Theoretical and Mathematical Physics

, Volume 191, Issue 3, pp 924–938 | Cite as

Critical behavior of a monoaxial chiral helimagnet

  • A. S. Ovchinnikov
  • I. G. Bostrem
  • Vl. E. Sinitsyn
  • J. Kishine


We analyze the critical behavior of magnetically ordered phases appearing in a monoaxial chiral helimagnet in a weak external magnetic field. Using the formalism of the equations of state in the critical region, we determine the temperature dependence of the order parameters for the conical phase and the soliton-lattice phase. We calculated the critical exponents and show that they coincide with those in the three-dimensional Heisenberg model.


Dzyaloshinskii–Moriya interaction phase transition critical index 


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  1. 1.
    Y. Ishikawa, K. Tajima, D. Bloch, and M. Roth, “Helical spin structure in manganese silicide MnSi,” Solid State Commun., 19, 525–528 (1976).ADSCrossRefGoogle Scholar
  2. 2.
    S. Mühlbauer, B. Binz, F. Jonietz, C. Pfleiderer, A. Rosch, A. Neuebauer, R. Georgii, and P. Böni, “Skyrmion lattice in a chiral magnet,” Science, 323, 915–919 (2009).ADSCrossRefGoogle Scholar
  3. 3.
    X. Z. Yu, Y. Onose, N. Kanazawa, J. H. Park, J. H. Han, Y. Matsui, N. Nagaosa, and Y. Tokura, “Real-space observation of a two-dimensional skyrmion crystal,” Nature, 465, 901–904 (2010).ADSCrossRefGoogle Scholar
  4. 4.
    W. Münzer, A. Neubauer, T. Adams, S. Mühlbauer, C. Franz, F. Jonietz, R. Georgii, P. Böni, B. Pedersen, M. Schmidt, A. Rosch, and C. Pfleiderer, “Skyrmion lattice in the doped semiconductor Fe1−xCoxSi,” Phys. Rev. B, 81, 041203 (2010).ADSCrossRefGoogle Scholar
  5. 5.
    B. Lebech, J. Bernhard, and T. Freltoft, “Magnetic structures of cubic FeGe studied by small-angle neutron scattering,” J. Phys.: Condens. Matter, 1, 6105–6122 (1989).ADSGoogle Scholar
  6. 6.
    X. Z. Yu, N. Kanazawa, Y. Onose, K. Kimoto, W. Z. Zhang, S. Ishiwata, Y. Matsui, and Y. Tokura, “Near room-temperature formation of a skyrmion crystal in thin-films of the helimagnet FeGe,” Nature Mater., 10, 106–109 (2011).ADSCrossRefGoogle Scholar
  7. 7.
    K. Kohn, “A new ferrimagnet Cu2SeO4,” J. Phys. Soc. Japan, 42, 2065–2066 (1977).ADSCrossRefGoogle Scholar
  8. 8.
    S. Seki, X. Z. Yu, S. Ishiwata, and Y. Tokura, “Observation of skyrmions in a multiferroic material,” Science, 336, 198–201 (2012).ADSCrossRefGoogle Scholar
  9. 9.
    T. Moriya and T. Miyadai, “Evidence for the helical spin structure due to antisymmetric exchange interaction in Cr13NbS2,” Solid State Commun., 42, 209–212 (1982).ADSCrossRefGoogle Scholar
  10. 10.
    T. Miyadai, K. Kikuchi, H. Kondo, S. Sakka, M. Arai, and Y. Ishikawa, “Magnetic properties of Cr13NbS2,” J. Phys. Soc. Japan, 52, 1394–1401 (1983).ADSCrossRefGoogle Scholar
  11. 11.
    U. K. Rößler, A. N. Bogdanov, and C. Pfleiderer, “Spontaneous skyrmion ground states in magnetic metals,” Nature, 442, 797–801 (2006).ADSCrossRefGoogle Scholar
  12. 12.
    N. Nagaosa and Y. Tokura, “Topological properties and dynamics of magnetic skyrmions,” Nature Nanotech., 8 (2013).Google Scholar
  13. 13.
    I. E. Dzyaloshinskii, “Theory of helicoidal structures in antiferromagnets: I. Nonmetals,” Sov. Phys. JETP, 19, 960–971 (1964); “The theory of helicoidal structures in antiferromagnets: II. Metals,” Sov. Phys. JETP, 20, 223–231 (1965).Google Scholar
  14. 14.
    Yu. A. Izyumov, “Modulated, or long-periodic, magnetic structures of crystals,” Sov. Phys. Usp., 27, 845–887 (1984).ADSCrossRefGoogle Scholar
  15. 15.
    Y. Togawa, T. Koyama, K. Takayanagi, S. Mori, Y. Kousaka, J. Akimitsu, S. Nishihara, K. Inoue, A. S. Ovchinnikov, and J. Kishine, “Chiral magnetic soliton lattice on a chiral helimagnet,” Phys. Rev. Lett., 108, 107202 (2012).ADSCrossRefGoogle Scholar
  16. 16.
    J. Kishine and A. S. Ovchinnikov, “Theory of monoaxial chiral helimagnet,” in: Solid State Physics (R. E. Camley and R. L. Stamps, eds.), Vol. 66, Acad. Press, New York (2015), pp. 1–130.Google Scholar
  17. 17.
    I. Dzyaloshinskii, “A thermodynamic theory of ‘weak’ ferromagnetism of antiferromagnetics,” J. Phys. Chem. Solids, 4, 241–255 (1958).ADSCrossRefGoogle Scholar
