Phase instability induced by polar nanoregions in a
relaxor ferroelectric system
, Jinsheng Wen1,2, C. Stock3,4, P. M. Gehring4
1Condensed Matter Physics and Materials Science Department, Brookhaven National
Laboratory, Upton, New York 11973
2Department of Materials Science, State University of New York, Stony Brook, New York
3Department of Physics and Astronomy, The Johns Hopkins University, Baltimore,
4 NIST Center for Neutron Research, National Institute of Standards and Technology,
Gaithersburg, Maryland 20899-6100
Local inhomogeneities known as polar nanoregions (PNR) play a key role in
governing the dielectric properties of relaxor ferroelectrics – a special class of
material that exhibits an enormous electromechanical response and is easily
polarized with an external field. Using neutron inelastic scattering methods, we
show that the PNR can also significantly affect the structural properties of the
relaxor ferroelectric Pb(Zn1/3Nb2/3)O3-4.5%PbTiO3 (PZN-4.5%PT). A strong
interaction is found between the PNR and the propagation of sound waves, i.e.
acoustic phonons, the visibility of which can be enhanced with an external electric
field. A comparison between acoustic phonons propagating along different
directions reveals a large asymmetry in the lattice dynamics that is induced by the
PNR. We suggest that a phase instability induced by this PNR-phonon interaction
may contribute to the ultrahigh piezoelectric response of this and related relaxor
ferroelectric materials. Our results also naturally explain the emergence of the
various observed monoclinic phases in these systems.
Understanding the effects of local inhomogeneities on the properties of materials has
always presented a great challenge to condensed matter physicists and materials scientists.
The effort to elucidate the role played by local, polar clusters known as polar nanoregions
(PNR) that are observed in relaxor ferroelectrics is a prime example of such a challenge.
Relaxor ferroelectrics (henceforth "relaxors") belong to a special class of disordered
materials that, because of their extraordinary piezoelectric and dielectric properties1,2,3,
show enormous potential for industrial applications such as next generation sensors,
actuators, and transducers that convert between mechanical and electrical forms of energy.
The inhomogeneities in these materials arise from chemical and valence mixing, and the
resulting local polar structures can significantly affect macroscopic properties. For
example, one of the defining features of relaxors – the broad and highly frequency
dependent dielectric permittivity peak – is directly associated with the relaxation process
of the PNR4, which appear a few hundred degrees above the Curie temperature TC5. With
cooling the PNR are believed to become larger in volume and/or more ordered in polarity.
There have been extensive studies of the interplay between the PNR and long-range polar
order in relaxor systems6,7,8. On the other hand, the relationship between the PNR and the
electromechanical and other structural properties of relaxor systems remains unclear.
The structures of the PNR have been well characterized in many lead based,
perovskite relaxor systems9,10,11,12,13,14 and in particular in the prototypical relaxors
Pb(Zn1/3Nb2/3)O3 (PZN), Pb(Mg1/3Nb2/3)O3 (PMN), and their solid solutions with the
conventional ferroelectric PbTiO3 (PT). The local structure of PNR is usually different
from the average lattice structure of the compound in which they reside. For example,
whereas the PNR in PMN-xPT and PZN-xPT (for small x) exhibit orthorhombic <110>
polarizations14, the average macroscopic structure of these compounds is actually
rhombohedral (R). In this article, we establish a link between these different structures by
studying the influence of the PNR on the lattice dynamics in a relaxor system. In general,
atoms in solids can move about their equilibrium positions and, through their motion,
propagate energy in the form of sound waves, or acoustic phonons. We find that the
dynamics of relaxors is significantly influenced by these local inhomogeneities.
Specifically, we have discovered a strong coupling between the PNR and transverse
acoustic (TA) phonons polarized along <110>. The PNR can scatter TA phonons
having a parallel polarization; such phonons thus propagate more slowly and have shorter
lifetimes. In other words, although the lattice of the bulk still remains virtually cubic
(having only a slight rhombohedral distortion), the material itself can appear “softer”
along a particular <110> direction due to the effects of the PNR. Our work therefore
provides a scenario wherein the interaction of the PNR and the bulk lattice introduces an
underlying structural instability, which could provide the microscopic origin of the large
piezoelectric properties of relaxor systems.
