Ferro-ionic states and domains morphology in Hf x Zr 1–x O 2 nanoparticles
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 surface, interfaces, and/or internal grain boundaries. Here, we calculated the phase diagrams, dielectric permittivity, spontaneous polar, and antipolar ordering, as well as the domain structure morphology in Hf x Zr 1–x O 2 nanoparticles covered by ionic–electronic charge originating from surface electrochemical adsorption. We revealed that the ferro-ionic coupling supports the polar long-range order in nanoscale Hf x Zr 1–x O 2 , induces, and/or enlarges the stability region of the labyrinthine domains toward smaller sizes and smaller environmental dielectric constant at low concentrations of the surface ions. The ferro-ionic coupling 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.