Local polarization dynamics in ferroelectric materials

Rep. Prog. Phys. 73 (2010) 056502
S V Kalinin et al
20 nm
H
0 nm
h 2
(a)
50 nm
(b)
(e)
Imprint:
(c)
(d)
(f)
Offset
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Figure 50. (a) Topography, (b) mixed PFM, (c) initial piezoresponse and (d) the work of switching for the nanoparticle shown in (a).
(e) Schematic showing the polarization within a nanoparticle and (f ) the corresponding loop which is shifted along the voltage axis due to
imprint and the response axis due to the frozen polarization. Reproduced from [362]. Copyright 2008, John Wiley and Sons, Inc.
device behavior; however, experimental studies of specific
nucleation centers are quite challenging given the predicted
size of nucleation centers (below 10 nm), low densities in
high quality films, and the difficulties distinguishing nucleation
from domain wall propagation.
SS-PFM has allowed real-space imaging of nucleation
centers in ferroelectrics via mapping positive and negative
nucleation biases. To relate the PNB and NNB maps to
local materials properties, RB disorder was introduced as
a variation in wall energy, ψ S (x, y) = ψS 0 α(x,y) (or,
equivalently, thickness), and RF disorder is introduced as
built-in polarization disorder, P S (x, y) = PS 0(1+β(x,y)),
or frozen polarization. Here, ψS 0 and P S
0 correspond to the
parameters of the ideal material and α(x,y) and β(x,y)
describe variations in materials properties on length scales
larger than the characteristic nucleating domain size (∼2 nm,
as estimated from activation energy). The local nucleation
bias is then Ucr 2 = Aψ S(x, y)P S (x, y), where A is a constant
determined by the tip properties and the dielectric properties of
the material. Assuming that the latter are position independent,
the positive and negative nucleation biases are
U+ 2 = Aψ S 0 P S 0 α (x,y)(1+β (x,y)) , (4.17a)
U− 2 = Aψ S 0 P S 0 α (x,y)(1 − β (x,y)) . (4.17b)
Thus, analysis of the nucleation biases allows the random
bond and random field components of the disorder potential
to be separated and subsequently correlated with the local
microstructure (figure 52).
4.4.4. Barkhausen jumps at the nanoscale. The analysis
of hysteresis loops from a variety of materials systems has
shown that often the loops possess fine features, as shown
in figure 53. The features are highly localized, reproducible
and in some cases are associated with the visible structural
defects. The studies by the Alexe group have associated the
presence of the fine structure features with the proximity to a
ferroelastic domain wall [364, 365]. Bdikin et al [366] have
performed simultaneous imaging and spectroscopic studies
and illustrated that the fine structure is associated with the nonmonotonic
jumps in wall motion, i.e. individual pinning events
(figure 54). Notably, the defect–defect spacing in the highquality
epitaxial films can be of the order of 100–300 nm [367],
well above the resolution of the PFM. Hence, single defect
imaging can be feasible provided that (a) the defect signature in
hysteresis loop measurements is known and (b) the sensitivity
of the method is sufficient to detect a single defect. Recently,
single-defect imaging from SS-PFM was demonstrated
(figure 54) [319].
4.5. Time resolved spectroscopies of ferroelectrics
One of the most interesting aspects of ferroelectric behavior
is the polarization dynamics. In most materials, domain
nucleation occurs at the ∼nanosecond time scale, and wall
velocities are extremely high. Consequently, PFM limited
to ∼100 Hz bandwidth for spectroscopy and ∼1 mHz for
imaging cannot be expected to provide direct time resolved
information on ferroelectric domain resolution, necessitating
the development of stroboscopic modes [342, 343, 368] or
alternative time-resolved probes such as focused x-ray [369].
However, an important exception is the relaxor ferroelectric
and ferroelectric polymers that often have extremely large
(hours to days) relaxation times, enabling PFM-based dynamic
studies. Furthermore, domain wall dynamics at small fields
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