Ferro-ionic States and Domains Morphology in Hf$_x$Zr$_{1-x}$O$_2$ Nanoparticles

TL;DR

This study investigates the polar properties, phase diagrams, and domain structures of Hf$_x$Zr$_{1-x}$O$_2$ nanoparticles, revealing how surface ionic-electronic interactions influence ferroelectric and labyrinthine domain stability at the nanoscale.

Contribution

It introduces a theoretical analysis of ferro-ionic coupling effects on domain morphology and phase stability in Hf$_x$Zr$_{1-x}$O$_2$ nanoparticles, highlighting new mechanisms for polar order.

Findings

Ferro-ionic coupling supports long-range polar order.

Labyrinthine domains are stabilized at smaller sizes and low dielectric constants.

Transition to single-domain ferro-ionic state occurs at high surface ion concentrations.

Abstract

Unique polar properties of nanoscale hafnia-zirconia oxides (Hf$_x$Zr$_{1-x}$O$_2$) are of great interest for condensed matter physics, nanophysics and advanced applications. These properties are connected (at least partially) to the ionic-electronic and electrochemical phenomena at the hafnia surface, interfaces and/or internal grain boundaries. Here we calculated the phase diagrams, dielectric permittivity, spontaneous polar and antipolar ordering, and domain structure morphology in Hf$_x$Zr$_{1-x}$O$_2$ nanoparticles covered by ionic-electronic charge, originated from the surface electrochemical adsorption. We revealed that the ferro-ionic coupling supports the polar long-range order in the nanoscale Hf$_x$Zr$_{1-x}$O$_2$, induces and/or enlarges the stability region of the labyrinthine domains towards smaller sizes and smaller environmental dielectric constant at low concentrations of the surface ions, and causes the transition to the single-domain ferro-ionic state at high concentrations of the surface ions. We predict that the labyrinthine domain states, being multiple-degenerated, may significantly affect the emergence of the negative differential capacitance state in the nanograined/nanocrystalline Hf$_x$Zr$_{1-x}$O$_2$ films.