Impact of ferroelectric nonlinearity and correlation effects on nanodomain formation

TL;DR

This paper analytically investigates how ferroelectric nonlinearity and correlation effects influence nanodomain shapes and formation thresholds under a biased scanning probe, aligning with experimental observations.

Contribution

It introduces an analytical model combining variational and thermodynamic approaches to describe nanodomain formation considering nonlinear and correlation effects.

Findings

Nanodomain shape can be oblate or prolate depending on nonlinearity.

Domain aspect ratio aligns with dielectric anisotropy.

Coercive biases match experimental data.

Abstract

Using direct variational method with 2-parametric trial function and Landau-Ginzburg-Devonshire thermodynamical approach, we derived analytical expressions for polarization spatial redistribution in the ferroelectrics caused by the biased Scanning Probe Microscope probe. We demonstrate that the shape of nanodomain induced by the probe electric field can be either oblate or prolate depending on the ferroelectric nonlinearity strength. For typical ferroelectric material parameters and probe apex geometry the domain nucleus aspect ratio is close to dielectric anisotropy factor. Corresponding coercive biases of a stable domain formation are in reasonable agreement with available experimental results. Spike-like domains typical for Landauer-Molotskii rigid approach appear in the considered case only when depolarization field energy contribution strongly dominates over the nonlinear correlation and field effects and domain wall energy.