The system we have studied is Pb(Zn1/3Nb2/3)O3-4.5%PbTiO3 (PZN-4.5%PT), which
lies on the left (rhombohedral) side of the morphotropic phase boundary (MPB) in the
region of the PZN-xPT phase diagram where the ultra-high piezoelectric response is
observed; indeed, the piezoelectric coefficient d33 of this crystal is one of the highest
known. While a monoclinic phase can be induced in PZN-4.5%PT by applying an
electric field along the  direction15, under zero field it still exhibits a cubic (C)
high-temperature phase and a rhombohedral (R) low-temperature phase, with a Curie
temperature TC ~ 475 K. Neutron inelastic scattering measurements were performed in
the neighborhood of the (220) and
)202( Bragg peaks (expressed using pseudocubic
notation) using the constant-Q method, i.e. by scanning the neutron energy transfer ћω
while sitting at a fixed wavevector transfer Q located a distance q in reciprocal space
from a given Bragg peak G (Q = G + q). It is important to note that both the PNR and
phonon neutron scattering cross sections involve the atomic displacements, whether static
or dynamic; therefore both cross sections are subject to the factor
, where ε ε is the
unit vector along the polarization (atomic displacement) direction. Consequently, near the
) Bragg peak neutron scattering probes only those PNR with  (
polarizations as well as  (
]101 [) polarized phonons propagating along q. This
situation is shown schematically in Fig. 1A, where q is chosen transverse to the Bragg
peak G such that we measure TA phonons propagating along  and ] 01 1 [ near
) 202( and (220), respectively.
When PZN-4.5%PT is zero-field cooled (ZFC), the diffuse scattering from PNR
forms ellipsoids13, 14 of equivalent shape and intensity centered on the (220) and )202(
Bragg peaks. In order to identify the interaction between the PNR and phonons explicitly,
an ability to tune the diffuse scattering intensities independently and watch for changes in
the phonon spectra is required. Fortunately, this can be achieved by cooling the single
crystal sample under a moderate external electric field E = 2 kV/cm applied along .
When this is done, PNR with different polarizations are reoriented, which leads to a
redistribution of the diffuse scattering in reciprocal space16 as shown in Fig. 1A. A linear
scan of the scattering intensity measured along [H, 2.1, 0] after field cooling to 200 K
(Fig. 1B) includes contributions from PNR having both  and
and illustrates this redistribution. In other words, diffuse scattering intensities from PNR
having  polarizations (shown in blue in Fig. 1 A and B) weaken while those from
] 101 [ polarizations (shown in red in Fig. 1 A and B) strengthen when the
system is field-cooled (FC) under a field applied along . Remarkably, we find that
the TA phonons polarized along  and
] 101 [
are significantly modified at the same
time. Figs. 1 C and D show contour maps of the phonon intensities measured near the
)202( Bragg peaks after field cooling to T=200 K. Near (220), the
lower-energy acoustic mode (i.e. the TA2 mode polarized along ) is sharp and
well-defined in energy, whereas the identical TA2 mode (but polarized along
] 101 [)
is comparatively very soft and broad. By contrast, the transverse optic
(TO2) modes are essentially unaffected by the diffuse scattering as they do not differ
noticeably between the two Bragg peaks.
Constant-Q scans are shown in Fig. 2 to provide a comparison between FC and ZFC
results at different temperatures. After cooling below TC, a difference becomes noticeable
between the ZFC (black solid lines) and FC spectra measured near (220) (blue lines) and
)202( (red lines). At 400 K, the data in Fig. 2 B and E show that where the diffuse
scattering is strong (near
)202(), the corresponding TA2 phonon is soft and broad in
energy; conversely, where the diffuse scattering is weak (near (220)), the TA2 mode is
hard and well-defined. These results unambiguously demonstrate the presence of a strong
coupling between the diffuse scattering (PNR) and the TA2 phonons in PZN-4%PT,
evidence of which has also observed in the relaxor PMN17. If the PNR grow upon
cooling, then this effect should become more pronounced at lower temperatures; the data
in Figs. 2 C and F, measured at 200 K, clearly show this to be the case.
