Citation: Zhang, J.; Du, X.; Zhao, J.;
Duan, Y. Explaining the Frequency
Dependence of the DC-Biased
Dielectric Response of Polar
Nanoregions by Field-Enhanced
Correlation Length. Nanomaterials
2022, 12, 1293. https://doi.org/
10.3390/nano12081293
Academic Editors: Ki-Hyun Kim and
Deepak Kukkar
Received: 24 February 2022
Accepted: 4 April 2022
Published: 11 April 2022
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Article
Explaining the Frequency Dependence of the DC-Biased
Dielectric Response of Polar Nanoregions by Field-Enhanced
Correlation Length
Jianwei Zhang
1
, Xiaoping Du
2,
*, Jiguang Zhao
2
and Yongsheng Duan
3
1
Graduate Schools, Space Engineering University, Beijing 101416, China; quantum_pho@163.com
2
Department of Electron & Optics Engineering, Space Engineering University, Beijing 101416, China;
zhaoyy8600@163.com
3
Department of Aerospace Science and Technology, Space Engineering University, Beijing 101416, China;
duanys_vip@yeah.net
* Correspondence: ele_phy@163.com
Abstract:
Understanding the effects of polar nanoregions (PNRs) dynamics on dielectric properties
is a complex question of essential importance for both fundamental studies of relaxor ferroelectrics
and their applications to electro-optic devices. The frequency dependence of dielectric response
to the bias electric field opens a brand new window for the study of this problem. A novel model
from mesoscopic to macroscopic, revealing the relationship between the dielectric permittivity to the
applied electric field, temperature, and PNRs, was established based on mean field approximation
and the theory of continuum percolation, and not only validates the field-induced percolation and the
relaxation time divergency at the freezing temperature, but also predicts the frequency dependence
of dielectric response. Unexpectedly, the model reveals the field-enhanced correlation length results
in the nonmonotonic behavior of dielectric response, and implies that the increased orientation
consistency of dipolar clusters and coercive fields originated from inherent inhomogeneity slow
down the relaxation time of PNR reorientation. Considering the multi-scale heterogeneity of PNRs
in relaxor, we found that the increased heterogeneity degree reduces the dielectric permittivity, but
changes the slope of dielectric response to the bias electric field.
Keywords: dielectric; polar nanoregions; frequency dependence; correlation length
1. Introduction
Dielectric properties of relaxor ferroelectrics have been widely studied theoretically
and experimentally, owing to their potential for wide application. KTa
1-x
Nb
x
O
3
(KTN)
crystal is a composition-disordered relaxor ferroelectric with perovskite structure. It has
attracted considerable attention due to its potential applications in functional devices,
including optical switches [
1
–
3
], electro-optic (EO) modulators [
4
,
5
], and deflectors [
6
–
8
].
All of them benefit from dielectric permittivity that diverges at the Curie temperature. The
giant dielectric permittivity is generally believed to originate from the reorientation dynam-
ics of polar nanoregions (PNRs) under the electric field [
9
]. Below the Burn temperature
(T
B
) [
10
], the PNR begins to rapidly form through the interaction among adjacent dipoles
and orients between the states with the same energy, and contributes less to the dielectric
permittivity because of violent thermal fluctuation. Dropping to the intermediate temper-
ature (T*) [
11
], enhanced interaction among the dipole clusters increases the correlation
length, giving the PNR local field properties. The PNR will be reoriented under the effect
of the electric field, which greatly changes the dielectric permittivity of the KTN crystal,
characterized by the obvious deviation from Curie–Weiss law.
The dielectric response to the electric field has received extensive attention owing to
the anomalous behavior of paraelectric KTN near the Curie temperature [
12
–
16
], and it
Nanomaterials 2022, 12, 1293. https://doi.org/10.3390/nano12081293 https://www.mdpi.com/journal/nanomaterials
