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
  • Letter
  • Open Access

Magnetoelectricity induced by rippling of magnetic nanomembranes and wires

Carmine Ortix1,* and Jeroen van den Brink2

  • 1Dipartimento di Fisica “E. R. Caianiello,” Universitá di Salerno, IT-84084 Fisciano (SA), Italy
  • 2Institute for Theoretical Solid State Physics, IFW Dresden, Helmholtzstrasse 20, D-01069 Dresden, Germany

  • *cortix@unisa.it

Phys. Rev. Research 5, L022063 – Published 23 June, 2023

DOI: https://doi.org/10.1103/PhysRevResearch.5.L022063

Abstract

Magnetoelectric crystals have the interesting property that they allow electric fields to induce magnetic polarizations, and vice versa, magnetic fields to generate ferroelectric polarizations. Having such a magnetoelectric coupling usually requires complex types of magnetic textures, e.g., of spiraling type. Here, we establish a previously unknown approach to generate linear magnetoelectric coupling in ferromagnetic insulators with intrinsic Dzyaloshinskii-Moriya interaction (DMI). We show that the effect of nanoscale curved geometries combined with the intrinsic DMI of the magnetic shell lead to a reorganization of the magnetic texture that spontaneously breaks inversion symmetry and thereby induces macroscopic magnetoelectric multipoles. Specifically, we prove that structural deformation in the form of controlled ripples activates a magnetoelectric monopole in the recently synthesized two-dimensional magnets. We also demonstrate that in zigzag-shaped ferromagnetic wires in planar architectures, a magnetic toroidal moment triggers direct linear magnetoelectric coupling.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (46)

