- Physical Review Journals
All JournalsPhysics Magazine

Physical Review B

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
  • Editors' Suggestion
  • Letter
  • Open Access

Antichiral ferromagnetism

Filipp N. Rybakov1,*, Anastasiia Pervishko2, Olle Eriksson3, and Egor Babaev1

  • 1Department of Physics, KTH Royal Institute of Technology, SE-10691 Stockholm, Sweden
  • 2Skolkovo Institute of Science and Technology, Moscow 121205, Russia
  • 3Department of Physics and Astronomy, Uppsala University, Box 516, SE-75120 Uppsala, Sweden

  • *prybakov@kth.se
PDF

Phys. Rev. B 104, L020406 – Published 13 July, 2021

DOI: https://doi.org/10.1103/PhysRevB.104.L020406

Abstract

Here, by combining a symmetry-based analysis with numerical computations, we predict a different kind of magnetic ordering—antichiral ferromagnetism. This term aims to reflect that spontaneous modulation of the magnetization direction m(r) appears in a way that both types of chirality (handedness) exist simultaneously, and alternate in space. Without loss of generality, we focus our investigation on crystals with full tetrahedral symmetry where chiral interaction terms—Lifshitz invariants—are forbidden by symmetry. However, we demonstrate that the leading chirality-related term leads to nontrivial smooth magnetic textures exhibiting antichirality. In addition to the unconventional ground state, the revealed ordering gives rise to rich phenomena such as unique magnetic domains and skyrmions.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (50)

  1. D. E. Kharzeev, The chiral magnetic effect and anomaly-induced transport, Prog. Part. Nucl. Phys. 75, 133 (2014).
  2. P. Bak and M. H. Jensen, Theory of helical magnetic structures and phase transitions in MnSi and FeGe, J. Phys. C 13, L881 (1980).
  3. Y. Tokunaga, X. Z. Yu, J. S. White, H. M. Rønnow, D. Morikawa, Y. Taguchi, and Y. Tokura, A new class of chiral materials hosting magnetic skyrmions beyond room temperature, Nat. Commun. 6, 7638 (2015).
  4. S. S. P. Parkin, M. Hayashi, and L. Thomas, Magnetic domain-wall racetrack memory, Science 320, 190 (2008).
  5. A. Fert, V. Cros, and J. Sampaio, Skyrmions on the track, Nat. Nanotechnol. 8, 152 (2013).
  6. K. Koumpouras, A. Bergman, O. Eriksson, and D. Yudin, A spin dynamics approach to solitonics, Sci. Rep. 6, 25685 (2016).
  7. C. Back, V. Cros, H. Ebert, K. Everschor-Sitte, A. Fert, M. Garst, T. 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).
  8. Y. Kitano and T. Nagamiya, Magnetization process of a screw spin system. II, Prog. Theor. Phys. 31, 1 (1964).
  9. Y. A. Izyumov, Modulated, or long-periodic, magnetic structures of crystals, Sov. Phys. Usp. 27, 845 (1984).
  10. R. A. P. Rogers, Some differential properties of the orthogonal trajectories of a congruence of curves, with an application to curl and divergence of vectors, Proc. R. Ir. Acad., Sect. A: Math. Phys. Sci. 29, 92 (1912).
  11. Y. Aminov, The Geometry of Vector Fields (Gordon and Breach, Amsterdam, 2000).
  12. J. Villain, La structure des substances magnetiques, J. Phys. Chem. Solids 11, 303 (1959).
  13. A. Yoshimori, A new type of antiferromagnetic structure in the rutile type crystal, J. Phys. Soc. Jpn. 14, 807 (1959).
  14. S. Paul, S. Haldar, S. von Malottki, and S. Heinze, Role of higher-order exchange interactions for skyrmion stability, Nat. Commun. 11, 4756 (2020).
  15. M. Takahashi, Half-filled Hubbard model at low temperature, J. Phys. C: Solid State Phys. 10, 1289 (1977).
  16. A. H. MacDonald, S. M. Girvin, and D. Yoshioka, tU expansion for the Hubbard model, Phys. Rev. B 37, 9753 (1988).
  17. Ph. Kurz, G. Bihlmayer, K. Hirai, and S. Blügel, Three-Dimensional Spin Structure on a Two-Dimensional Lattice: Mn/Cu(111), Phys. Rev. Lett. 86, 1106 (2001).
  18. 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).
  19. A. O. Leonov and M. Mostovoy, Multiply periodic states and isolated skyrmions in an anisotropic frustrated magnet, Nat. Commun. 6, 8275 (2015).
  20. S. Hayami, R. Ozawa, and Y. Motome, Effective bilinear-biquadratic model for noncoplanar ordering in itinerant magnets, Phys. Rev. B 95, 224424 (2017).
  21. N. Romming, H. Pralow, A. Kubetzka, M. Hoffmann, S. von Malottki, S. Meyer, B. Dupé, R. Wiesendanger, K. von Bergmann, and S. Heinze, Competition of Dzyaloshinskii-Moriya and Higher-Order Exchange Interactions in Rh/Fe Atomic Bilayers on Ir(111), Phys. Rev. Lett. 120, 207201 (2018).
  22. S. Meyer, M. Perini, S. von Malottki, A. Kubetzka, R. Wiesendanger, K. von Bergmann, and S. Heinze, Isolated zero field sub-10 nm skyrmions in ultrathin Co films, Nat. Commun. 10, 3823 (2019).
  23. S. M. Stishov and A. E. Petrova, Itinerant helimagnet MnSi, Phys. Usp. 54, 1117 (2011).
  24. V. G. Bar'yakhtar and E. P. Stefanovsky, Spin wave spectrum in antiferromagnets having a spiral magnetic structure, Sov. Phys. Solid State 11, 1566 (1970).
  25. S. Sportouch and M. G. Kanatzidis, Th3Co3Sb4: A new room temperature magnet, J. Solid State Chem. 162, 158 (2001).
  26. S. Lee, H. Xu, H. Xu, R. Jacobs, and D. Morgan, Valleyite: A new magnetic mineral with the sodalite-type structure, Am. Mineral. 104, 1238 (2019).
  27. T. Komatsubara, T. Suzuki, and E. Hirahara, Magnetization process and spin-structure diagram in manganese phosphide single crystal, J. Phys. Soc. Jpn. 28, 317 (1970).
  28. K. Siratori, J. Akimitsu, E. Kita, and M. Nishi, A method of controlling the sense of the screw spin structure, J. Phys. Soc. Jpn. 48, 1111 (1980).
  29. S.-Z. Lin and S. Hayami, Ginzburg-Landau theory for skyrmions in inversion-symmetric magnets with competing interactions, Phys. Rev. B 93, 064430 (2016).
  30. S. Hayami, S.-Z. Lin, Y. Kamiya, and C. D. Batista, Vortices, skyrmions, and chirality waves in frustrated Mott insulators with a quenched periodic array of impurities, Phys. Rev. B 94, 174420 (2016).
  31. I. A. Ado, A. Qaiumzadeh, A. Brataas, and M. Titov, Chiral ferromagnetism beyond Lifshitz invariants, Phys. Rev. B 101, 161403(R) (2020).
  32. A. N. Bogdanov and D. A. Yablonskii, Thermodynamically stable “vortices” in magnetically ordered crystals. the mixed state of magnets, Sov. Phys. JETP 68, 101 (1989).
  33. I. Ado, presentation delivered at the SPICE-SPIN+X Seminars, Mainz, Germany, February 2020 (unpublished).
  34. M. Titov, online presentation delivered at the Ultrafast Dynamics of Correlated Electrons in Solids workshop, May 2020, https://youtu.be/OgpP13ZcDRw.
  35. S. Grytsiuk, J.-P. Hanke, M. Hoffmann, J. Bouaziz, O. Gomonay, G. Bihlmayer, S. Lounis, Y. Mokrousov, and S. Blügel, Topological–chiral magnetic interactions driven by emergent orbital magnetism, Nat. Commun. 11, 511 (2020).
  36. R. Cardias, A. Szilva, M. M. Bezerra-Neto, M. S. Ribeiro, A. Bergman, Y. O. Kvashnin, J. Fransson, A. B. Klautau, O. Eriksson, and L. Nordström, First-principles Dzyaloshinskii–Moriya interaction in a non-collinear framework, Sci. Rep. 10, 20339 (2020).
  37. S. Mankovsky, S. Polesya, and H. Ebert, Extension of the standard Heisenberg Hamiltonian to multispin exchange interactions, Phys. Rev. B 101, 174401 (2020).
  38. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevB.104.L020406 for data points and examples of compounds with the Td crystallographic point group.
  39. J. Müller, J. Rajeswari, P. Huang, Y. Murooka, H. M. Rønnow, F. Carbone, and A. Rosch, Magnetic Skyrmions and Skyrmion Clusters in the Helical Phase of Cu2OSeO3, Phys. Rev. Lett. 119, 137201 (2017).
  40. P. Schoenherr, J. Müller, L. Köhler, A. Rosch, N. Kanazawa, Y. Tokura, M. Garst, and D. Meier, Topological domain walls in helimagnets, Nat. Phys. 14, 465 (2018).
  41. M. Speight and T. Winyard, Skyrmions and spin waves in frustrated ferromagnets at low applied magnetic field, Phys. Rev. B 101, 134420 (2020).
  42. M. F. Crommie, C. P. Lutz, and D. M. Eigler, Imaging standing waves in a two-dimensional electron gas, Nature (London) 363, 524 (1993).
  43. P. Schattschneider, S. Rubino, C. Hébert, J. Rusz, J. Kuneš, P. Novák, E. Carlino, M. Fabrizioli, G. Panaccione, and G. Rossi, Detection of magnetic circular dichroism using a transmission electron microscope, Nature (London) 441, 486 (2006).
  44. I. A. Ado, O. Tchernyshyov, and M. Titov, Non-collinear ground state from a four-spin chiral exchange in a tetrahedral magnet, arXiv:2012.07666.
  45. P. Atkins and R. Friedman, Molecular Quantum Mechanics (Oxford University Press, Oxford, U.K., 2005).
  46. Y. Xu and X. Chen, Exploring the group representation theory of the full symmetry of regular tetrahedron, arXiv:1910.07143 (2019).
  47. D. Arovas, Lecture Notes on Group Theory in Physics (University of California, San Diego, 2020), https://courses.physics.ucsd.edu/2016/Spring/physics220/LECTURES/GROUP_THEORY.pdf.
  48. M. Donahue and R. McMichael, Exchange energy representations in computational micromagnetics, Phys. B: Condens. Matter 233, 272 (1997).
  49. F. N. Rybakov and E. Babaev, Excalibur software, http://quantumandclassical.com/excalibur/.
  50. F. N. Rybakov, A. B. Borisov, S. Blügel, and N. S. Kiselev, New Type of Stable Particlelike States in Chiral Magnets, Phys. Rev. Lett. 115, 117201 (2015).

Outline

Information

Phys. Rev. B 104, L020406– Published 13 July, 2021
  • Received 22 December 2020
  • Revised 18 March 2021
  • Accepted 25 June 2021
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. Funded by Bibsam.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation