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ABSTRACT The Dzyaloshinskii–Moriya interaction (DMI) between two magnetic moments m_i_ and m_j_ is of the form \({\rm{D}}_{ij} \cdot ({\rm{m}}_i \times {\rm{m}}_j)\). It originates from

spin–orbit coupling, and is at the heart of fascinating phenomena involving non-collinear magnetism, such as magnetic topological defects (for example, skyrmions) as well as spin–orbit

torques and magnetically driven ferroelectricity, that are of significant fundamental and technological interest. In sharp contrast, its electric counterpart, which is an electric DMI

characterized by its \({{\bf{D}}}_{ij}^{\prime}\) strength and describing an interaction between two polar displacements u_i_ and u_j_, has rarely been considered, despite the striking

possibility that it could also generate new features associated with non-collinear patterns of electric dipoles. Here we report first-principles simulations combined with group theoretical

symmetry analysis which not only demonstrate that electric DMI does exist and has a one-to-one correspondence with its magnetic analogue, but also reveals a physical source for it. These

findings can be used to explain and/or design phenomena of possible technological importance in ferroelectrics and multiferroics. Access through your institution Buy or subscribe This is a

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* Log in * Learn about institutional subscriptions * Read our FAQs * Contact customer support SIMILAR CONTENT BEING VIEWED BY OTHERS MAGNETOELECTRIC COUPLING OF DOMAINS, DOMAIN WALLS AND

VORTICES IN A MULTIFERROIC WITH INDEPENDENT MAGNETIC AND ELECTRIC ORDER Article Open access 25 May 2021 MULTIFERROIC KINKS AND SPIN-FLOP TRANSITION IN NI2INSBO6 FROM FIRST PRINCIPLES Article

Open access 03 June 2024 FRACTIONAL QUANTUM FERROELECTRICITY Article Open access 02 January 2024 DATA AVAILABILITY All the data (for example, raw data and Matplotlib-based scripts for

analysing and visualizing the data) supporting the present work are available from the corresponding author upon request. Please note that our data figures were prepared with the use of some

Matplotlib-based scripts (for example, with some mathematical processes such as post-processing of the data or fitting inside the scripts). Consequently, we prefer to share our raw data as

well as the scripts to interested readers on request, so that we can help them in case of need. We do not upload our data and scripts because the latter may depend on the version of Python.

CODE AVAILABILITY The VASP code for the numerical simulations in this work can be found at https://www.vasp.at; the code L-INVARIANT can be found at https://github.com/PaulChern/LINVARIANT/;

the Mathematica software is available at https://www.wolfram.com/mathematica; the Matplotlib is available at https://matplotlib.org; other codes and scripts can be obtained on request from

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Google Scholar  Download references ACKNOWLEDGEMENTS H.J.Z and L.B. thank the Department of Energy, Office of Basic Energy Sciences, under award number DESC0002220 for the DFT simulations.

P.C. and S.P. acknowledge the Office of Naval Research under grant number N00014-17-1-2818 for symmetry analysis. The simulations based on DFT were done using the Arkansas High Performance

Computing Center. AUTHOR INFORMATION AUTHORS AND AFFILIATIONS * Physics Department and Institute for Nanoscience and Engineering, University of Arkansas, Fayetteville, AR, USA Hong Jian

Zhao, Peng Chen, Sergey Prosandeev & Laurent Bellaiche * Quantum Materials Theory, Italian Institute of Technology, Genoa, Italy Sergey Artyukhin Authors * Hong Jian Zhao View author

publications You can also search for this author inPubMed Google Scholar * Peng Chen View author publications You can also search for this author inPubMed Google Scholar * Sergey Prosandeev

View author publications You can also search for this author inPubMed Google Scholar * Sergey Artyukhin View author publications You can also search for this author inPubMed Google Scholar *

Laurent Bellaiche View author publications You can also search for this author inPubMed Google Scholar CONTRIBUTIONS L.B. and H.J.Z. conceived the work. H.J.Z. performed the DFT

simulations. H.J.Z., P.C., S.P. and S.A. carried out symmetry analysis. All authors participated in the discussion and preparation of this work. CORRESPONDING AUTHORS Correspondence to Peng

Chen or Laurent Bellaiche. ETHICS DECLARATIONS COMPETING INTERESTS The authors declare no competing interests. ADDITIONAL INFORMATION PUBLISHER’S NOTE Springer Nature remains neutral with

regard to jurisdictional claims in published maps and institutional affiliations. SUPPLEMENTARY INFORMATION SUPPLEMENTARY INFORMATION Supplementary Figs. 1-7, Discussion I–VII, Tables I–VI

and refs. 1–22. RIGHTS AND PERMISSIONS Reprints and permissions ABOUT THIS ARTICLE CITE THIS ARTICLE Zhao, H.J., Chen, P., Prosandeev, S. _et al._ Dzyaloshinskii–Moriya-like interaction in

ferroelectrics and antiferroelectrics. _Nat. Mater._ 20, 341–345 (2021). https://doi.org/10.1038/s41563-020-00821-3 Download citation * Received: 28 April 2020 * Accepted: 03 September 2020

* Published: 12 October 2020 * Issue Date: March 2021 * DOI: https://doi.org/10.1038/s41563-020-00821-3 SHARE THIS ARTICLE Anyone you share the following link with will be able to read this

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