  1. F. Guinea, M. I. Katsnelson, and A. K. Geim, Energy gaps and a zero-field quantum Hall effect in graphene by strain engineering, Nat. Phys. 6, 30 (2010).
  2. N. Levy, S. A. Burke, K. L. Meaker, M. Panlasigui, A. Zettl, F. Guinea, A. H. C. Neto, and M. F. Crommie, Strain-induced pseudo–magnetic fields greater than 300 tesla in graphene nanobubbles, Science 329, 544 (2010).
  3. Y. Jiang, J. Mao, J. Duan, X. Lai, K. Watanabe, T. Taniguchi, and E. Y. Andrei, Visualizing strain-induced pseudomagnetic fields in graphene through an hBn magnifying glass, Nano Lett. 17, 2839 (2017).
  4. P. Nigge, A. C. Qu, E. Lantagne-Hurtubise, E. Mårsell, S. Link, G. Tom, M. Zonno, M. Michiardi, M. Schneider, S. Zhdanovich, G. Levy, U. Starke, C. Gutierrez, D. Bonn, S. A. Burke, M. Franz, and A. Damascelli, Room temperature strain-induced Landau levels in graphene on a wafer-scale platform, Sci. Adv. 5, eaaw5593 (2019).
  5. J. Mao, S. P. Milovanović, M. Andelković, X. Lai, Y. Cao, K. Watanabe, T. Taniguchi, L. Covaci, F. M. Peeters, A. K. Geim, Y. Jiang, and E. Y. Andrei, Evidence of flat bands and correlated states in buckled graphene superlattices, Nature (London) 584, 215 (2020).
  6. C. Gong, L. Li, Z. Li, H. Ji, A. Stern, Y. Xia, T. Cao, W. Bao, C. Wang, Y. Wang, Z. Q. Qiu, R. J. Cava, S. G. Louie, J. Xia, and X. Zhang, Discovery of intrinsic ferromagnetism in two-dimensional van der Waals crystals, Nature (London) 546, 265 (2017).
  7. B. Huang, G. Clark, E. Navarro-Moratalla, D. R. Klein, R. Cheng, K. L. Seyler, D. Zhong, E. Schmidgall, M. A. McGuire, D. H. Cobden, W. Yao, D. Xiao, P. Jarillo-Herrero, and X. Xu, Layer-dependent ferromagnetism in a van der Waals crystal down to the monolayer limit, Nature (London) 546, 270 (2017).
  8. N. Samarth, Magnetism in flatland, Nature (London) 546, 216 (2017).
  9. K. S. Burch, D. Mandrus, and J.-G. Park, Magnetism in two-dimensional van der Waals materials, Nature (London) 563, 47 (2018).
  10. M. Gibertini, M. Koperski, A. F. Morpurgo, and K. S. Novoselov, Magnetic 2D materials and heterostructures, Nat. Nanotechnol. 14, 408 (2019).
  11. N. A. Spaldin, M. Fechner, E. Bousquet, A. Balatsky, and L. Nordström, Monopole-based formalism for the diagonal magnetoelectric response, Phys. Rev. B 88, 094429 (2013).
  12. R. Streubel, P. Fischer, F. Kronast, V. P. Kravchuk, D. D. Sheka, Y. Gaididei, O. G. Schmidt, and D. Makarov, Magnetism in curved geometries, J. Phys. D 49, 363001 (2016).
  13. D. D. Sheka, A perspective on curvilinear magnetism, Appl. Phys. Lett. 118, 230502 (2021).
  14. D. Makarov, O. M. Volkov, A. Kákay, O. V. Pylypovskyi, B. Budinská, and O. V. Dobrovolskiy, New dimension in magnetism and superconductivity: 3D and curvilinear nanoarchitectures, Adv. Mater. 34, 2101758 (2022).
  15. M. Yan, C. Andreas, A. Kakay, F. Garcia-Sanchez, and R. Hertel, Chiral symmetry breaking and pair-creation mediated Walker breakdown in magnetic nanotubes, Appl. Phys. Lett. 100, 252401 (2012).
  16. A. Fernández-Pacheco, R. Streubel, O. Fruchart, R. Hertel, P. Fischer, and R. P. Cowburn, Three-dimensional nanomagnetism, Nat. Commun. 8, 15756 (2017).
  17. D. Ghazaryan, M. T. Greenaway, Z. Wang, V. H. Guarochico-Moreira, I. J. Vera-Marun, J. Yin, Y. Liao, S. V. Morozov, O. Kristanovski, A. I. Lichtenstein, M. I. Katsnelson, F. Withers, A. Mishchenko, L. Eaves, A. K. Geim, K. S. Novoselov, and A. Misra, Magnon-assisted tunnelling in van der Waals heterostructures based on CrBr3, Nat. Electron. 1, 344 (2018).
  18. Z. Wang, I. Gutiérrez-Lezama, D. Dumcenco, N. Ubrig, T. Taniguchi, K. Watanabe, E. Giannini, M. Gibertini, and A. F. Morpurgo, Magnetization dependent tunneling conductance of ferromagnetic barriers, Nat. Commun. 12, 6659 (2021).
  19. J. Zhang, Y. Zhou, F. Wang, X. Shen, J. Wang, and X. Lu, Coexistence and Coupling of Spin-Induced Ferroelectricity and Ferromagnetism in Perovskites, Phys. Rev. Lett. 129, 117603 (2022).
  20. H. Murakawa, Y. Onose, S. Miyahara, N. Furukawa, and Y. Tokura, Ferroelectricity Induced by Spin-Dependent Metal-Ligand Hybridization in Ba2CoGe2O7, Phys. Rev. Lett. 105, 137202 (2010).
  21. N. A. Spaldin, M. Fiebig, and M. Mostovoy, The toroidal moment in condensed-matter physics and its relation to the magnetoelectric effect, J. Phys.: Condens. Matter 20, 434203 (2008).
  22. As noted in Ref. [11], magnetic states with finite magnetoelectric monopoles do not imply a diverging B field. The divergence of the magnetization is compensated for by the divergence of the H field.
