
polydispersivity,
5
which is observed in quite different sys-
tems like disordered solid solutions like PMN Ref. 1 or
PLZT Ref. 2, or doped quantum paraelectrics like
SrTiO
3
:Bi Ref. 6.
Hence, finding out the microscopic origin of the polar
precursor clusters is the key to understanding relaxor prop-
erties. Very probably, different mechanisms with different
degrees of complexity have to be envisaged. They may range
from purely statistical aggregation of polar centers in the
sense of percolation theory probably realized in the case of
doped quantum paraelectrics like SrTiO
3
:Ca Refs. 7 and 8
to the appearance of weak “exponentially rare” singulari-
ties within a dilution-induced Griffiths phase
9
possibly real-
ized in the case of solid solutions like PLZT, which reveal
anomalies of the refractive index below the phase transition
temperature T
c
of the parent PZT phase irrespective of the
amount of La doping.
10
. Apart from such very special
mechanisms, however, the random-field RF mechanism
11
is
supposed to be a widely applicable concept. Since spatial
fluctuations of the RF’s give rise to correlations between the
fluctuating dipole moments, the formation of precursor clus-
ters of mesoscopic size is expected in systems with charge
disorder.
12–14
Starting from the existence of polar nanoregions and as-
suming random interactions between them, a spherical
random-bond random-field SRBRF theory
15
has success-
fully been introduced to describe the phase transition into a
disordered low-T cluster glass phase. By assuming fully frus-
trated superspin interactions and dominance of these random
bonds RB’s over the RF’s, it models the glassy freezing of
mesoscopic nanoregions in cubic relaxors like PMN Ref.
15 and PLZT Ref. 16. Indeed, quite weak RF’s are gener-
ally expected to act on the polar clusters, since only the
fluctuations of the microscopic RF’s are effective on a nano-
scale. While cubic relaxors with nearly continuous order pa-
rameter have no chance to experience ferroelectric long-
range order,
11
this must not be the case for random-field sys-
tems with a discrete order parameter. This is the reason why
the well-known family of uniaxial relaxor crystals related to
strontium-barium niobate, Sr
x
Ba
1-x
Nb
2
O
6
SBN,
17
is con-
sidered as a prototypical three-dimensional 3D random-
field Ising-model RFIM system since recently.
18
In contrast to the cubic perovskite family related to
PMN,
1
the polarization of the SBN family is a single-
component vector directed along the tetragonal c direction,
which drives the point group from 4 / mmm to 4mm at the
phase transition into the low-T polar phase. Only at low tem-
peratures is a slight tilt of the polarization out of the 001
direction observed, giving rise to a monoclinic structure
monoclinic point group m below T
0
70 K.
19
At T T
0
,
however, SBN is tetragonal on the average and thus belongs
to an Ising model universality class rather than to a Heisen-
berg one as suggested for the PMN family.
12
Assuming the
presence of quenched RF’s, theory in this case predicts the
existence of a phase transition into long-range order LRO
within the RFIM universality class
11
preceded by a giant
critical slowing-down above T
c
. Hence, when approaching
the ferroelectric state, the polar nanoregions, which are cor-
related by RF’s in the paraelectric phase, should exhibit ac-
tivated dynamics.
20
Below T
c
the polar nanoregions are expected to transform
into polar LRO, provided that cooling is performed at a suf-
ficiently low rate.
12
Recent studies of SBN and SBN:Ce
have, indeed, evidenced that i the dielectric susceptibility
probes clusters above and domains below T
c
, respectively,
21
while ii the linear birefringence is a measure of polar pre-
PHYSICAL REVIEW B 72, 024106 2005
1098-0121/2005/722/0241066/$23.00 ©2005 The American Physical Society 024106-1