Stability of Vortex Phases in Ferroelectric Easy-Plane nano-Cylinders

TL;DR

This paper investigates the stability and characteristics of vortex phases in ferroelectric nano-cylinders, focusing on how geometry influences multivortex states and their critical temperatures.

Contribution

It provides a self-consistent analysis of multivortex toroidal states in ferroelectric nano-cylinders using Ginzburg-Landau and electrostatic equations, highlighting stability regions.

Findings

Identification of stable multivortex toroidal states

Calculation of critical temperatures for vortex stability

Mapping of stability regions based on geometry

Abstract

Bounded charges induced by the polarization gradient in finite-size ferroelectrics are known to produce the unfavorable depolarization electric field that suppresses the uniform ferroelectric state. To reduce the depolarization energy the non-uniform vortex (toroidal) state is formed inside ferroelectric nano-particles, nano-disks, and nano-rods. Based on self-consistent solution of Ginzburg-Landau equations coupled with electrostatic equations, we study the multivortex toroidal states appearing in the nanometric easy-plane ferroelectric cylinder. The geometrical textures, critical temperatures and stability regions for these states are calculated.