It is important to note that if we average the two FC phonon spectra measured below
TC near (220) and
(represented by the black lines in Fig. 2), the result agrees
almost exactly with the ZFC spectra. Since our ZFC measurements were all performed by
heating the sample well above TC and then cooling in zero field, any residue electric field
effect or field-induced piezoelectric strain should have been completely removed. This
shows that cooling under this moderate field merely rearranges the multiple
<111>-polarized ferroelectric domains such that the system adopts a single domain state
with polarization along the  field direction; any other effect of the field on the
phonons or PNR is negligible. In other words, the electric field does not soften or
broaden the TA phonon modes, and the PNR-phonon coupling effect is intrinsic. If this
were not true, then the average of the FC spectra would not match the ZFC spectra. In
the ZFC state the effects of the PNR on the phonon modes are still present (for T < TC);
however because the ZFC data represent an average over different domains, the
measurements made near (220) and
) 202( cannot be distinguished.
The half widths at half maximum (HWHM) in energy of the TA2 phonons measured
at 200 K are shown in Fig. 3 C. The broad widths of the
] 101 [ polarized TA2 phonons
indicate a short-lived mode. While cooling in a field oriented along  stabilizes a
single domain R phase, many PNR having
] 101 [
polarizations are present16; these PNR
appear to interact strongly with
]101 [ polarized TA2 phonons, thereby reducing the
phonon lifetime. However, because there are far fewer PNR having  polarizations,
the  polarized TA2 phonons are relatively unaffected (see Fig. 3 A and C).
The data in Fig. 3 A show that the TO2 mode is overdamped at small q at 600 K, in
agreement with previous measurements on similar systems18,19,20; this q-dependent
damping produces the dynamical feature known as the “waterfall”. Upon cooling to 200
K, the optic modes harden and sharpen in energy (see Fig. 3 A and B), and are unaffected
by the diffuse scattering changes below TC as can be seen by comparing the TO2 modes
near the two Bragg peaks. This behaviour differs from the strong TA-TO coupling
effects previously observed in similar systems at temperatures above TC20,21. For T < TC
the lack of any significant change in the TO modes compared to the large change in TA
mode energies (between the two Bragg peaks) proves that any coupling between the TA
and TO modes with <110> polarizations is extremely weak.
Phonons describe collective modes of atomic motions; acoustic phonons are directly
associated with strains in the crystal lattice. A very soft and overdamped acoustic phonon
mode is usually indicative of a phase instability and a tendency toward a structural
transition. After the phase transition takes place and the system becomes stable, the
phonon mode recovers and becomes well-defined again. For instance, the softening of
acoustic modes is common in other ferroelectric systems where the TA-TO coupling is
strong, and the soft TA mode recovers after the structural phase transition takes place22.
However, in PZN-4.5%PT the structure remains rhombohedral for T < TC. While no
phase transition associated with this
] 10 1 [-TA2 phonon anomaly ever occurs, the
phonon mode remains anomalously soft and broad, and the system remains (structurally)
unstable at low temperature. In other words, the anomaly in this
]10 1 [-TA2 mode is
indicative of a phase instability in the low temperature R-phase of PZN-4.5%PT.
Despite the large orthorhombic-type asymmetry between the TA2 phonon modes
polarized along  and
]10 1 [
, the static strain, or the deviation from a cubic structure,
along these two orthorhombic directions in PZN-4.5%PT is rather small. The average
structure of PZN-4.5%PT at low temperature is rhombohedral with a relatively small
distortion with or without a moderate electric field applied along . In our case, the
%2 . 0/
along the  direction (determined from the size of the
splitting between Bragg peaks - see also ref. 23); this is clearly not consistent with the
large (>70%) difference in phonon energies between the two TA2 modes polarized along
] 10 1 [, especially when compared with values observed in other
relaxor/ferroelectric systems having similar structures. For example, in PMN-60%PT24 at
400 K in the tetragonal phase, one has a much larger strain
%7 . 1~/dd
while the splitting of the TA1 mode is less than 30% (estimated from the ZFC TA1
phonon broadening). Another example is the classic ferroelectric PbTiO3, for which the
tetragonal strain is about 6% at 200 K, whereas the TA1 phonons along the a and c
directions only differ by ~20% in energy25. Note that these two systems have relatively
large static strains, are both ferroelectric, and show no evidence of PNR. Intriguingly,
similar to what we observe in PZN-4.5%PT, phonon studies on another relaxor system
where PNR are present, K0.965Li0.035TaO3 (KLT x=0.035)26, report a large splitting
(Δω~25% at T=4.8 K) of the TA1 phonon modes polarized along the a and c directions
as well, while the static tetragonal strain in that system is small (~0.2%). These examples
suggest that in ferroelectric perovskites, the situation where a small static strain is
accompanied by a large asymmetry in the lattice dynamics is unique to relaxors where
PNR are present. Once the external field and small static lattice strain have been excluded
as origins of the anomalous asymmetry between TA modes measured at ) 202( and (220),
an interaction between the TA modes and the PNR becomes the only viable explanation.
