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Dzyaloshinskii–Moriya-like interaction in ferroelectrics and antiferroelectrics

Nature Materials volume 20, pages 341–345 (2021)Cite this article

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Abstract

The Dzyaloshinskii–Moriya interaction (DMI) between two magnetic moments mi and mj 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 ui and uj, 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.

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Fig. 1: Sketches of the atomic motions associated with the 12 trilinear mechanisms.
Fig. 2: Forces acting on Bi and Al ions when displacing, along the x direction, Al ions within R and Mz modulations.
Fig. 3: Sketches for the ferroelectric and antiferroelectric motions of the A and B ions in ABO3 perovskites.
Fig. 4: The renormalized weak magnetic and/or ferroelectric components of LaFeO3 and BiAlO3 as a function of anti-phase tiltings \({\omega }_{z}^{R}\).

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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 the corresponding author.

References

  1. Dzyaloshinskii, I. E. Thermodynamic theory of ‘weak’ ferromagnetism in antiferromagnetic substances. Sov. Phys. JETP 5, 1259–1266 (1957).

    Google Scholar 

  2. Moriya, T. Anisotropic superexchange interaction and weak ferromagnetism. Phys. Rev. 120, 91–98 (1960).

    CAS  Google Scholar 

  3. Heinze, S. et al. Spontaneous atomic-scale magnetic skyrmion lattice in two dimensions. Nat. Phys. 7, 713–718 (2011).

    CAS  Google Scholar 

  4. Wiesendanger, R. Nanoscale magnetic skyrmions in metallic films and multilayers: a new twist for spintronics. Nat. Rev. Mater. 1, 16044 (2016).

    CAS  Google Scholar 

  5. Bera, S. & Mandal, S. S. Theory of the skyrmion, meron, antiskyrmion, and antimeron in chiral magnets. Phys. Rev. Res. 1, 033109 (2019).

    CAS  Google Scholar 

  6. Im, M.-Y. et al. Symmetry breaking in the formation of magnetic vortex states in a permalloy nanodisk. Nat. Commun. 3, 983 (2012).

    Google Scholar 

  7. Kwon, H. Y., Kang, S. P., Wu, Y. Z. & Won, C. Magnetic vortex generated by Dzyaloshinskii–Moriya interaction. J. Appl. Phys. 113, 133911 (2013).

    Google Scholar 

  8. Pereiro, M. et al. Topological excitations in a kagome magnet. Nat. Commun. 5, 4815 (2014).

    CAS  Google Scholar 

  9. Gao, N. et al. Creation and annihilation of topological meron pairs in in-plane magnetized films. Nat. Commun. 10, 5603 (2019).

    CAS  Google Scholar 

  10. Ishikuro, Y., Kawaguchi, M., Kato, N., Lau, Y.-C. & Hayashi, M. Dzyaloshinskii–Moriya interaction and spin–orbit torque at the Ir/Co interface. Phys. Rev. B 99, 134421 (2019).

    CAS  Google Scholar 

  11. Dong, S., Xiang, H. & Dagotto, E. Magnetoelectricity in multiferroics: a theoretical perspective. Natl. Sci. Rev. 6, 629–641 (2019).

    CAS  Google Scholar 

  12. Dong, S., Liu, J.-M., Cheong, S.-W. & Ren, Z. Multiferroic materials and magnetoelectric physics: symmetry, entanglement, excitation, and topology. Adv. Phys. 64, 519–626 (2015).

    CAS  Google Scholar 

  13. Dubovik, V. & Tugushev, V. Toroid moments in electrodynamics and solid-state physics. Phys. Rep. 187, 145–202 (1990).

    Google Scholar 

  14. Lin, L.-F., Zhang, Y., Moreo, A., Dagotto, E. & Dong, S. Frustrated dipole order induces noncollinear proper ferrielectricity in two dimensions. Phys. Rev. Lett. 123, 067601 (2019).

    CAS  Google Scholar 

  15. Prosandeev, S., Malashevich, A., Raevski, I. P. & Bellaiche, L. Dynamical magnetoelectric effects associated with ferroelectric domain walls. Phys. Rev. B 91, 100101 (2015).

    Google Scholar 

  16. Prosandeev, S. et al. Natural optical activity and its control by electric field in electrotoroidic systems. Phys. Rev. B 87, 195111 (2013).

    Google Scholar 

  17. Prosandeev, S., Ponomareva, I., Naumov, I., Kornev, I. & Bellaiche, L. Original properties of dipole vortices in zero-dimensional ferroelectrics. J. Phys. Condens. Matter 20, 193201 (2008).

    Google Scholar 

  18. Prosandeev, S., Kornev, I. & Bellaiche, L. Tensors in ferroelectric nanoparticles: first-principles-based simulations. Phys. Rev. B 76, 012101 (2007).

    Google Scholar 

  19. Nahas, Y. et al. Discovery of stable skyrmionic state in ferroelectric nanocomposites. Nat. Commun. 6, 8542 (2015).

    CAS  Google Scholar 

  20. Lu, L. et al. Topological defects with distinct dipole configurations in PbTiO3/SrTiO3 multilayer films. Phys. Rev. Lett. 120, 177601 (2018).

    Google Scholar 

  21. Yadav, A. K. et al. Observation of polar vortices in oxide superlattices. Nature 530, 198–201 (2016).

    CAS  Google Scholar 

  22. Jia, C.-L., Urban, K. W., Alexe, M., Hesse, D. & Vrejoiu, I. Direct observation of continuous electric dipole rotation in flux-closure domains in ferroelectric Pb(Zr,Ti)O3. Science 331, 1420–1423 (2011).

    CAS  Google Scholar 

  23. Nelson, C. T. et al. Spontaneous vortex nanodomain arrays at ferroelectric heterointerfaces. Nano Lett. 11, 828–834 (2011).

    CAS  Google Scholar 

  24. Zhang, Q. et al. Nanoscale bubble domains and topological transitions in ultrathin ferroelectric films. Adv. Mater. 29, 1702375 (2017).

    Google Scholar 

  25. Das, S. et al. Observation of room-temperature polar skyrmions. Nature 568, 368–372 (2019).

    CAS  Google Scholar 

  26. Prosandeev, S. et al. In Nanoscale Ferroelectrics and Multiferroics (eds Algueró, M. et al.) 700–728 (John Wiley, 2016).

  27. Naumov, I. I., Bellaiche, L. & Fu, H. Unusual phase transitions in ferroelectric nanodisks and nanorods. Nature 432, 737–740 (2004).

    CAS  Google Scholar 

  28. Erb, K. C. & Hlinka, J. Vector, bidirector, and Bloch skyrmion phases induced by structural crystallographic symmetry breaking. Phys. Rev. B 102, 024110 (2020).

    CAS  Google Scholar 

  29. Bellaiche, L., Gui, Z. & Kornev, I. A. A simple law governing coupled magnetic orders in perovskites. J. Phys. Condens. Matter 24, 312201 (2012).

    CAS  Google Scholar 

  30. Zhao, H. J., Íñiguez, J., Chen, X. M. & Bellaiche, L. Origin of the magnetization and compensation temperature in rare-earth orthoferrites and orthochromates. Phys. Rev. B 93, 014417 (2016).

    Google Scholar 

  31. White, R. L. Review of recent work on the magnetic and spectroscopic properties of the rare-earth orthoferrites. J. Appl. Phys. 40, 1061–1069 (1969).

    CAS  Google Scholar 

  32. Bousquet, E. & Cano, A. Non-collinear magnetism in multiferroic perovskites. J. Phys. Condens. Matter 28, 123001 (2016).

    Google Scholar 

  33. Zhao, H. J., Ren, W., Yang, Y., Chen, X. M. & Bellaiche, L. Effect of chemical and hydrostatic pressures on structural and magnetic properties of rare-earth orthoferrites: a first-principles study. J. Phys. Condens. Matter 25, 466002 (2013).

    Google Scholar 

  34. Varignon, J., Bristowe, N. C. & Ghosez, P. Electric field control of Jahn–Teller distortions in bulk perovskites. Phys. Rev. Lett. 116, 057602 (2016).

    Google Scholar 

  35. Yang, Y., Ren, W., Stengel, M., Yan, X. H. & Bellaiche, L. Revisiting properties of ferroelectric and multiferroic thin films under tensile strain from first principles. Phys. Rev. Lett. 109, 057602 (2012).

    Google Scholar 

  36. Yang, Y., Stengel, M., Ren, W., Yan, X. H. & Bellaiche, L. Epitaxial short-period PbTiO3/BiFeO3 superlattices studied by first-principles calculations. Phys. Rev. B 86, 144114 (2012).

    Google Scholar 

  37. Zhao, H. J. et al. Creating multiferroics with large tunable electrical polarization from paraelectric rare-earth orthoferrites. J. Phys.: Condens. Matter 26, 472201 (2014).

    Google Scholar 

  38. Belik, A. A., Stefanovich, S. Y., Lazoryak, B. I. & Takayama-Muromachi, E. BiInO3: a polar oxide with GdFeO3-type perovskite structure. Chem. Mater. 18, 1964–1968 (2006).

    CAS  Google Scholar 

  39. Katsura, H., Nagaosa, N. & Balatsky, A. V. Spin current and magnetoelectric effect in noncollinear magnets. Phys. Rev. Lett. 95, 057205 (2005).

