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Thermally driven ratchet motion of a skyrmion microcrystal and topological magnon Hall effect

Nature Materials volume 13, pages 241–246 (2014)Cite this article

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Abstract

Spontaneously emergent chirality is an issue of fundamental importance across the natural sciences1. It has been argued that a unidirectional (chiral) rotation of a mechanical ratchet is forbidden in thermal equilibrium, but becomes possible in systems out of equilibrium2. Here we report our finding that a topologically nontrivial spin texture known as a skyrmion—a particle-like object in which spins point in all directions to wrap a sphere3—constitutes such a ratchet. By means of Lorentz transmission electron microscopy we show that micrometre-sized crystals of skyrmions in thin films of Cu2OSeO3 and MnSi exhibit a unidirectional rotation motion. Our numerical simulations based on a stochastic Landau–Lifshitz–Gilbert equation suggest that this rotation is driven solely by thermal fluctuations in the presence of a temperature gradient, whereas in thermal equilibrium it is forbidden by the Bohr–van Leeuwen theorem4,5. We show that the rotational flow of magnons driven by the effective magnetic field of skyrmions gives rise to the skyrmion rotation, therefore suggesting that magnons can be used to control the motion of these spin textures.

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Figure 1: Experimentally observed skyrmions and unidirectional rotation of microscale skyrmion-crystal domains in MnSi.
Figure 2: Set-up of the numerical simulation.
Figure 3: Simulated thermally driven rotation of the skyrmion microcrystal.
Figure 4: Simulation of the magnon current density.

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Change history

  • 30 January 2014

    In the version of this Letter originally published online, in Fig. 4c, the solid blue curve was missing. This error has now been corrected in all versions of the Letter.

References

  1. Gardner, M. The New Ambidextrous Universe (Freeman, (1990).

    Google Scholar 

  2. Feynman, R. P. The Feynman Lectures on Physics Vol. 1, Ch. 46 (Addison-Wesley, (1963).

    Google Scholar 

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

    Article  CAS  Google Scholar 

  4. Bohr, N. Studier over Metallernes Elektrontheori (Kobenhavns Universitet, 1911).

    Google Scholar 

  5. Van Leeuwen, H. J. Problemes de la theorie electronique du magnetisme. J. Phys-Paris 2, 361–377 (1921).

    Google Scholar 

  6. Bogdanov, A. N. & Yablonskiî, D. A. ‘Thermodynamically stable vortices’ in magnetically ordered crystals: The mixed state of magnets. Sov. Phys. JETP 68, 101–103 (1989).

    Google Scholar 

  7. Bogdanov, A. & Hubert, A. Thermodynamically stable magnetic vortex states in magnetic crystals. J. Magn. Magn. Mater. 138, 255–269 (1994).

    Article  CAS  Google Scholar 

  8. Rößler, U. K., Bogdanov, A. N. & Pfleiderer, C. Spontaneous skyrmion ground states in magnetic metals. Nature 442, 797–801 (2006).

    Article  Google Scholar 

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

    Article  Google Scholar 

  10. Tonomura, A. et al. Real-space observation of skyrmion lattice in helimagnet MnSi thin samples. Nano Lett. 12, 1673–1677 (2012).

    Article  CAS  Google Scholar 

  11. Pfleiderer, C. et al. Skyrmion lattices in metallic and semiconducting B20 transition metal compounds. J. Phys. Condens. Matter 22, 164207 (2010).

    Article  CAS  Google Scholar 

  12. Münzer, A. et al. Skyrmion lattice in the doped semiconductor Fe1−xCoxSi. Phys. Rev. B 81, 041203(R) (2010).

    Article  Google Scholar 

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

    Article  CAS  Google Scholar 

  14. Yu, X. Z. et al. Near room-temperature formation of a skyrmion crystal in thin-films of the helimagnet FeGe. Nature Mater. 10, 106–109 (2010).

    Article  Google Scholar 

  15. Seki, S., Yu, X. Z., Ishiwata, S. & Tokura, Y. Observation of skyrmions in a multiferroic material. Science 336, 198–201 (2012).

    Article  CAS  Google Scholar 

  16. Adams, T. et al. Long-wavelength helimagnetic order and skyrmion lattice phase in Cu2OSeO3 . Phys. Rev. Lett. 108, 237204 (2012).

    Article  CAS  Google Scholar 

  17. Seki, S. et al. Formation and rotation of skyrmion crystal in the chiral-lattice insulator Cu2OSeO3 . Phys. Rev. B 85, 220406 (2012).

    Article  Google Scholar 

  18. Jonietz, F. et al. Spin transfer torques in MnSi at ultralow current densities. Science 330, 1648–1651 (2010).

    Article  CAS  Google Scholar 

  19. Everschor, K. et al. Rotating skyrmion lattices by spin torques and field or temperature gradients. Phys. Rev. B 86, 054432 (2012).

