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Updated: Dec 21, 2025

Bulk and Thin Film Synthesis of Compositionally Variant Entropy-stabilized Oxides
Published on: May 29, 2018
Hopfions emerge in ferroelectrics.
I Luk'yanchuk1, Y Tikhonov1,2, A Razumnaya2
1Laboratory of Condensed Matter Physics, University of Picardie, 80039, Amiens, France.
Hopfions, topological solitons, are demonstrated as fundamental polarization field configurations in ferroelectric nanoparticles. This discovery reveals their crucial role in electromagnetic behavior and potential for advanced material functionalities.
Area of Science:
- Physics
- Condensed Matter Physics
- Materials Science
Background:
- Hopfions are topological solitons characterized by the Hopf invariant, attracting interest across diverse scientific fields.
- Despite broad interest, Hopfions remain elusive and under-explored in many physical systems.
Purpose of the Study:
- To demonstrate the emergence of Hopfions as a fundamental configuration of the polarization field.
- To investigate the role of Hopfions in the electromagnetic behavior of confined ferroelectric nanoparticles.
Main Methods:
- Theoretical analysis of polarization fields in confined ferroelectric nanoparticles.
- Simulation or experimental validation of Hopfion formation.
Main Results:
- Hopfions naturally emerge as a basic polarization field configuration in ferroelectric nanoparticles.
- These Hopfion configurations are of fundamental importance for the electromagnetic properties of the nanocomposites.
Conclusions:
- Hopfions are not just theoretical constructs but observable phenomena in specific material systems.
- The presence of Hopfions in ferroelectric nanoparticles offers pathways to developing advanced functionalities in electromagnetic materials.
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