Skip to content
naulon

No retraction, correction or concern found when last checked on Oct 25, 2026.

Multiply periodic states and isolated skyrmions in an anisotropic frustrated magnet

A. O. Leonov, M. Mostovoy

Nature Communications · 2015 · CC BY

doi:10.1038/ncomms9275

Abstract

Multiply periodic states appear in a wide variety of physical contexts, such as the Rayleigh–Bénard convection, Faraday waves, liquid crystals and skyrmion crystals recently observed in chiral magnets. Here we study the phase diagram of an anisotropic frustrated magnet which contains five different multiply periodic states including the skyrmion crystal. We clarify the mechanism for stabilization of these states and discuss how they can be observed in magnetic resonance and electric polarization measurements. We also find stable isolated skyrmions with topological charge 1 and 2. Their spin structure, interactions and dynamics are more complex than those in chiral magnets. In particular, magnetic resonance in the skyrmion crystal should be accompanied by oscillations of the electric polarization with a frequency depending on the amplitude of the a.c. magnetic field. These results show that skyrmion materials with rich physical properties can be found among frustrated magnets. We formulate rules to help the search.

Full text

Its licence does not allow us to show the full text. Read it at PubMed Central:

Read at PubMed Central

References 47

  1. 1.

    Nagaosa N. & Tokura Y. Topological properties and dynamics of magnetic skyrmions. Nat. Nanotechnol. 8, 899–911 (2013 ).

    Not in our library10.1038/nnano.2013.243

  2. 2.

    Bogdanov N. & Yablonskii D. A. Thermodynamically stable “vortices”' in magnetically ordered crystals. The mixed state of magnets. Sov. Phys. JETP 68, 101–103 (1989 ).

    Not in our library

  3. 3.

    Mühlbauer S.. Skyrmion lattice in a chiral magnet. Science 323, 915–919 (2009 ).

    Not in our library10.1126/science.1166767

  4. 4.

    Yu X. Z.. Real-space observation of a two-dimensional skyrmion crystal. Nature 465, 901–904 (2010 ).

    Not in our library10.1038/nature09124

  5. 5.

    Dirac P. A. M. Quantized singularities in the electromagnetic field. Proc. R. Soc. A 133, 60 (1931 ).

    Not in our library

  6. 6.

    Skyrme T. H. R. A unified field theory of mesons and baryons. Nucl. Phys. 31, 556–569 (1962 ).

    Not in our library

  7. 7.

    Lee M., Kang W., Onose Y., Tokura Y. & Ong N. P. Unusual Hall anomaly in MnSi under pressure. Phys. Rev. Lett. 102, 186601 (2009 ).

    Not in our library10.1103/physrevlett.102.186601

  8. 8.

    Neubauer A.. Topological Hall effect in the A phase of MnSi. Phys. Rev. Lett. 102, 186602 (2009 ).

    Not in our library10.1103/physrevlett.102.186602

  9. 9.

    Zang J., Mostovoy M., Han J. H. & Nagaosa N. Dynamics of skyrmion crystals in metallic thin films. Phys. Rev. Lett. 107, 136804 (2011 ).

    Not in our library10.1103/physrevlett.107.136804

  10. 10.

    Schulz T.. Emergent electrodynamics of skyrmions in a chiral magnet. Nat. Phys. 8, 301–304 (2012 ).

    Not in our library

  11. 11.

    Van Hoogdalem K. A., Tserkovnyak Y. & Loss D. Magnetic texture-induced thermal Hall effects. Phys. Rev. B 87, 024402 (2013 ).

    Not in our library

  12. 12.

    Mochizuki M.. Thermally driven ratchet motion of a skyrmion microcrystal and topological magnon Hall effect. Nat. Mater. 13, 241–246 (2014 ).

    Not in our library10.1038/nmat3862

  13. 13.

    Fert A., Cros V. & Sampaio J. Skyrmions on the track. Nat. Nanotechnol. 8, 152–156 (2013 ).

    Not in our library10.1038/nnano.2013.29

  14. 14.

    Iwasaki J., Mochizuki M. & Nagaosa N. Current-induced skyrmion dynamics in constricted geometries. Nat. Nanotechnol. 8, 742–747 (2013 ).

    Not in our library10.1038/nnano.2013.176

  15. 15.

    Zhou Y. & Ezawa M. A reversible conversion between a skyrmion and a domain-wall pair in a junction geometry. Nat. Commun. 5, 4652 (2014 ).

    Not in our library10.1038/ncomms5652

  16. 16.

    Tomasello E. M. R., Zivieri R., Torres L., Carpentieri M. & Finocchio G. A strategy for the design of skyrmion racetrack memories. Sci. Rep. 4, 6784 (2014 ).

    Not in our library10.1038/srep06784

  17. 17.

    Butenko A. B., Leonov A. A., Roessler U. K. & Bogdanov A. N. Stabilization of skyrmion textures by uniaxial distortions in noncentrosymmetric cubic helimagnets. Phys. Rev. B 82, 052403 (2010 ).

    Not in our library

  18. 18.

    Rößler U. K., Leonov A. A. & Bogdanov A. N. Chiral skyrmionic matter in non-centrosymmetric magnets. J. Phys. Conf. Ser. 303, 012105 (2011 ).