For materials to be considered “good” piezoelectrics it is not enough to exhibit a
large static strain (e.g. PbTiO3 is not considered a good piezoelectric despite its large
tetragonal strain); instead a material must have a large derivative of strain with respect to
external electric field, i.e. the lattice/strain must be able to change significantly under
field. Various previous theoretical, computational, and experimental work27,28,29,30,31 has
suggested a link between the phase instability in these compounds and the enhanced
piezoelectric responses. In fact, acoustic phonons are directly related to the elastic
constants in solids, and a soft TA mode is consistent with a system that is easier to distort
(along a certain direction). Our results provide strong evidence that in relaxors such a
phase instability does exist and is indeed induced by the PNR and manifested as an
asymmetry in the lattice dynamics. Note that this instability is intrinsic and not dependent
on the external field (along ); the  field only rearranges large ferroelectric
domains for the effect to be observed macroscopically as discussed previously. In the
case of an external field oriented along  or , where the field direction does not
align with the natural rhombohedral () domain polarization, the intrinsic instability
apparently helps to facilitate the field-induced structural change and contributes to the
large piezoelectric response32. Nevertheless, how or if the PNR react to the field is not yet
entirely clear; only very limited studies exist so far, e.g. Ref. 33, and further study is
While we have explicitly shown the existence of a strong PNR-phonon interaction in
PZN-4.5%PT, this effect is not limited to one composition. It has been shown by neutron
and x-ray diffuse scattering measurements that PNR are present in all compositions to the
left of the MPB in both PMN-xPT and PZN-xPT solid solutions14,34 as well as for
compositions inside the MPB (see Fig. S1). There is also evidence for a PNR-phonon
interaction in other PT compositions such as PMN-20%PT35 and pure PMN17 where an
anomalous TA phonon broadening has been observed and attributed to diffuse-phonon
coupling. While PT doping toward the MPB or an external electric field31 does enhance
the electromechanical and piezoelectric properties in both PMN-xPT and PZN-xPT, the
relaxor character itself plays an important and fundamental role. In fact, even in the
absence of any PT, both pure PZN and PMN already exhibit extraordinarily high field
induced piezoelectric strains36. With increasing PT content some relaxor properties, such
as the frequency dispersion in dielectric permittivity, are gradually suppressed; yet the
elastic diffuse scattering from PNR is still present near the MPB. In fact, diffuse
scattering measurements from PMN-xPT single crystals34 have suggested that the
Q-integrated diffuse scattering intensity increases with increasing PT and reaches a
maximum near the MPB – precisely where the piezoelectric response is optimal, which is
likely more than just coincidence. When these relaxor-ferroelectric solid solutions cross
the MPB into the tetragonal side of the phase diagram with even larger PT content, PNR
are no longer present24,34 and the piezoelectric property drops dramatically1 (to values
below even those of pure PMN and PZN).
The orthorhombic asymmetry in the lattice dynamics induced by the PNR also has
clear implications on the emergence of various monoclinic (M) phases in relaxor
ferroelectric solid-solutions. Monoclinic phases37,38,39,40 have been found in PMN-xPT
and PZN-xPT for compositions near the MPB and can be induced in lower PT
compositions with a external field applied along 41,42. These are believed to appear
as a result of the “polarization rotation” scheme proposed by Fu and Cohen27. Here, the
polarization of the system can be rotated by an external field in a monoclinic plane,
instead of being confined to a certain crystallographic orientation as in the R or T phases
(see Fig. 4 for details). While PT doping tends to drive the system toward a tetragonal
(T) phase due to the large tetragonal strain of PbTiO3 itself, the low symmetry M phases
are considered as a bridge between the R and T phases. One dilemma remains however.
