- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Letters

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Antiskyrmions in Ferroelectric Barium Titanate

Mauro A. P. Gonçalves, Marek Paściak, and Jiří Hlinka*

  • *Contact author: hlinka@fzu.cz
PDF

Phys. Rev. Lett. 133, 066802 – Published 9 August, 2024

DOI: https://doi.org/10.1103/PhysRevLett.133.066802

Abstract

Typical magnetic skyrmion is a string of inverted magnetization within a ferromagnet, protected by a sleeve of a vortexlike spin texture, such that its cross-section carries an integer topological charge. Some magnets form antiskyrmions, the antiparticle strings which carry an opposite topological charge. Here we demonstrate that topologically equivalent but purely electric antiskyrmion can exist in a ferroelectric material as well. In particular, our computer experiments reveal that the archetype ferroelectric, barium titanate, can host antiskyrmions at zero field. The polarization pattern around their cores reminds ring windings of decorative knots rather than the typical magnetic antiskyrmion texture. We show that the antiskyrmion of barium titanate has just 2–3 nm in diameter, a hexagonal cross section, and an exotic topological charge with doubled magnitude and opposite sign when compared to the standard skyrmion string.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (60)

  1. S. Mühlbauer, B. Binz, F. Jonietz, C. Pfleiderer, A. Rosch, A. Neubauer, R. Georgii, and P. Böni, Skyrmion lattice in a chiral magnet, Science 323, 915 (2009).
  2. U. K. Rößler, A. N. Bogdanov, and C. Pfleiderer, Spontaneous skyrmion ground states in magnetic metals, Nature (London) 442, 797 (2006).
  3. A. Fert, N. Reyren, and V. Cros, Magnetic skyrmions: Advances in physics and potential applications, Nat. Rev. Mater. 2, 17031 (2017).
  4. A. Neubauer, C. Pfleiderer, B. Binz, A. Rosch, R. Ritz, P. G. Niklowitz, and P. Böni, Topological Hall effect in the A phase of MnSi, Phys. Rev. Lett. 102, 186602 (2009).
  5. T. Schulz, R. Ritz, A. Bauer, M. Halder, M. Wagner, C. Franz, C. Pfleiderer, K. Everschor, M. Garst, and A. Rosch, Emergent electrodynamics of skyrmions in a chiral magnet, Nat. Phys. 8, 301 (2012).
  6. P. Bruno, V. K. Dugaev, and M. Taillefumier, Topological Hall effect and Berry phase in magnetic nanostructures, Phys. Rev. Lett. 93, 096806 (2004).
  7. J. Zang, M. Mostovoy, J. H. Han, and N. Nagaosa, Dynamics of skyrmion crystals in metallic thin films, Phys. Rev. Lett. 107, 136804 (2011).
  8. K. Litzius, I. Lemesh, B. Krüger, P. Bassirian, L. Caretta, K. Richter, F. Büttner, K. Sato, O. A. Tretiakov, J. Förster, R. M. Reeve, M. Weigand, I. Bykova, H. Stoll, G. Schütz, G. S. D. Beach, and M. Kläui, Skyrmion Hall effect revealed by direct time-resolved X-ray microscopy, Nat. Phys. 13, 170 (2017).
  9. W. Jiang, X. Zhang, G. Yu, W. Zhang, X. Wang, M. B. Jungfleisch, J. E. Pearson, X. Cheng, O. Heinonen, K. L. Wang, Y. Zhou, A. Hoffmann, and S. G. E. te Velthuis, Direct observation of the skyrmion Hall effect, Nat. Phys. 13, 162 (2017).
  10. Y. Fujishiro, N. Kanazawa, T. Nakajima, X. Z. Yu, K. Ohishi, Y. Kawamura, K. Kakurai, T. Arima, H. Mitamura, A. Miyake, K. Akiba, M. Tokunaga, A. Matsuo, K. Kindo, T. Koretsune, R. Arita, and Y. Tokura, Topological transitions among skyrmion- and hedgehog-lattice states in cubic chiral magnets, Nat. Commun. 10, 1059 (2019).
  11. N. Kent, N. Reynolds, D. Raftrey, I. T. G. Campbell, S. Virasawmy, S. Dhuey, R. V. Chopdekar, A. Hierro-Rodriguez, A. Sorrentino, E. Pereiro, S. Ferrer, F. Hellman, P. Sutcliffe, and P. Fischer, Creation and observation of Hopfions in magnetic multilayer systems, Nat. Commun. 12, 1562 (2021).
  12. S. Zhang, F. Kronast, G. van der Laan, and T. Hesjedal, Real-space observation of skyrmionium in a ferromagnet-magnetic topological insulator heterostructure, Nano Lett. 18, 1057 (2018).
  13. M. Finazzi, M. Savoini, A. R. Khorsand, A. Tsukamoto, A. Itoh, L. Duò, A. Kirilyuk, Th. Rasing, and M. Ezawa, Laser-induced magnetic nanostructures with tunable topological properties, Phys. Rev. Lett. 110, 177205 (2013).
  14. J. Barker and O. A. Tretiakov, Static and dynamical properties of antiferromagnetic skyrmions in the presence of applied current and temperature, Phys. Rev. Lett. 116, 147203 (2016).
  15. C. Back, V. Cros, H. Ebert, K. Everschor-Sitte, A. Fert, M. Garst, Tianping Ma, S. Mankovsky, T. L. Monchesky, M. Mostovoy, N. Nagaosa, S. S. P. Parkin, C. Pfleiderer, N. Reyren, A. Rosch, Y. Taguchi, Y. Tokura, K. von Bergmann, and J. Zang, The 2020 skyrmionics roadmap, J. Phys. D 53, 363001 (2020).
  16. S. Das et al., Observation of room-temperature polar skyrmions, Nature (London) 568, 368 (2019).
  17. M. A. P. Gonçalves, C. Escorihuela-Sayalero, P. Garca-Fernández, J. Junquera, and J. Íñiguez, Theoretical guidelines to create and tune electric skyrmion bubbles, Sci. Adv. 5, eaau7023 (2019).
  18. Y. Nahas, S. Prokhorenko, L. Louis, Z. Gui, I. Kornev, and L. Bellaiche, Discovery of stable skyrmionic state in ferroelectric nanocomposites, Nat. Commun. 6, 8542 (2015).
  19. S. Das et al., Local negative permittivity and topological phase transition in polar skyrmions, Nat. Mater. 20, 194 (2021).
  20. R. Zhu et al., Dynamics of polar skyrmion bubbles under electric fields, Phys. Rev. Lett. 129, 107601 (2022).
  21. K. T. Kim et al., Chiral structures of electric polarization vectors quantified by X-ray resonant scattering, Nat. Commun. 13, 1769 (2022).
  22. Y.-T. Shao, S. Das, Z. Hong, R. Xu, S. Chandrika, F. Gómez-Ortiz, P. García-Fernández, L.-Q. Chen, H. Y. Hwang, J. Junquera, L. W. Martin, R. Ramesh, and D. A. Muller, Emergent chirality in a polar meron to skyrmion phase transition, arXiv:2101.04545.
  23. P. Shafer, P. García-Fernández, P. Aguado-Puente, A. R. Damodaran, A. K. Yadav, C. T. Nelson, S.-L. Hsu, J. C. Wojdeł, J. Íñiguez, L. W. Martin, E. Arenholz, J. Junquera, and R. Ramesh, Emergent chirality in the electric polarization texture of titanate superlattices, Proc. Natl. Acad. Sci. U.S.A. 115, 915 (2018).
  24. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevLett.133.066802 for more information about the terminological issues (note 1), invariant sign of the skyrmion topological charge (note 2), description of the model (note 3), computational details (note 4), histograms of atomic displacement sizes (note 5), small displacement stability (note 6), stability vs temperature fluctuations (Suppl. note 7), sensitivity to the size of the simulation box (note 8), antiskyrmion geometry elaboration and decay of R180 domain walls (note 9), nanodomains in lead titanate and potassium niobate (note 10), and auxiliary comparison of shell model and DFT calculations of a dense system of planar R180 domain walls (note 11).
