- Open Access
Low-temperature skyrmions and spiral reorientation processes in chiral magnets with cubic anisotropy: Guidelines for bridging theory and experiment
Phys. Rev. Research 8, 013130 – Published 5 February, 2026
DOI: https://doi.org/10.1103/645q-nz7t
Abstract
We revisit the phenomenological Dzyaloshinskii framework, a central theoretical approach for describing magnetization processes in bulk chiral magnets, and demonstrate how magnetocrystalline cubic anisotropy reshapes the phase diagrams of states and provides the key mechanism stabilizing low-temperature skyrmion phases. We show that, for magnetic field directions along the easy anisotropy axes, the phase diagrams feature stable skyrmion pockets for both signs of the anisotropy constant. We further analyze the nature of the transitions at the critical field , associated with the reorientation of stable and metastable spirals along the field. We also examine the transition at , where the conical state closes into the homogeneous state accompanied by a deviation of the wave vector from the field direction. By mapping characteristic anisotropy-dependent parameters in the theoretical phase diagrams, we provide guidelines for connecting theory with experiment and for estimating the cubic anisotropy constant in and MnSi. Our results indicate that samples with small possess sufficiently strong cubic anisotropy to stabilize a low-temperature skyrmion phase. Overall, these theoretical findings establish a quantitative framework for predicting and interpreting skyrmion stability in other cubic helimagnets as well.
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References (49)
- Y. Ishikawa and M. Arai, Magnetic phase diagram of MnSi near critical temperature studied by neutron small angle scattering, J. Phys. Soc. Jpn. 53, 2726 (1984).
- 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).
- L. Ludgren, O. Beckmann, V. Attia, S. P. Bhattacherjee, and M. Richardson, Helical spin arrangement in cubic FeGe, Phys. Scr. 1, 69 (1970).
- H. Wilhelm, M. Baenitz, M. Schmidt, U. K. Roessler, A. A. Leonov, and A. N. Bogdanov, Precursor phenomena at the magnetic ordering of the cubic helimagnet FeGe, Phys. Rev. Lett. 107, 127203 (2011).
- S. Seki, X. Z. Yu, S. Ishiwata, and Y. Tokura, Observation of skyrmions in a multiferroic material, Science 336, 198 (2012).
- T. Adams, et al., Long-wavelength helimagnetic order and skyrmion lattice phase in , Phys. Rev. Lett. 108, 237204 (2012).
- A. N. Bogdanov and D. A. Yablonsky, Thermodynamically stable vortices in magnetically ordered crystals. Mixed state of magnetics, Zh. Eksp. Teor. Fiz. 95, 178 (1989) [Sov. Phys. JETP 68, 101 (1989)].
- A. Bogdanov and A. Hubert, Thermodynamically stable magnetic vortex states in magnetic crystals, J. Magn. Magn. Mater. 138, 255 (1994); The stability of vortex-like structures in uniaxial ferromagnets, 195, 182 (1999).
- X. Z. Yu, et al., Real-space observation of a two-dimensional skyrmion crystal, Nature (London) 465, 901 (2010).
- X. Z. Yu, et al., Near room-temperature formation of a skyrmion crystal in thin-films of the helimagnet FeGe, Nat. Mater. 10, 106 (2011).
- E. M. R. Tomasello, R. Zivieri, L. Torres, M. Carpentieri, and G. Finocchio, A strategy for the design of skyrmion racetrack memories, Sci. Rep. 4, 6784 (2014).
- D. Cortes-Ortuno, W. Wang, M. Beg, R. A. Pepper, M.-A. Bisotti, R. Carey, M. Vousden, T. Kluyver, O. Hovorka, and H. Fangohr, Thermal stability and topological protection of skyrmions in nanotracks, Sci. Rep. 7, 4060 (2017).
- P. Bak and M. H. Jensen, Theory of helical magnetic structures and phase transitions in MnSi and FeGe, J. Phys. C: Solid State Phys. 13, L881 (1980).