    Not in our library

  19. 19.

    Garel T. & Doniach S. Phase transitions with spontaneous modulation - the dipolar Ising ferromagnet. Phys. Rev. B 26, 325–329 (1982 ).

    Not in our library

  20. 20.

    Buhrandt S. & Fritz L. Skyrmion lattice phase in three-dimensional chiral magnets from Monte Carlo simulations. Phys. Rev. B 88, 195137 (2013 ).

    Not in our library

  21. 21.

    Okubo T., Chung S. & Kawamura H. Multiple-q states and the skyrmion lattice of the triangular-lattice Heisenberg antiferromagnet under magnetic fields. Phys. Rev. Lett. 108, 017206 (2012 ).

    Not in our library10.1103/physrevlett.108.017206

  22. 22.

    Braun H.-B. Topological effects in nanomagnetism: from superparamagnetism to chiral quantum solitons. Adv. Phys. 61, 1–116 (2012 ).

    Not in our library

  23. 23.

    Yu X. Z.. Near room-temperature formation of a skyrmion crystal in thin-films of the helimagnet FeGe. Nat. Mater. 10, 106–109 (2011 ).

    Not in our library10.1038/nmat2916

  24. 24.

    Huang S. X. & Chien C. L. Extended skyrmion phase in epitaxial FeGe(111) thin films. Phys. Rev. Lett. 108, 267201 (2012 ).

    Not in our library10.1103/physrevlett.108.267201

  25. 25.

    Spaldin N. A., Fiebig M. & Mostovoy M. The toroidal moment in condensed-matter physics and its relation to the magnetoelectric effect. J. Phys. Condens. Matter 20, 434203 (2008 ).

    Not in our library

  26. 26.

    Yu X. Z.. Magnetic stripes and skyrmions with helicity reversals. Proc. Natl Acad. Sci. USA 109, 8856–8860 (2012 ).

    Not in our library10.1073/pnas.1118496109

  27. 27.

    Babaev E., Carlström A., Garaud B., Silaev A. & Speight J. M. Type-1.5 superconductivity in multiband systems: magnetic response, broken symmetries and microscopic theory. A brief overview. Physica C: Superconductivity 479, 2–14 (2012 ).

    Not in our library

  28. 28.

    Yu X. Z.. Biskyrmion states and their current-driven motion in a layered manganite. Nat. Commun. 5, 3198 (2014 ).

    Not in our library10.1038/ncomms4198

  29. 29.

    Cheong S.-W. & Mostovoy M. Multiferroics: a magnetic twist for ferroelectricity. Nat. Mater. 6, 13–20 (2007 ).

    Not in our library10.1038/nmat1804

  30. 30.

    Cava R. J.. in Introduction to Frustrated Magnetism 164, 131–154Springer Series in Solid-State Sciences (2011 ).

    Not in our library

  31. 31.

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

    Not in our library10.1103/physrevlett.95.057205

  32. 32.

    Sergienko I. A. & Dagotto E. Role of the Dzyaloshinskii-Moriya interaction in multiferroic perovskites. Phys. Rev. B 73, 094434 (2006 ).

    Not in our library

  33. 33.

    Mostovoy M. Ferroelectricity in spiral magnets. Phys. Rev. Lett. 96, 067601 (2006 ).

    Not in our library10.1103/physrevlett.96.067601

  34. 34.

    Arima T. Ferroelectricity induced by proper-screw type magnetic order. J. Phys. Soc. Jpn 76, 073702 (2007 ).

    Not in our library

  35. 35.

    Goto T., Kimura T., Lawes G., Ramirez A. P. & Tokura Y. Ferroelectricity and giant magnetocapacitance in perovskite rare-earth manganites. Phys. Rev. Lett. 92, 257201 (2004 ).

    Not in our library10.1103/physrevlett.92.257201

  36. 36.

    Yamasaki Y.. Magnetic reversal of the ferroelectric polarization in a multiferroic spinel oxide. Phys. Rev. Lett. 96, 207204 (2006 ).

    Not in our library10.1103/physrevlett.96.207204

  37. 37.

    Mochizuki M. Spin-wave modes and their intense excitation effects in skyrmion crystals. Phys. Rev. Lett. 108, 017601 (2012 ).

    Not in our library10.1103/physrevlett.108.017601

  38. 38.

    Zhou Y.. Dynamical magnetic skyrmions. Preprint at http://arxiv.org/abs/1404.3281 (2014 ).

    Not in our library

  39. 39.

    Nakatsuji S.. Spin disorder on a triangular lattice. Science 309, 1697–1700 (2005 ).

    Not in our library10.1126/science.1114727

  40. 40.

    Stock C.. Neutron-scattering measurement of incommensurate short-range order in single crystals of the S =1 triangular antiferromagnet NiGa2S4. Phys. Rev. Lett. 105, 037402 (2010 ).

    Not in our library10.1103/physrevlett.105.037402

All 47 references

Cited by papers we hold 1

Reads

Read by people on this page

None yet.

Checked or read by AI through naulon

None yet.

A person counts once a day per paper. We keep no cookie and no address: a reader is a hash that changes every day. Any month under five reads shows no number.

Are you an author?

Is this your paper?

Claim it to add your note and be paid when agents cite it. Free.