  23. C. Ederer and N. A. Spaldin, Towards a microscopic theory of toroidal moments in bulk periodic crystals, Phys. Rev. B 76, 214404 (2007).
  24. H. Yang, A. Thiaville, S. Rohart, A. Fert, and M. Chshiev, Anatomy of Dzyaloshinskii-Moriya Interaction at Co/Pt Interfaces, Phys. Rev. Lett. 115, 267210 (2015).
  25. C. Xu, J. Feng, S. Prokhorenko, Y. Nahas, H. Xiang, and L. Bellaiche, Topological spin texture in Janus monolayers of the chromium trihalides Cr(I,X)3, Phys. Rev. B 101, 060404(R) (2020).
  26. F. Zhang, X. Li, Y. Wu, X. Wang, J. Zhao, and W. Gao, Strong Dzyaloshinskii-Moriya interaction in monolayer CrI3 on metal substrates, Phys. Rev. B 106, L100407 (2022).
  27. J. Liu, M. Shi, J. Lu, and M. P. Anantram, Analysis of electrical-field-dependent Dzyaloshinskii-Moriya interaction and magnetocrystalline anisotropy in a two-dimensional ferromagnetic monolayer, Phys. Rev. B 97, 054416 (2018).
  28. Y. Gaididei, V. P. Kravchuk, and D. D. Sheka, Curvature Effects in Thin Magnetic Shells, Phys. Rev. Lett. 112, 257203 (2014).
  29. V. P. Kravchuk, U. K. Rößler, O. M. Volkov, D. D. Sheka, J. van den Brink, D. Makarov, H. Fuchs, H. Fangohr, and Y. Gaididei, Topologically stable magnetization states on a spherical shell: Curvature-stabilized skyrmions, Phys. Rev. B 94, 144402 (2016).
  30. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.5.L022063 for the details on the magnetic energy functional, the estimate of the magnetoelectric monopolization in Janus monolayers of chromium trihalides, and the multiferroic Landau theory.
  31. We note that magnetochirality is neither necessary nor sufficient for the occurrence of magnetoelectric multipole moments. Magnetic states with mirror symmetries can display a finite toroidal moment as exemplified by the case of a magnetic vortex on a square palette [21]. Combined antiunitary symmetries can instead force the multipoles of magnetochiral states to vanish.
  32. R. D. King-Smith and D. Vanderbilt, Theory of polarization of crystalline solids, Phys. Rev. B 47, 1651 (1993).
  33. R. Resta, Macroscopic polarization in crystalline dielectrics: The geometric phase approach, Rev. Mod. Phys. 66, 899 (1994).
  34. D. Vanderbilt and R. D. King-Smith, Electric polarization as a bulk quantity and its relation to surface charge, Phys. Rev. B 48, 4442 (1993).
  35. M. Mostovoy, Ferroelectricity in Spiral Magnets, Phys. Rev. Lett. 96, 067601 (2006).
  36. J. J. Betouras, G. Giovannetti, and J. van den Brink, Multiferroicity Induced by Dislocated Spin-Density Waves, Phys. Rev. Lett. 98, 257602 (2007).
  37. The difference between the two mechanisms is also shown in the fact that helicoidal spin density waves [35] do not possess magnetoelectric multipoles.
  38. O. M. Volkov, D. D. Sheka, Y. Gaididei, V. P. Kravchuk, U. K. Rößler, J. Fassbender, and D. Makarov, Mesoscale Dzyaloshinskii-Moriya interaction: Geometrical tailoring of the magnetochirality, Sci. Rep. 8, 866 (2018).
  39. D. D. Sheka, O. V. Pylypovskyi, O. M. Volkov, K. V. Yershov, V. P. Kravchuk, and D. Makarov, Fundamentals of curvilinear ferromagnetism: Statics and dynamics of geometrically curved wires and narrow ribbons, Small 18, 2105219 (2022).
  40. D. Cortés-Ortuño and P. Landeros, Influence of the Dzyaloshinskii–Moriya interaction on the spin-wave spectra of thin films, J. Phys.: Condens. Matter 25, 156001 (2013).
  41. O. M. Volkov, U. K. Rössler, J. Fassbender, and D. Makarov, Concept of artificial magnetoelectric materials via geometrically controlling curvilinear helimagnets, J. Phys. D 52, 345001 (2019).
  42. D. D. Sheka, O. V. Pylypovskyi, P. Landeros, Y. Gaididei, A. Kákay, and D. Makarov, Nonlocal chiral symmetry breaking in curvilinear magnetic shells, Commun. Phys. 3, 128 (2020).
  43. B. B. Van Aken, J.-P. Rivera, H. Schmid, and M. Fiebig, Observation of ferrotoroidic domains, Nature (London) 449, 702 (2007).
  44. J. Lehmann, C. Donnelly, P. M. Derlet, L. J. Heyderman, and M. Fiebig, Poling of an artificial magneto-toroidal crystal, Nat. Nanotechnol. 14, 141 (2019).
  45. S. Bhowal and N. A. Spaldin, Magnetoelectric Classification of Skyrmions, Phys. Rev. Lett. 128, 227204 (2022).
  46. P. Gentile, M. Cuoco, O. M. Volkov, Z.-J. Ying, I. J. Vera-Marun, D. Makarov, and C. Ortix, Electronic materials with nanoscale curved geometries, Nat. Electron. 5, 551 (2022).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation