Open Access

Colossal dielectric response of $H f_{x} Z r_{1 − x} O_{2}$ nanoparticles

Oleksandr S. Pylypchuk ¹, Victor V. Vainberg ^1,*, Vladimir N. Poroshin ¹, Oksana V. Leshchenko², Victor N. Pavlikov², Irina V. Kondakova ², Serhii E. Ivanchenko ², Lesya P. Yurchenko ², Lesya Demchenko ^3,4 et al.

Anna O. Diachenko ⁵, Myroslav V. Karpets ^2,4, Eugene A. Eliseev ^2,†, and Anna N. Morozovska ^1,‡

¹Institute of Physics, National Academy of Sciences of Ukraine,46, Nauky Avenue, 03028 Kyiv, Ukraine
²Frantsevich Institute for Problems in Materials Science, National Academy of Sciences of Ukraine, 3, street Omeliana Pritsaka, 03142 Kyiv, Ukraine
³Stockholm University, Department of Chemistry, Stockholm, Sweden
⁴Ye. O. Paton Institute of Materials Science and Welding, National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, 37, Beresteisky Avenue, 03056 Kyiv, Ukraine
⁵Oles Honchar Dnipro National University, 72, Nauky Avenue, 49000 Dnipro, Ukraine

^*Contact author: viktor.vainberg@gmail.com
^†Contact author: eugene.a.eliseev@gmail.com
^‡Contact author: anna.n.morozovska@gmail.com

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Phys. Rev. Materials 9, 114412 – Published 17 November, 2025

DOI: https://doi.org/10.1103/y2pb-5g5w

Abstract

We observed a colossal dielectric response of small (5–10 nm) oxygen-deficient $H f_{x} Z r_{1 - x} O_{2}$ nanoparticles ( $x = 1 - 0.4$ ), prepared by solid-state organonitrate synthesis. The effective dielectric permittivity of the pressed $H f_{x} Z r_{1 - x} O_{2}$ nanopowders has a pronounced maximum at $38 - 88^{\circ} C$ , the shape of which can be fitted by the Curie-Weiss type dependence modified for the diffuse ferroelectric-paraelectric phase transition. The maximal value of the dielectric permittivity increases from $1.5 \times 10^{3}$ (for $x = 1$ ) to $1.5 \times 10^{5}$ (for $x = 0.4$ ) at low frequencies ( $\sim 4$ Hz), being much smaller, namely, changing from 7 (for $x = 1$ ) to 20 (for $x = 0.4$ ) at high frequencies ( $\sim 500$ kHz). The frequency dispersion of the dielectric permittivity maximum position is almost absent; meanwhile, the shape and width of the maximum changes in a complex way with increase in frequency. The temperature dependencies of the dielectric permittivity and resistivity are almost mirrorlike turned over with respect to each other, which means that all their features, such as position and shape of maxima, plateau, minima, and inflexions, almost coincide after the mirror reflection with respect to the temperature axis. These correlations of resistivity and dielectric permittivity are well described in the Heywang barrier model applied together with the variable range hopping conduction model in semiconducting ferroelectrics. Ferroelectriclike behavior of the small oxygen-deficient $H f_{x} Z r_{1 - x} O_{2}$ nanoparticles is expected from the Landau-Ginzburg-Devonshire approach and density functional theory calculations. Obtained results may be useful for developing silicon-compatible functional nanomaterials based on $H f_{x} Z r_{1 - x} O_{2}$ nanoparticles.

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See Supplemental Material at http://link.aps.org/supplemental/10.1103/y2pb-5g5w for additional figures and details of calculations.
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Phys. Rev. Materials 9, 114412– Published 17 November, 2025

Vol. 9, Iss. 11 — November 2025

Received 8 August 2025
Accepted 30 October 2025

DOI: https://doi.org/10.1103/y2pb-5g5w

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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Colossal dielectric response of $H f_{x} Z r_{1 − x} O_{2}$ nanoparticles

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Colossal dielectric response of HfxZr1−xO2 nanoparticles

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Colossal dielectric response of $H f_{x} Z r_{1 − x} O_{2}$ nanoparticles