Local polarization dynamics in ferroelectric materials

Rep. Prog. Phys. 73 (2010) 056502
S V Kalinin et al
Figure 59. (a) Domain structure of epitaxial PbZr 0.2 Ti 0.8 O 3 thin film with a pre-existing a 2 -positive domain (polarization along [0 1 0])
within a matrix of c-negative domain (polarization along [0 0 −1] under short-circuit boundary condition. The dots show the locations of the
PFM tip along the profile A–M–N–B; (b) spatial distribution of nucleation potential at selected locations; (c) distribution of electrostatic
energy density (MJ m −3 ) without applied potential [388]. Copyright 2008, American Institute of Physics.
Figure 60. (a) Domain structure of an (0 0 1)-oriented epitaxial PbZr 0.2 Ti 0.8 O 3 thin film; (b) spatial distribution of the nucleation potential
along the profile P–Q–R–S–T–U–V [388]. Copyright 2008, American Institute of Physics.
represents the nucleation potential corresponding to a dot in
figure 59(a). It is shown that the potential required to nucleate
a 180 ◦ domain is lower near the ferroelastic twin defects
(∼1.6 V) as compared with ∼2.6 V away from the twin defect
within the matrix. It is also found that the two parallel twin
walls are not equivalent. The potential required to nucleate a
180 ◦ domain is lower near the left twin boundary compared
with the right one.
The origins of the asymmetric variation of the nucleation
voltage near the two twin walls can be easily understood by
analyzing the electrostatic energy density on the surface of the
thin film without any applied electric potential (figure 59(c)).
The observation that the locations of the lowest nucleation
voltage (figure 59(b)) do not coincide with the locations of
the twin walls (point M or N in figure 59(c)) in the initial
domain structure in figure 59(a) can be attributed to the
in-plane electric field of PFM which slightly displaces the wall
positions. Finally, the small a-domain size (∼10 nm) was not
resolved since the tip parameter γ was 30 nm, and hence only
a single large asymmetric dip in the nucleation voltage near
the a-domain is observed.
5.6. Nucleation potential distribution in a domain structure
As shown above that the nucleation potential is different
near ferroelastic twin walls and within a homogeneous
domain matrix, it is expected that the nucleation potential is
inhomogeneous within a domain structure. As an example,
the spatial distribution of nucleation voltage was probed in
a more realistic domain structure of PZT epitaxial thin film
(figure 60(a))using phase-field simulations [388]. The domain
structure is generated under a short-circuit boundary condition
starting from an initial paraelectric state with small random
perturbations. Each of the colors represents a tetragonal
variant. The domain structure consists of a 1 and a 2 domains
embedded in a c-domain matrix. To understand the correlation
between the spatial variation of nucleation voltage and with
the locations of ferroelectric twin walls and wall junctions, the
PFM tip position was moved along the line P–Q–R–S–T–U–V
in figure 60(a). The nucleation voltage as a function of position
is recorded in figure 60(b). It is observed that the nucleation
potential is correlated with the number of local twin domain
variants. For example, the nucleation voltage is highest within
the c-domain matrix (points R and U) followed by a single twin
wall (point S), and then by the area where a 1 and a 2 intersect
(point Q). The lowest nucleation potential is observed near the
triple junctions (point T) where three domains meet.
Remarkably, these examples illustrate that the combination
of the phase-field modeling and piezoresponse force
microscopy and spectroscopy studies effectively allow us to
study polarization dynamics at the level of a single mesoscopic
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