- O. Nakanishi, A. Yanase, A. Hasegawa, and M. Kataoka, The origin of the helical spin density wave in MnSi, Solid State Commun. 35, 995 (1980).
- D. Belitz, T. R. Kirkpatrick, and A. Rosch, Theory of helimagnons in itinerant quantum system, Phys. Rev. B 73, 054431 (2006).
- A. B. Butenko, A. A. Leonov, U. K. Rößler, and A. N. Bogdanov, Stabilization of skyrmion textures by uniaxial distortions in noncentrosymmetric cubic helimagnets, Phys. Rev. B 82, 052403 (2010).
- A. O. Leonov, C. Pappas, and I. Kezsmarki, Field and anisotropy driven transformations of spin spirals in cubic skyrmion hosts, Phys. Rev. Res. 2, 043386 (2020).
- K. Kadowaki, K. Okuda, and M. Date, Magnetization and magnetoresistance of MnSi, J. Phys. Soc. Jpn. 51, 2433 (1982).
- S. Buhrandt and L. Fritz, Skyrmion lattice phase in three-dimensional chiral magnets from Monte Carlo simulations, Phys. Rev. B 88, 195137 (2013).
- M. Janoschek, M. Garst, A. Bauer, P. Krautscheid, R. Georgii, P. Böni, and C. Pfleiderer, Fluctuation-induced first-order phase transition in Dzyaloshinskii-Moriya helimagnets, Phys. Rev. B 87, 134407 (2013).
- A. O. Leonov and A. N. Bogdanov, Crossover of skyrmion and helical modulations in noncentrosymmetric ferromagnets, New J. Phys. 20, 043017 (2018).
- U. K. Roessler, A. A. Leonov, and A. N. Bogdanov, Skyrmionic textures in chiral magnets, J. Phys.: Conf. Ser. 200, 022029 (2010).
- S. V. Grigoriev, S. V. Maleyev, A. I. Okorokov, Y. O. Chetverikov, P. Böni, R. Georgii, D. Lamago, H. Eckerlebe, and K. Pranzas, Magnetic structure of MnSi under an applied field probed by polarized small-angle neutron scattering, Phys. Rev. B 74, 214414 (2006).
- S. V. Grigoriev, S. V. Maleyev, A. I. Okorokov, Y. O. Chetverikov, and H. Eckerlebe, Field-induced reorientation of the spin helix in MnSi near c, Phys. Rev. B 73, 224440 (2006).
- A. Bauer and C. Pfleiderer, Magnetic phase diagram of MnSi inferred from magnetization and ac susceptibility, Phys. Rev. B 85, 214418 (2012).
- A. O. Leonov and C. Pappas, Skyrmion clusters and conical droplets in bulk helimagnets with cubic anisotropy, Phys. Rev. B 99, 144410 (2019).
- M. L. Plumer and M. B. Walker, Wavevector and spin reorientation in MnSi, J. Phys. C: Solid State Phys. 14, 4689 (1981).
- P. R. Baral, O. I. Utesov, C. Luo, F. Radu, A. Magrez, J. S. White, and V. Ukleev, Direct observation of exchange anisotropy in the helimagnetic insulator , Phys. Rev. Res. 5, L032019 (2023).
- L. J. Bannenberg, et al., Multiple low-temperature skyrmionic states in a bulk chiral magnet, npj Quantum Mater. 4, 11 (2019).
- M. Halder, A. Chacon, A. Bauer, W. Simeth, S. Muehlbauer, H. Berger, L. Heinen, M. Garst, A. Rosch, and C. Pfleiderer, Thermodynamic evidence of a second skyrmion lattice phase and tilted conical phase in Cu2OSeO3, Phys. Rev. B 98, 144429 (2018).