Intuitively, the bridging phase for low-PT R and high-PT T phases should be MA, where
the polarization lies in the (110) plane (see Fig. 4B); in reality, however, in both
PZN-xPT and PMN-xPT systems the zero-field phase near the MPB is MC, not MA (in
fact it is orthorhombic (O) in PZN-xPT, which is a special case of MC), where the
polarization can rotate in the (001) plane (Fig. 4C). An MC phase is also often observed
when an electric field is applied along . Using our results on the orthorhombic-type
strain induced by PNR, manifested by an asymmetry in the lattice dynamics, this
situation can now be understood in simple phenomenological terms. The combination of
a rhombohedral (R) distortion and a tetragonal strain (T), either from PT doping or an
external  field, can only produce an MA phase; however both MA and MC phases are
possible (see Fig. 4 B, C) by combining T distortion with an orthorhombic (O) strain
In summary, we have shown that PNR significantly affect the lattice stability in
relaxor systems through a fundamental interaction with transverse acoustic phonons.
While the average, static structure of the bulk is not explicitly modified by the PNR, the
local structure of the PNR can be mapped onto the low energy lattice dynamics
macroscopically. The resulting relaxor phase has a nearly cubic structure with a large
asymmetry in the lattice dynamics that also helps to explain intuitively the emergence of
various M phases in relaxor ferroelectric solid solutions. Our results therefore provide
evidence that the ultra-high piezoelectric properties of relaxor ferroelectrics may arise
from a structural instability resulting from a competition between the static bulk structure
and local inhomogeneities that is mediated by acoustic phonons.
Figure 1. Neutron scattering measurements performed on a PZN-4.5PT single
crystal with dimensions of 10× ×10× ×3 mm3. The experiment was performed on the
NCNR BT7 triple-axis-spectrometer using beam collimations of 50’-50’-40’-240’. The
final neutron energy was fixed at 14.7 meV. A pyrolytic graphite (PG) filter was placed
after the sample to reduce higher order neutrons. Lines are guides to the eye. (A) A
schematic diagram of the neutron scattering measurements, performed near the (220) and
Bragg peaks. The blue and red ellipsoids represent the FC diffuse scattering
intensity distributions for E along . The polarization and propagation vectors for the
phonons are also noted. (B) Profile of the diffuse scattering intensity measured along (H
2.1 0) (dashed line in (A)) under ZFC and FC conditions. (C) Intensity contours measured
)202(. (D) Intensity contours measured near (220).
Figure 2. Constant-Q scans measured near the (220) and
Bragg peaks at
q=0.1 and 0.2 r.l.u. The blue and red points are data taken near
and (220) after
cooling in a field E=2 kV/cm oriented along . The black points are ZFC data. Red
and blue lines are guides to the eye. The black lines are calculated as an average of the
two FC data sets (blue and red data points), and can be compared directly to the ZFC
Figure 3. Phonon dispersions and energy widths (HWHM) measured around the
Bragg peaks under FC and ZFC conditions. The solid lines in (A)
are guides to the eye. The dashed lines in (B) and (C) denote the instrumental energy
resolution. The error bars in the figure are fitting errors obtained though least-square fits
to the data, assuming the phonon modes having Lorentzian line shapes.
Figure 4. Schematic diagrams of the different polarization directions (marked by
arrows) in the relaxor perovskite structure. (A) Polarizations along T and R. (B) The
MA phase, for which the polarization lies in the (110) plane, can be obtained by
combining T and O. (C) The MC phase, for which the polarization lies in the (100) plane,
can also be obtained by combining T and O.
Acknowledgements We would like to thank S. M. Shapiro and J. M. Tranquada for
stimulating discussions. The financial support of the U.S. Department of Energy under
contract No. DE-AC02-98CH10886, the U.S. Office of Naval Research under Grant No.
N00014-99-1-0738, and the Natural Science and Research Council of Canada (NSERC)
is also gratefully acknowledged.
Competing Interests The authors declare that they have no competing financial interests.
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