Pis’ma v ZhETF, vol. 116, iss. 4, pp. 249 - 250
© 2022 August 25
Ferroelectric domain reversal: The role of domain wall conduction1)
B.Sturman2), E.Podivilov
Institute of Automation and Electrometry, Russian Academy of Sciences, 630090 Novosibirsk, Russia
Submitted 13 June 2022
Resubmitted
4 July 2022
Accepted 5
July 2022
DOI: 10.31857/S1234567822160091, EDN: jhxesl
∫
Ferroelectric domain reversal is a vast research area
surface, δEs =
w dS, where w is a positive surface den-
relevant to the fundamental science and applications.
sity. As DW is typically charged, w must depend on the
Here, the general feature is that the coercive field Ec is
angle θ between the DW surface normal and the z axis.
orders of magnitude smaller than the characteristic de-
We model this by the relation w = w0 + w1 cos θ with
polarizing field E0d = 4πPs/εzz, where Ps is the sponta-
w1/w0 ≫ 1 leading to δEs = w0S + w1S⊥, where S is
neous polarization. The real reversal process is viewed as
the domain surface and S⊥ its maximal cross-section.
nucleation and growth of numerous microscopic counter-
The electrostatic contribution δEel crucially depends
domains [1, 2]. While compensation of the arising bound
on the charge compensation assumptions. In the absence
charge ±2Ps occurs at electrodes, it is not generally al-
of DW charge compensation, we obtain the classical re-
lowed at domain walls (DWs) inside the crystal. This
lation of [4] leading to unrealistically large values of δE
leads to the generation of depolarizing field Ed ranging
and thus to practically forbidden reversal process. Ad-
from 0 to E0d, i.e., to an apparent inconsistency of the re-
mission for DW conduction means that the dielectric
versal concept. To overcome it, counter-domains are as-
boundary conditions (BCs) must be replaced by the
sumed to be needle-like [1-4]. This assumption is satis-
metal BCs for the electrostatic potential, ϕ(rDW) = U,
factory only for an initial stage of the reversal. Moreover,
where U is the applied voltage. The actual values of δEel
there are documented cases [5-7] where Ed ≫ Ec and
can be substantially smaller here facilitating the domain
the reversal concept not including the charge compen-
formation.
sation experiences serious difficulties. This is relevant to
Figures 1a, b illustrate the dependence of δE on the
both capacitor and AFM experimental configurations.
applied electric field E0 in the capacitor configuration
We claim that the DW conduction, which is now de-
and on the transverse and longitudinal domain sizes (l⊥
tected in many ferroelectrics [8-10], has to be regarded
and lz) for a half-spheroidal domain shape. We have
as a crucial and general ingredient of the domain rever-
employed parameters relevant to lithium niobate (LN)
sal processes. Its importance is in providing an auto-
crystals: Ps = 70 µC/cm2, εzz = 30, ε⊥ = 85 and rep-
matic compensation of typically huge depolarizing elec-
resentative values w0 = 3, w1 = 15 erg/cm2. One sees
tric fields. The presence of DW conduction modifies the
from Fig. 1a that for E0 = 4 kV/mm, which is represen-
basics of domain reversal processes. Concerning AFM
tative for Ec in LN crystals, the maximal in lz values
applications, domain reversal theories have to include
of δE are about 1 eV. Figure 1b shows that increase of
injection models from conductive tip electrodes. We pro-
E0 causes a rapid decrease of the values of lz and δE(lz)
vide some primary results relevant to the basics of DW
relevant to the maximum of δE(lz). The predictions of
conduction mediated domain reversal. For simplicity, we
Figure 1 are beneficial for the domain reversal as com-
consider uniaxial ferroelectrics where the spontaneous
pared to those relevant to the absence of the DW charge
polarization is parallel to the z axis and acquires the
compensation.
values ±Ps.
Consider now the effect of DW conduction charge
The values of domain formation energy δE are cru-
compensation in the case of lateral domain growth in
cial for domain reversal [1-4]. The main contributions
the AFM configurations. Experiments with application
to δE are the surface and electrostatic ones. The sur-
of U, τ voltage pules show that the inverted domain ra-
face contribution is given by the integral over the DW
dius r0(U, τ) exceeds 1 µm in LN crystals for U ≈ 100 V
and τ ≈ 103s [6, 7]. This is much larger than the conduc-
1)Supplementary materials are available for this article at DOI:
and are accessible for authorized users.
tive tip radius. In the absence of charge compensation,
2)e-mail: sturman@iae.nsk.su
this would lead to the existence of depolarizing fields
Письма в ЖЭТФ том 116 вып. 3 - 4
2022
249
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