    Google Scholar 

  40. Bellaiche, L. & Íñiguez, J. Universal collaborative couplings between oxygen-octahedral rotations and antiferroelectric distortions in perovskites. Phys. Rev. B 88, 014104 (2013).

    Google Scholar 

  41. Bousquet, E. et al. Improper ferroelectricity in perovskite oxide artificial superlattices. Nature 452, 732–736 (2008).

    CAS  Google Scholar 

  42. Benedek, N. A. & Fennie, C. J. Hybrid improper ferroelectricity: a mechanism for controllable polarization–magnetization coupling. Phys. Rev. Lett. 106, 107204 (2011).

    Google Scholar 

  43. Mulder, A. T., Benedek, N. A., Rondinelli, J. M. & Fennie, C. J. Turning ABO3 antiferroelectrics into ferroelectrics: design rules for practical rotation-driven ferroelectricity in double perovskites and A3B2O7 Ruddlesden–Popper compounds. Adv. Funct. Mater. 23, 4810–4820 (2013).

    CAS  Google Scholar 

  44. Rondinelli, J. M. & Fennie, C. J. Octahedral rotation-induced ferroelectricity in cation ordered perovskites. Adv. Mater. 24, 1961–1968 (2012).

    CAS  Google Scholar 

  45. Zhao, H. J., Íñiguez, J., Ren, W., Chen, X. M. & Bellaiche, L. Atomistic theory of hybrid improper ferroelectricity in perovskites. Phys. Rev. B 89, 174101 (2014).

    Google Scholar 

  46. Wojdeł, J. C. & Íñiguez, J. Ferroelectric transitions at ferroelectric domain walls found from first principles. Phys. Rev. Lett. 112, 247603 (2014).

    Google Scholar 

  47. Wang, Y. J., Chen, D., Tang, Y. L., Zhu, Y. L. & Ma, X. L. Origin of the Bloch-type polarization components at the 180∘ domain walls in ferroelectric PbTiO3. J. Appl. Phys. 116, 224105 (2014).

    Google Scholar 

  48. Hlinka, J. & Márton, P. Phenomenological model of a 90∘ domain wall in BaTiO3-type ferroelectrics. Phys. Rev. B 74, 104104 (2006).

    Google Scholar 

  49. Gonçalves, M. A. P., Escorihuela-Sayalero, C., Garca-Fernández, P., Junquera, J. & Íñiguez, J. Theoretical guidelines to create and tune electric skyrmion bubbles. Sci. Adv. 5, eaau7023 (2019).

    Google Scholar 

  50. Kresse, G. & Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 54, 11169–11186 (1996).

    CAS  Google Scholar 

  51. Kresse, G. & Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B 59, 1758–1775 (1999).

    CAS  Google Scholar 

  52. Csonka, G. I. et al. Assessing the performance of recent density functionals for bulk solids. Phys. Rev. B 79, 155107 (2009).

    Google Scholar 

  53. Blöchl, P. E. Projector augmented-wave method. Phys. Rev. B 50, 17953–17979 (1994).

    Google Scholar 

  54. Koster, G. F., Dimmock, J. D., Wheeler, R. G. & Statz, H. Properties of the Thirty-Two Point Group (MIT Press, 1963).

  55. Momma, K. & Izumi, F. VESTA3 for three-dimensional visualization of crystal, volumetric and morphology data. J. Appl. Crystal. 44, 1272–1276 (2011).

    CAS  Google Scholar 

  56. Hunter, J. D. Matplotlib: a 2D graphics environment. Comput. Sci. Eng. 9, 90–95 (2007).

    Google Scholar 

  57. Ceperley, D. M. & Alder, B. J. Ground state of the electron gas by a stochastic method. Phys. Rev. Lett. 45, 566–569 (1980).

    CAS  Google Scholar 

  58. Dudarev, S. L., Botton, G. A., Savrasov, S. Y., Humphreys, C. J. & Sutton, A. P. Electron-energy-loss spectra and the structural stability of nickel oxide: an LSDA+U study. Phys. Rev. B 57, 1505–1509 (1998).

    CAS  Google Scholar 

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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.

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Authors and Affiliations

  1. Physics Department and Institute for Nanoscience and Engineering, University of Arkansas, Fayetteville, AR, USA

    Hong Jian Zhao, Peng Chen, Sergey Prosandeev & Laurent Bellaiche

  2. Quantum Materials Theory, Italian Institute of Technology, Genoa, Italy

    Sergey Artyukhin

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  1. Hong Jian Zhao
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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.

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Correspondence to Peng Chen or Laurent Bellaiche.

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Supplementary Figs. 1-7, Discussion I–VII, Tables I–VI and refs. 1–22.

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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

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