- A. Chacon, L. Heinen, M. Halder, A. Bauer, W. Simeth, S. Muehlbauer, H. Berger, M. Garst, A. Rosch, and C. Pfleiderer, Observation of two independent skyrmion phases in a chiral magnetic material, Nat. Phys. 14, 936 (2018).
- I. E. Dzyaloshinskii, Theory of helicoidal structures in antiferromagnets. I. Nonmetals, J. Sov. Phys. JETP-USSR 19, 960 (1964).
- S. V. Maleyev, Cubic magnets with Dzyaloshinskii-Moriya interaction at low temperature, Phys. Rev. B 73, 174402 (2006).
- Yu A. Izyumov, Modulated, or long-periodic, magnetic structures of crystals, Sov. Phys. Usp. 27, 845 (1984).
- U. K. Rößler, A. N. Bogdanov, and C. Pfleiderer, Spontaneous skyrmion ground states in magnetic metals, Nature (London) 442, 797 (2006).
- C. Back, V. Cros, H. Ebert, K. Everschor-Sitte, A. Fert, and M. Garst, et al., The 2020 skyrmionics roadmap, J. Phys. D: Appl. Phys. 53, 363001 (2020).
- A. Vansteenkiste, J. Leliaert, M. Dvornik, M. Helsen, F. Garcia-Sanchez, and B. Van Waeyenberge, The design and verification of mumax3, AIP Adv. 4, 107133 (2014).
- A. O. Leonov, C. Pappas, and I. I. Smalyukh, Field-driven metamorphoses of isolated skyrmions within the conical state of cubic helimagnets, Phys. Rev. B 104, 064432 (2021).
- A. O. Leonov and C. Pappas, Multiple skyrmionic states and oblique spirals in bulk cubic helimagnets, in Magnetic Skyrmions and Their Applications, edited by G. Finocchio, C. Panagopoulos (Woodhead Publishing, Elsevier, Oxford, 2021).
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/645q-nz7t for details of the helical-to-conical phase transition at the critical field for different orientations of the applied magnetic field relative to the easy and hard axes of the cubic anisotropy.
- N. Mukai and A. O. Leonov, Skyrmion and meron ordering in quasi-two-dimensional chiral magnets, Phys. Rev. B 106, 224428 (2022).
- G. Gödecke, A. O. Leonov, J. Grefe, S. Süllow, and D. Menzel, Cubic magnetic anisotropy in magnets: Interplay of anisotropy and magnetic order in , arXiv:2510.09268.
- A. O. Leonov and K. Inoue, Homogeneous and heterogeneous nucleation of skyrmions in thin layers of cubic helimagnets, Phys. Rev. B 98, 054404 (2018).
- J. Beille, J. Voiron, F. Towfiq, M. Roth, and Z. Y. Zhang, Helimagnetic structure of the alloys, J. Phys. F 11, 2153 (1981).
- N. Manyala, Y. Sidis, J. F. DiTusa, G. Aeppli, D. P. Young, and Z. Fisk, Large anomalous Hall effect in a silicon-based magnetic semiconductor, Nat. Mater. 3, 255 (2004).
- J. Grefe, P. Herre, Y. Hilgers, F. Labbus, N. Lüer-Epping, N. Radomski, M. A. C. de Melo, F. J. Litterst, D. Menzel, and S. Süllow, Near coincidence of metal-insulator transition and quantum critical fluctuations: Electronic ground state and magnetic order in , Phys. Rev. B 109, 054414 (2024).
- S. M. Sauther, De Haas-van Alphen effect and magnetic anisotropy in correlated electron systems studied by cantilever magnetometry, Ph.D. thesis, Technische Universität München (2021).
- A. O. Leonov, Swirling of horizontal skyrmions into hopfions in bulk cubic helimagnets, Magnetism 3, 297 (2023).
- A. O. Leonov and C. Pappas, Topological boundaries between helical domains as a nucleation source of skyrmions in the bulk cubic helimagnet , Phys. Rev. Res. 4, 043137 (2022).