  25. S. Seki and M. Mochizuki, Skyrmions in Magnetic Materials (Springer International Publishing, New York, 2016).
  26. N. Nagaosa and Y. Tokura, Topological properties and dynamics of magnetic skyrmions, Nat. Nanotechnol. 8, 899 (2013).
  27. I. Kézsmárki, S. Bordács, P. Milde, E. Neuber, L. M. Eng, J. S. White, H. M. Rønnow, C. D. Dewhurst, M. Mochizuki, K. Yanai, H. Nakamura, D. Ehlers, V. Tsurkan, and A. Loidl, Néel-type skyrmion lattice with confined orientation in the polar magnetic semiconductor GaV4S8, Nat. Mater. 14, 1116 (2015).
  28. P. Marton, I. Rychetsky, and J. Hlinka, Domain walls of ferroelectric BaTiO3 within the Ginzburg-Landau-Devonshire phenomenological model, Phys. Rev. B 81, 144125 (2010).
  29. J. C. Wojdeł and J. Íñiguez, Ferroelectric transitions at ferroelectric domain walls found from first principles, Phys. Rev. Lett. 112, 247603 (2014).
  30. M. Taherinejad, D. Vanderbilt, P. Marton, V. Stepkova, and J. Hlinka, Bloch-type domain walls in rhombohedral BaTiO3, Phys. Rev. B 86, 155138 (2012).
  31. V. Stepkova, P. Marton, and J. Hlinka, Stress-induced phase transition in ferroelectric domain walls of BaTiO3, J. Phys. Condens. Matter 24, 212201 (2012).
  32. J. Hlinka, V. Stepkova, P. Marton, and P. Ondrejkovic, Topological Structures in Ferroic Materials, edited by J. Seidel (Springer, Switzerland, 2016), pp. 161–180.
  33. S. Tinte, M. G. Stachiotti, S. R. Phillpot, M. Sepliarsky, D. Wolf, and R. L. Migoni, Ferroelectric properties of BaxSr1−xTiO3 solid solutions obtained by molecular dynamics simulation, J. Phys. Condens. Matter 16, 3495 (2004).
  34. M. Sepliarsky, A. Asthagiri, S. R. Phillpot, M. G. Stachiotti, and R. L. Migoni, Atomic-level simulation of ferroelectricity in oxide materials, Curr. Opin. Solid State Mater. Sci. 9, 107 (2005).
  35. M. Paściak, T. R. Welberry, J. Kulda, S. Leoni, and J. Hlinka, Dynamic displacement disorder of cubic BaTiO3, Phys. Rev. Lett. 120, 167601 (2018).
  36. T. Hashimoto and H. Moriwake, Structure of amorphous BaTiO3 by molecular dynamics simulations using a shell model, Physica (Amsterdam) 579B, 411799 (2020).
  37. I. T. Todorov, W. Smith, K. Trachenko, and M. T. Dove, DL POLY 3: New dimensions in molecular dynamics simulations via massive parallelism, J. Mater. Chem. 16, 1911 (2006).
  38. J. D. Gale and A. L. Rohl, The General Utility Lattice Program (GULP), Mol. Simul. 29, 291 (2003).
  39. A. K. Nayak, V. Kumar, T. Ma, P. Werner, E. Pippel, R. Sahoo, F. Damay, U. K. Rößler, C. Felser, and S. S. P. Parkin, Magnetic antiskyrmions above room temperature in tetragonal Heusler materials, Nature (London) 548, 561 (2017).
  40. A. N. Bogdanov and D. A. Yablonskii, Thermodynamically stable “vortices” in magnetically ordered crystals. The mixed state of magnets, Zh. Eksp. Teor. Fiz. 95, 178 (1989).
  41. A. N. Bogdanov and C. Panagopoulos, Physical foundations and basic properties of magnetic skyrmions, Nat. Rev. Phys. 2, 492 (2020).
  42. K. C. Erb and J. Hlinka, Vector, bidirector, and Bloch skyrmion phases induced by structural crystallographic symmetry breaking, Phys. Rev. B 102, 024110 (2020).