  18. 18.
    T. Moriya, “Anisotropic superexchange interaction and weak ferromagnetism,” Phys. Rev., 120, 91–98 (1960).ADSCrossRefGoogle Scholar
  19. 19.
    Y. Kousaka, Y. Nakao, J. Kishine, M. Akita, K. Inoue, and J. Akimitsu, “Chiral helimagnetism in T1/3NbS2 (T = Cr and Mn),” Nucl. Instrum. Methods Phys. Res. A, 600, 250–253 (2009).ADSCrossRefGoogle Scholar
  20. 20.
    N. J. Ghimire, M. A. McGuire, D. S. Parker, B. Sipos, S. Tang, J.-Q. Yan, B. C. Sales, and D. Mandrus, “Magnetic phase transition in single crystals of the chiral helimagnet Cr1/3NbS2,” Phys. Rev. B, 87, 104403 (2013).ADSCrossRefGoogle Scholar
  21. 21.
    S. V. Grigoriev, S. V. Maleyev, A. I. Okorokov, Yu. O. Chetverikov, and H. Eckerlebe, “Field-induced reorientation of the spin helix in MnSi near T c,” Phys. Rev. B, 73, 224440 (2006).ADSCrossRefGoogle Scholar
  22. 22.
    S. V. Grigoriev, V. A. Dyadkin, D. Menzel, J. Schoenes, Yu. O. Chetverikov, A. I. Okorokov, H. Eckerlebe, and S. V. Maleyev, “Magnetic structure of Fe1−xCoxSi in a magnetic field studied via small-angle polarized neutron diffraction,” Phys. Rev. B, 76, 224424 (2007).ADSCrossRefGoogle Scholar
  23. 23.
    C. Pappas, E. Lelièvre-Berna, P. Falus, P. M. Bentley, E. Moskvin, S. Grigoriev, P. Fouquet, and B. Farago, “Chiral paramagnetic skyrmion-like phase in MnSi,” Phys. Rev. Lett., 102, 197202 (2009).ADSCrossRefGoogle Scholar
  24. 24.
    S. A. Brazovskii, “Phase transition of an isotropic system to a nonuniform state,” Sov. Phys. JETP, 41, 85–89 (1975).ADSGoogle Scholar
  25. 25.
    F. B. Mushenok, “Homogeneous and Goldstone modes of spin excitations in Cr1/3NbS2 helimagnet,” Eur. Phys. J. B, 86, 342 (2013).ADSCrossRefGoogle Scholar
  26. 26.
    V. Dyadkin, F. Mushenok, A. Bosak, D. Menzel, S. Grigoriev, P. Pattison, and D. Chernyshov, “Structural disorder versus chiral magnetism in Cr1/3NbS2,” Phys. Rev. B, 91, 184205 (2015).ADSCrossRefGoogle Scholar
  27. 27.
    I. Živković, J. S. White, H. M. Rønnow, K. Prša, and H. Berger, “Critical scaling in the cubic helimagnet Cu2OSeO3,” Phys. Rev. B, 89, 060401 (2014).Google Scholar
  28. 28.
    Y. Nishikawa and K. Hukushima, “Phase transitions and ordering structures of a model of chiral helimagnet in three dimensions,” Phys. Rev. B, 94, 064428 (2016); arXiv:1603.04200v1 [cond-mat.stat-mech] (2016).ADSCrossRefGoogle Scholar
  29. 29.
    L. Klein and A. Aharony, “Crossover and multicriticality due to the Dzyaloshinsky–Moriya interaction,” Phys. Rev. B, 44, 856–858 (1991).ADSCrossRefGoogle Scholar
  30. 30.
    L. L. Liu, “Effect of antisymmetric interactions on critical phenomena: A system with helical ground state,” Phys. Rev. Lett., 31, 459–462 (1973).ADSCrossRefGoogle Scholar
  31. 31.
    E. Brézin, D. J. Wallace, and K. G. Wilson, “Feynman-graph expansion for the equation of state near the critical point,” Phys. Rev. B, 7, 232–239 (1973).ADSCrossRefGoogle Scholar
  32. 32.
    S.-K. Ma, Modern Theory of Critical Phenomena, Benjamin, Reading, Mass. (1976).Google Scholar
  33. 33.
    B. I. Halperin and P. C. Hohenberg, “Scaling laws for dynamic critical phenomena,” Phys. Rev., 177, 952–971 (1969).ADSCrossRefGoogle Scholar
  34. 34.
    K. G. Wilson and J. Kogut, “The renormalization group and the ϵ expansion,” Phys. Rep. C, 12, 75–199 (1974).ADSCrossRefGoogle Scholar
  35. 35.
    A. Aharony, “Equation of state for cubic ferromagnets,” Phys. Rev. B, 10, 3006–3009 (1974).ADSCrossRefGoogle Scholar
  36. 36.
    M. Shinozaki, S. Hoshino, Y. Masaki, J. Kishine, and Y. Kato, “Finite-temperature properties of threedimensional chiral helimagnets,” J. Phys. Soc. Japan, 85, 074710 (2016); arXiv:1512.00235v3 [cond-mat.str-el] (2015).ADSCrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2017

Authors and Affiliations

  • A. S. Ovchinnikov
    • 1
  • I. G. Bostrem
    • 1
  • Vl. E. Sinitsyn
    • 1
  • J. Kishine
    • 2
  1. 1.Institute of Natural SciencesYeltsin Ural Federal UniversityEkaterinburgRussia
  2. 2.Division of Natural and Environmental SciencesThe Open University of JapanChibaJapan

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