Local polarization dynamics in ferroelectric materials

Rep. Prog. Phys. 73 (2010) 056502
(a)
Effective piezoresponse PR (pm/V)
10
0
-10
0
-10
x=0
x=20
10 x=60
τ=0
τ≠0
1
-30 0 30
4
-30 0 30
Applied bias V (V)
Polarization P3/PS
1
0
τ=0
5
x=30 10
0
2
-10
3
0
-10
0 1
4
6
(b)
-1
-30 0 30
-30 0 30
10 x=100
5
-30 0 30
Applied bias V (V)
2
Applied bias V (V)
Polarization P3/PS
1
0
0
τ≠0
x=40 10
0
3
-10
-10
-30 0 30
x=300
10
0
6
6 5
-30 0 30
Applied bias V (V)
4
3
(c)
1
2
-1
-30 0 30
Applied bias V (V)
x (nm)
S V Kalinin et al
Figure 49. (a) Effective piezoelectric response (pm V −1 ) versus applied bias (V) calculated from equation (2) for different distances x 0 from
the domain wall for x = 0, 20, 30, 40, 60, 100, 300 nm (plots 1–6). Dotted curves are static dependences calculated at τ = 0, while solid
curves are kinetic loops calculated for τ = 10 −8 s and applied bias frequency f = 500 kHz. (b), (c) Normalized polarization P 3 versus
applied bias for τ = 0(b) and τ = 10 −8 s(c) for x = 0, 20, 30, 40, 60, 100, 300 nm (curves 0–6). Effective distance d = 25 nm. Material
parameters for LNO are ε 11 = 84, α =−2 × 10 9 SI units, P S = 0.75Cm −2 . Poisson ratio is ν = 0.3; electrostriction coefficients are
Q 44 = 0.038, Q 12 =−0.003, Q 11 = 0.016 m 4 C −2 ; L ⊥ = 1 nm.
in figure 50. A two-layer model for the nanoparticle consisting
of a switchable (ferroelectric) layer characterized by the
presence of a built-in electric field and a non-switchable (frozen
polarization) layer as shown in figure 50 was introduced and
relevant parameters were analyzed using the 1D model, as
described previously [180, 334]. Specifically, the vertical shift
of a hysteresis loop is related to the relative thickness of
the non-switchable polarization component and defines the
distribution of the frozen polarization within the system, while
the lateral shift of the hysteresis loop defines the built-in field
in the ferroelectric component.
4.4.2. Imaging of multiferroic structures. The role of interfaces
on ferroelectric switching behavior and on multiferroic
coupling ferroelectric–ferromagentic heterostructures [363]
was studied in [104]. Topography, PFM and SS-PFM (work of
switching, PNB and NNB) images for a BFO–CoFe 2 O 4 (CFO)
nanostructure sample are shown in figure 51, along with characteristic
loops from the BFO, CFO and BFO–CFO interface
regions. The corresponding bias parameters are defined in
figure 51(h). The SS-PFM maps illustrate that coercive and
nucleation biases are uniformly distributed within the ferroelectric
regions and do not exhibit any systematic trends in
the vicinity of the interface. While the work of switching and
the electromechanical response are reduced in the vicinity of
the interfaces, analysis of the SS-PFM data shows that this is
a purely geometric effect due to the reduction of the domain
volume at the interface [104].
4.4.3. Disorder potential mapping. The role of defects
as nucleation centers in polarization reversal is the central
theme of ferroelectric switching models and at the heart of
50