    Article  Google Scholar 

  20. Yu, X. Z. et al. Skyrmion flow near room temperature in an ultralow current density. Nature Commun. 3, 988 (2012).

    Article  CAS  Google Scholar 

  21. Iwasaki, J., Mochizuki, M. & Nagaosa, N. Universal current–velocity relation of skyrmion motion in chiral magnets. Nature Commun. 4, 1463 (2013).

    Article  Google Scholar 

  22. Yi, S. D., Onoda, S., Nagaosa, N. & Han, J. H. Skyrmions and anomalous Hall effect in a Dzyaloshinskii–Moriya spiral magnet. Phys. Rev. B 80, 054416 (2009).

    Article  Google Scholar 

  23. Bak, P. & Jensen, M. H. Theory of helical magnetic structures and phase transitions in MnSi and FeGe. J. Phys. C 13, L881–L885 (1980).

    Article  CAS  Google Scholar 

  24. Brown, W. F. Jr. Thermal fluctuations of a single-domain particle. Phys. Rev. 130, 1677–1686 (1963).

    Article  Google Scholar 

  25. Kubo, R. & Hashitsume, N. Brownian motion of spins. Prog. Theor. Phys. Suppl. 46, 210–220 (1970).

    Article  Google Scholar 

  26. García, J. L. & Lázaro, F. J. Langevin-dynamics study of the dynamical properties of small magnetic particles. Phys. Rev. B 58, 14937–14958 (1998).

    Article  Google Scholar 

  27. Petrova, O. & Tchernyshyov, O. Spin waves in a skyrmion crystal. Phys. Rev. B 84, 214433 (2011).

    Article  Google Scholar 

  28. Kong, L. & Zang, J. Dynamics of an insulating skyrmion under a temperature gradient. Phys. Rev. Lett. 111, 067203 (2013).

    Article  Google Scholar 

  29. Nagaosa, N. & Tokura, Y. Emergent electromagnetism in solids. Phys. Scr. T 146, 014020 (2012).

    Google Scholar 

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

    Article  Google Scholar 

  31. Kruglyak, V. V., Demokritov, S. O. & Grundler, D. Magnonics. J. Phys. D 43, 260301 (2010).

    Article  Google Scholar 

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Acknowledgements

The authors thank A. Rosch, M. Ichikawa, Y. Matsui, Y. Ogimoto and E. Saito for discussions. X.Z.Y. is grateful to K. Nishizawa and T. Kikitsu for providing a transmission electron microscope (JEM2100F). This research was in part supported by JSPS KAKENHI (Grant Numbers 24224009, 24360036, 25870169 and 25287088), by the Funding Program for World-Leading Innovative R&D on Science and Technology (FIRST Program), Japan, and by G-COE Program ‘Physical Sciences Frontier’ from MEXT Japan. M. Mostovoy was supported by FOM grant 11PR2928 and the Niels Bohr International Academy. J.Z. is supported by the Theoretical Interdisciplinary Physics and Astrophysics Center and by the US Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Award DEFG02-08ER46544.

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Authors and Affiliations

  1. Department of Physics and Mathematics, Aoyama Gakuin University, Sagamihara, Kanagawa 229-8558, Japan

    M. Mochizuki

  2. PRESTO, Japan Science and Technology Agency, Kawaguchi, Saitama 332-0012, Japan

    M. Mochizuki & S. Seki

  3. RIKEN Center for Emergent Matter Science (CEMS), Wako, Saitama 351-0198, Japan

    X. Z. Yu, S. Seki, W. Koshibae, Y. Tokura & N. Nagaosa

  4. Department of Applied Physics, Quantum-Phase Electronics Center, The University of Tokyo, Bunkyo-ku Tokyo 113-8656, Japan

    S. Seki, Y. Tokura & N. Nagaosa

  5. Department of Applied Physics, The University of Tokyo, Bunkyo-ku, Tokyo 113-8656, Japan

    N. Kanazawa, Y. Tokura & N. Nagaosa

  6. Department of Physics and Astronomy, Johns Hopkins University, Baltimore, Maryland 21218, USA

    J. Zang

  7. Zernike Institute for Advanced Materials, University of Groningen, Nijenborgh 4, 9747 AG, Groningen, The Netherlands

    M. Mostovoy

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  1. M. Mochizuki
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Contributions

M. Mochizuki carried out the numerical simulations and analysed the simulation data. X.Z.Y. carried out the Lorentz TEM measurement and analysed the experimental data. S.S. carried out the crystal growth of Cu2OSeO3. N.K. carried out the crystal growth of MnSi. The whole work has been led by N.N. and Y.T. The results were discussed and interpreted by M. Mochizuki, X.Z.Y., W.K., J.Z., M. Mostovoy, Y.T. and N.N. The draft was written by M. Mochizuki, M. Mostovoy, Y.T. and N.N.

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Correspondence to M. Mochizuki.

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Mochizuki, M., Yu, X., Seki, S. et al. Thermally driven ratchet motion of a skyrmion microcrystal and topological magnon Hall effect. Nature Mater 13, 241–246 (2014). https://doi.org/10.1038/nmat3862

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