  43. M. Hoffmann, B. Zimmermann, G. P. Müller, D. Schürhoff, N. S. Kiselev, C. Melcher, and S. Blügel, Antiskyrmions stabilized at interfaces by anisotropic Dzyaloshinskii-Moriya interactions, Nat. Commun. 8, 308 (2017).
  44. B. Houchmandzadeh, J. Lajzerowicz, and E. Salje, Order parameter coupling and chirality of domain walls, J. Phys. Condens. Matter 3, 5163 (1991).
  45. P. V. Yudin, A. K. Tagantsev, E. A. Eliseev, A. N. Morozovska, and N. Setter, Bichiral structure of ferroelectric domain walls driven by flexoelectricity, Phys. Rev. B 86, 134102 (2012).
  46. P. V. Yudin, A. K. Tagantsev, and N. Setter, Bistability of ferroelectric domain walls: Morphotropic boundary and streain effects, Phys. Rev. B 88, 024102 (2013).
  47. J. Harada, J. D. Axe, and G. Shirane, Neutron-scattering study of soft modes in cubic BaTiO3, Phys. Rev. B 4, 155 (1971).
  48. R. Comes, M. Lambert, and A. Guinier, The chain structure of BaTiO3 and KNbO3, Solid State Commun. 6, 715 (1968).
  49. N. Mohanta and E. Dagotto, Interfacial phase frustration stabilizes unconventional skyrmion crystals, npj Quantum Mater. 7, 76 (2022).
  50. D. Amoroso, P. Barone, and S. Picozzi, Spontaneous skyrmionic lattice from anisotropic symmetric exchange in a Ni-halide monolayer, Nat. Commun. 11, 5784 (2020).
  51. R. Ozawa, S. Hayami, and Y. Motome, Zero-field skyrmions with a high topological number in itinerant magnets, Phys. Rev. Lett. 118, 147205 (2017).
  52. A. O. Leonov and M. Mostovoy, Multiply periodic states and isolated skyrmions in an anisotropic frustrated magnet, Nat. Commun. 6, 8275 (2015).
  53. M. N. Potkina, I. S. Lobanov, O. A. Tretiakov, H. Jónsson, and V. M. Uzdin, Stability of long-lived antiskyrmions in the Mn-Pt-Sn tetragonal Heusler material, Phys. Rev. B 102, 134430 (2020).
  54. B. Dupé, C. N. Kruse, T. Dornheim, and S. Heinze, How to reveal metastable skyrmionic spin structures by spin-polarized scanning tunneling microscopy, New J. Phys. 18, 055015 (2016).
  55. S. Heinze, K. von Bergmann, M. Menzel, J. Brede, A. Kubetzka, R. Wiesendanger, G. Bihlmayer, and S. Blügel, Spontaneous atomic-scale magnetic skyrmion lattice in two dimensions, Nat. Phys. 7, 713 (2011).
  56. S. Z. Lin, A. Saxena, and C. D. Batista, Skyrmion fractionalization and merons in chiral magnets with easy-plane anisotropy, Phys. Rev. B 91, 224407 (2015).
  57. Yu. Tikhonov, S. Kondovych, J. Mangeri, M. Pavlenko, L. Baudry, A. Sené, A. Galda, S. Nakhmanson, O. Heinonen, A. Razumnaya, I. Luk’yanchuk, and V. M. Vinokur, Controllable skyrmion chirality in ferroelectrics, Sci. Rep. 10, 8657 (2020).
  58. V. Stepkova, P. Marton, N. Setter, and J. Hlinka, Closed-circuit domain quadruplets in BaTiO3 nanorods embedded in a SrTiO3 film, Phys. Rev. B 89, 060101(R) (2014).
  59. J. M. Soler, E. Artacho, J. D. Gale, A. García, J. Junquera, P. Ordejón, and D. Sánchez-Portal, The SIESTA method for ab initio order-N materials simulation, J. Phys. Condens. Matter 14, 2745 (2002).
  60. Z. Wu and R. E. Cohen, More accurate generalized gradient approximation for solids, Phys. Rev. B 73, 235116 (2006).

Outline

Information

Phys. Rev. Lett. 133, 066802– Published 9 August, 2024
  • Received 12 September 2023
  • Revised 16 May 2024
  • Accepted 21 June 2024
Crossmark - Check for updates button
Creative Commons Logo

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.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation