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Topological properties and dynamics of magnetic skyrmions

Abstract

Magnetic skyrmions are particle-like nanometre-sized spin textures of topological origin found in several magnetic materials, and are characterized by a long lifetime. Skyrmions have been observed both by means of neutron scattering in momentum space and microscopy techniques in real space, and their properties include novel Hall effects, current-driven motion with ultralow current density and multiferroic behaviour. These properties can be understood from a unified viewpoint, namely the emergent electromagnetism associated with the non-coplanar spin structure of skyrmions. From this description, potential applications of skyrmions as information carriers in magnetic information storage and processing devices are envisaged.

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Figure 1: The skyrmion spin structures.
Figure 2: Phase diagrams of thin-film samples of chiral magnets as a function of magnetic field and temperature.
Figure 3: Various spin textures in dipolar-driven skyrmion systems.
Figure 4: Topological phenomena of skyrmions.
Figure 5: Experimental data for skyrmion magnetic resonances in Cu2OSeO3.
Figure 6: Simulations of the skyrmion motion driven by current.

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References

  1. Skyrme, T. H. R. A unified field theory of mesons and baryons. Nucl. Phys. 31, 556–569 (1962). This is the original paper that proposed the skyrmion as a model for hadrons.

    Article  CAS  Google Scholar 

  2. Sondhi, S. L., Karlhede, A., Kivelson, S. A. & Rezayi, E. H. Skyrmions and the crossover from the integer to fractional quantum Hall effect at small Zeeman energies. Phys. Rev. B 47, 16419–16426 ( 1993).

    CAS  Google Scholar 

  3. Wright, D. C. & Mermin, N. D. Crystalline liquids: the blue phases. Rev. Mod. Phys. 61, 385–432 (1989).

    CAS  Google Scholar 

  4. Ho, T. L. Spinor Bose condensates in optical traps. Phys. Rev. Lett. 81, 742–745 ( 1998).

    CAS  Google Scholar 

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

    Google Scholar 

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

    CAS  Google Scholar 

  7. Röβler, U. K., Bogdanov, N. & Pfleiderer, C. Spontaneous skyrmion ground states in magnetic metals. Nature 442, 797–801 (2006). This is an early theoretical work predicting the formation of skyrmions in a magnetic system.

    Google Scholar 

  8. Binz, B., Vishwanath, A. & Aji, V. Theory of the helical spin crystal: A candidate for the partially ordered state of MnSi. Phys. Rev. Lett. 96, 207202 (2006).

    CAS  Google Scholar 

  9. Tewari, S., Belitz, D. & Kirkpatrick, T. R. Blue quantum fog: Chiral condensation in quantum helimagnets. Phys. Rev. Lett. 96, 047207 (2006).

    Google Scholar 

  10. Mühlbauer, S. et al. Skyrmion lattice in a chiral magnet. Science 323, 915–919 (2009). This is the first experimental report on neutron scattering that identifies the A phase in a chiral magnet as the skyrmion crystal phase.

    Google Scholar 

  11. Yu, X. Z. et al. Real-space observation of a two-dimensional skyrmion crystal. Nature 465, 901–904 (2010). This paper reports the first real-space observation of a skyrmion crystal and individual skyrmions by using Lorentz microscopy.

    CAS  Google Scholar 

  12. Heinze, S. et al. Spontaneous atomic-scale magnetic skyrmion lattice in two dimensions. Nature Phys. 7, 713–718 (2011). This paper reports a spin-resolved STM study and theoretical analysis on the skyrmion crystal state at the interface.

    CAS  Google Scholar 

  13. Pfleiderer, C. Surfaces get hairy. Nature Phys. 7, 673–674 (2011).

    CAS  Google Scholar 

  14. Rajaraman, R. Solitons and Instantons (Elsevier, 1987).

    Google Scholar 

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

    CAS  Google Scholar 

  16. Tanygin, B. M. Symmetry theory of the flexomagnetoelectric interaction in the magnetic vortices and skyrmions. Physica B 407, 868–872 (2012).

    CAS  Google Scholar 

  17. Lin, Y. S., Grundy, J. & Giess, E. A. Bubble domains in magnetostatically coupled garnet films. Appl. Phys. Lett. 23, 485–487 (1973).

    CAS  Google Scholar 

  18. Malozemoff, A. P. & Slonczewski, J. C. Magnetic Domain Walls in Bubble Materials 306–314 (Academic, 1979).

    Google Scholar 

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

    Google Scholar 

  20. Suzuki, T. A study of magnetization distribution of submicron bubbles in sputtered Ho-Co thin films. J. Magn. Magn. Mater. 31–34, 1009–1010 (1983).

    Google Scholar 

  21. Dzyaloshinskii, I. A thermodynamic theory of “weak” ferromagnetism of antiferromagnetics. J. Phys. Chem. Solids 4, 241–255 (1958).

    Google Scholar 

  22. Moriya, T. Anisotropic superexchange interaction and weak ferromagnetism. Phys. Rev. 120, 91–98 (1960).

    CAS  Google Scholar 

  23. Ishikawa, Y., Tajima, K., Bloch, D. & Roth, M. Helical spin structure in manganese silicide MnSi. Solid State Commun. 19, 525–528 (1976).

    CAS  Google Scholar 

  24. Ishikawa, Y. & Arai, M. Magnetic phase diagram of MnSi near critical temperature studied by neutron small angle scattering. J. Phys. Soc. Jpn 53, 2726–2733 (1984).

    CAS  Google Scholar 

  25. Grigoriev, S. V. et al. Helical spin structure of Mn1−yFeySi under a magnetic field: Small angle neutron diffraction study. Phys. Rev. B 79, 144417 (2009).

    Google Scholar 

  26. Lebech, B. et al. Magnetic phase diagram of MnSi. J. Magn. Magn. Mater. 140–144, 119–120 (1995).

    Google Scholar 

  27. Pfleiderer, C. et al. Partial order in the non-Fermi-liquid phase of MnSi. Nature 427, 227–231 (2004).

    CAS  Google Scholar 

  28. Janoschek, M. et al. Fluctuation-induced first-order phase transition in Dzyaloshinskii-Moriya helimagnets. Phys. Rev. B 87, 134407 (2013).

    Google Scholar 

  29. Beille, J., Voiron, J. & Roth. M. Long period helimagnetism in the cubic B20 FexCo1−xSi and CoxMn1−x Si alloys. Solid State Commun. 47, 399–402 (1983).

    CAS  Google Scholar 

  30. Ishimoto, K. et al. Small-angle neutron diffraction from the helical magnet Fe0.8Co0.2Si. Physica B 213–214, 381–383 (1995).

    Google Scholar 

  31. Grigoriev, S. V. et al. Magnetic structure of Fe1−xCoxSi in a magnetic field studied via small-angle polarized neutron diffraction. Phys. Rev. B 76, 224424 (2007).

    Google Scholar 

  32. Grigoriev, S. V. et al. Crystal handedness and spin helix chirality in Fe1−xCoxSi. Phys. Rev. Lett. 102, 037204 (2009).

    CAS  Google Scholar 

  33. Onose, Y., Takeshita, N., Terakura, C., Takagi, H. & Tokura, Y. Doping dependence of transport properties in Fe1−xCoxSi. Phys. Rev. B 72, 224431 (2006).

    Google Scholar 

  34. Lebech, B., Bernhard, J. & Freltoft, T. Magnetic-structures of cubic FeGe studied by small-angle neutron scattering. J. Phys. Condens. Matter 1, 6105–6122 (1989).

    CAS  Google Scholar 

  35. Uchida, M. et al. Topological spin textures in the helimagnet FeGe. Phys. Rev. B 77, 184402 (2008).

    Google Scholar 

  36. 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 (2011).

    CAS  Google Scholar 

  37. Wilhelm, H. Precursor phenomena at the magnetic ordering of the cubic helimagnet FeGe. Phys. Rev. Lett. 107, 127203 (2011).

    CAS  Google Scholar 

  38. Shibata, K. et al. Towards control of the size and helicity of skyrmions in helimagnetic alloys by spin–orbit coupling. Nature Nanotech. 8, 723–728 (2013).

    CAS  Google Scholar 

  39. 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).

    Google Scholar 

  40. Bader, S. D. Colloquium: Opportunities in nanomagnetism. Rev. Mod. Phys. 78, 1–15 (2006).

    CAS  Google Scholar 

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

    CAS  Google Scholar 

  42. Rosch, A. Extra twist in magnetic bubbles. Proc. Natl Acad. Sci. USA 109, 8793–8794 (2012).

    CAS  Google Scholar 

  43. Jonietz, F. et al. Spin transfer torques in MnSi at ultralow current densities. Science 330, 1648–1651 (2010). This paper demonstrates the ultralow critical current density required for the current-driven motion of a skyrmion crystal.

    CAS  Google Scholar 

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

    CAS  Google Scholar 

  45. Volovik, G. The Universe in a Helium Droplet (Oxford Univ. Press, 2003).

    Google Scholar 

  46. Nagaosa, N. & Tokura, Y. Emergent electromagnetism in solids. Physica Scripta T146, 014020 (2012).

    Google Scholar 

  47. Nagaosa, N., Yu, X. Z. & Tokura, Y. Gauge fields in real and momentum spaces in magnets: monopoles and skyrmions. Phil. Trans. R. Soc. A 370, 5806–5819 (2012).

    CAS  Google Scholar 

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

    Google Scholar 

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

    CAS  Google Scholar 

  50. Kanazawa, N. et al. Large topological Hall effect in a short-period helimagnet MnGe. Phys. Rev. Lett. 106, 156603 (2011).

    CAS  Google Scholar 

  51. Yufan Li, Y. et al. Robust formation of skyrmions and topological Hall effect anomaly in epitaxial thin films of MnSi. Phys. Rev. Lett. 110, 117202 (2013).

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  54. Schulz, T. et al. Emergent electrodynamics of skyrmions in a chiral magnet. Nature Phys. 8, 301–304 (2012). This paper demonstrates the electromagnetic induction generated by the emergent electromagnetic field.

    CAS  Google Scholar 

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

    CAS  Google Scholar 

  56. Landau, L. D., Lifshitz, E. M. & Pitaevskii, L. P. Electrodynamics of Continuous Media Vol. 8, Ch. 5, 178–179 (Elsevier, 2008).

    Google Scholar 

  57. Bloch, D., Voiron, J., Jaccarino, V. & Wernick, J. H. The high field–high pressure magnetic properties of MnSi. Phys. Lett. A 51, 259–261 (1975).

    Google Scholar 

  58. Pfleiderer, C. et al. Magnetic quantum phase transition in MnSi under hydrostatic pressure. Phys. Rev. B 55, 8330–8338 (1997).

    CAS  Google Scholar 

  59. Pfleiderer, C. et al. Non-Fermi-liquid nature of the normal state of itinerant-electron ferromagnets. Nature 414, 427–430 (2001).

    CAS  Google Scholar 

  60. Doiron-Leyraud, N. et al. Fermi-liquid breakdown in the paramagnetic phase of a pure metal. Nature 425, 595–599 (2003).

    CAS  Google Scholar 

  61. Pfleiderer, C., Boeni, P., Keller, T., Roessler, U. K. & Rosch, A. Non-Fermi liquid metal without quantum criticality. Science 316, 1871–1874 (2007).

    CAS  Google Scholar 

  62. Hamann, A. et al. Magnetic blue phase in the chiral itinerant magnet MnSi. Phys. Rev. Lett. 107, 037207 (2011).

    CAS  Google Scholar 

  63. Pappas, C. et al. Magnetic fluctuations and correlations in MnSi: Evidence for a chiral skyrmion spin liquid phase. Phys. Rev. B 83, 224405 (2011).

    Google Scholar 

  64. Ritz, R. et al. Formation of a topological non-Fermi liquid in MnSi. Nature 497, 231–234 (2013).

    CAS  Google Scholar 

  65. Ritz, R. et al. Giant generic topological Hall resistivity of MnSi under pressure. Phys. Rev. B 87, 134424 (2013).

    Google Scholar 

  66. Kadowaki, K., Okuda, K. & Date, M. Magnetization and magnetoresistance of MnSi. I. J. Phys. Soc. Jpn 51, 2433–2438 (1982).

    CAS  Google Scholar 

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

    Google Scholar 

  68. Muenzer, W. et al. Skyrmion lattice in the doped semiconductor Fe1−xCoxSi. Phys. Rev. B 81, 041203 (2010).

    Google Scholar 

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

    Google Scholar 

  70. Moskvin, E. et al. Complex chiral modulations in FeGe close to magnetic ordering. Phys. Rev. Lett. 110, 077207 (2013).

    CAS  Google Scholar 

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

    Google Scholar 

  72. Kanazawa, N. et al. Possible skyrmion-lattice ground state in the B20 chiral-lattice magnet MnGe as seen via small-angle neutron scattering. Phys. Rev. B 86, 134425 (2012).

    Google Scholar 

  73. Adams, T. et al. Long-range crystalline nature of the skyrmion lattice in MnSi. Phys. Rev. Lett. 107, 217206 (2011).

    CAS  Google Scholar 

  74. Moskvin, E. et al. Complex chiral modulations in FeGe close to magnetic ordering. Phys. Rev. Lett. 110, 077207 (2013).

    CAS  Google Scholar 

  75. Bauer, A., Garst, M. & Pfleiderer, C. Specific heat of the skyrmion lattice phase and field-induced tricritical point in MnSi. Phys. Rev. Lett. 110, 177207 (2013).

    CAS  Google Scholar 

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

    CAS  Google Scholar 

  77. Milde, P. et al. Unwinding of a skyrmion lattice by magnetic monopoles. Science 340, 1076–1080 (2013).

    CAS  Google Scholar 

  78. Heinze, S. et al. Real-space imaging of two-dimensional antiferromagnetism on the atomic scale. Science 288, 1805–1808 (2000).

    CAS  Google Scholar 

  79. Khajetoorians, A. A. et al. Current-driven spin dynamics of artificially constructed quantum magnets. Science 339, 55–59 (2013).

    CAS  Google Scholar 

  80. Freeman, M. R. & Choi, B. C. Advances in magnetic microscopy. Science 294, 1484–1488 (2001).

    CAS  Google Scholar 

  81. Grundy, P. J. & Herd, S. R. Lorentz microscopy of bubble domains and changes in domain wall state in hexaferrites. Phys. Stat. Sol. A. 20, 295–307 (1973).

    CAS  Google Scholar 

  82. Grundy, P. J. & Tebble, R. S. Lorentz electron microscopy. Adv. Phys. 17, 153–242 (1968).

    CAS  Google Scholar 

  83. Ishizuka, K. & Allman, B. Phase measurement of atomic resolution image using transport of intensity equation. J. Electron Microsc. 54, 191–197 (2005).

    CAS  Google Scholar 

  84. Uchida, M., Onose, Y., Matsui, Y. & Tokura, Y. Real-space observation of helical spin order. Science 311, 359–361 (2006).

    CAS  Google Scholar 

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

    CAS  Google Scholar 

  86. Seki, S., Yu, X. Z., Ishiwata, S. & Tokura, Y. Observation of skyrmions in a multiferroic material. Science 336, 198–201 (2012). This paper describes the discovery of a skyrmion crystal state and multiferroic behaviour in an insulating magnet.

    CAS  Google Scholar 

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

    Google Scholar 

  88. Han, J. H. et al. Skyrmion lattice in a two-dimensional chiral magnet. Phys. Rev. B 82, 094429 (2010).

    Google Scholar 

  89. Li, Y.-Q., Liu, Y.-H. & Zhou, Y. General spin-order theory via gauge Landau-Lifshitz equation. Phys. Rev. B 84, 205123 (2011).

    Google Scholar 

  90. Kiselev, N. S., Bogdanov, A. N., Schäfer, R. & Röβler, U. K. Chiral skyrmions in thin magnetic films: new objects for magnetic storage technologies? J. Phys. D 44, 392001 (2011).

    Google Scholar 

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

    Google Scholar 

  92. Wilson, M. N. et al. Extended elliptic skyrmion gratings in epitaxial MnSi thin films. Phys. Rev. B 86, 144420 (2012).

    Google Scholar 

  93. Karhu, E. A. et al. Chiral modulations and reorientation effects in MnSi thin films. Phys. Rev. B 85, 094429 (2012).

    Google Scholar 

  94. Rybakov, F. N., Borisov, A. B. & Bogdanov, A. N. Three-dimensional skyrmion states in thin films of cubic helimagnets. Phys. Rev. B 87, 094424 (2013).

    Google Scholar 

  95. Kwon, H. Y. et al. Effect of anisotropy and dipole interaction on long-range order magnetic structures generated by Dzyaloshinskii-Moriya interaction. J. Magn. Magn. Mater. 324, 2171–2176 (2012).

    CAS  Google Scholar 

  96. Morikawa, D., Shibata, K., Kanazawa, N., Yu, X. Z. & Tokura, Y. Crystal chirality and skyrmion helicity in MnSi and (Fe,Co)Si as determined by transmission electron microscopy. Phys. Rev. B 88, 024408 (2013).

    Google Scholar 

  97. Bos, J.-W. G., Colin, C. V. & Palstra, T. T. M. Magnetoelectric coupling in the cubic ferrimagnet Cu2OSeO3 . Phys. Rev. B 78, 094416 (2008).

    Google Scholar 

  98. Fiebig, M. Revival of the magnetoelectric effect. J. Phys. D 38, R123–R152 (2005).

    CAS  Google Scholar 

  99. Tokura, Y. Materials science - Multiferroics as quantum electromagnets. Science 312, 1481–1482 (2006).

    CAS  Google Scholar 

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

    CAS  Google Scholar 

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

    Google Scholar 

  102. Jia, C., Onoda, S., Nagaosa, N. & Han, J. H. Microscopic theory of spin-polarization coupling in multiferroic transition metal oxides. Phys. Rev. B 76, 144424 (2007).

    Google Scholar 

  103. Seki, S., Ishiwata, S. & Tokura, Y. Magnetoelectric nature of skyrmions in a chiral magnetic insulator Cu2OSeO3 . Phys. Rev. B 86, 060403 (2012).

    Google Scholar 

  104. Belesi, M. et al. Magnetoelectric effects in single crystals of the cubic ferrimagnetic helimagnet Cu2OSeO3 . Phys. Rev. B 85, 224413 (2012).

    Google Scholar 

  105. White, J. S. et al. Electric field control of the skyrmion lattice in Cu2OSeO3 . J. Phys. Condens. Matter 24, 432201 (2012).

    CAS  Google Scholar 

  106. Liu, Y.-H., Li, Y.-Q. & Hoon, H. J. Skyrmion dynamics in multiferroic insulators. Phys. Rev. B 87, 100402 (2013).

    Google Scholar 

  107. Ono, T. in Spin Current (eds Maekawa, S., Valenzuela, S. O., Saitoh, E. & Kimura, T.) 402–423 (Oxford Univ. Press, 2012).

    Google Scholar 

  108. Thiaville, A., Nakatani, Y., Miltat, J. & Suzuki, Y. Micromagnetic understanding of current-driven domain wall motion in patterned nanowires. Europhys. Lett. 69, 990–996 (2005).

    CAS  Google Scholar 

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

    CAS  Google Scholar 

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

    CAS  Google Scholar 

  111. Ho, K-y., Kirkpatrick, T. R., Sang, Y. & Belitz, D. Ordered phases of itinerant Dzyaloshinsky-Moriya magnets and their electronic properties. Phys. Rev. B 82, 134427 (2010).

    Google Scholar 

  112. Kirkpatrick, T. R. & Belitz, D. Columnar fluctuations as a source of non-Fermi-liquid behavior in weak metallic magnets. Phys. Rev. Lett. 104, 256404 (2010).

    CAS  Google Scholar 

  113. Belitz, D. & Kirkpatrick, T. R. Quantum electrodynamics and the origins of the exchange, dipole-dipole, and Dzyaloshinsky-Moriya interactions in itinerant fermion systems. Phys. Rev. B 81, 184419 (2010).

    Google Scholar 

  114. Binz, B. & Vishwanath, A. Theory of helical spin crystals: Phases, textures, and properties. Phys. Rev. B 74, 214408 (2006).

    Google Scholar 

  115. Park, J.-H. & Han, J. H., Zero-temperature phases for chiral magnets in three dimensions. Phys. Rev. B 83, 184406 (2011).

    Google Scholar 

  116. Ishiwata, S. et al. Versatile helimagnetic phases under magnetic fields in cubic perovskite SrFeO3 . Phys. Rev. B 84, 054427 (2011).

    Google Scholar 

  117. Long, Y. W. et al. Evolution of magnetic phases in single crystals of SrFe1−xCoxO3 solid solution. Phys. Rev. B 86, 064436 (2012).

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  120. Moutafis, C., Komineas, S. & Bland, J. A. C. Dynamics and switching processes for magnetic bubbles in nanoelements. Phys. Rev. B 79, 224429 (2009).

    Google Scholar 

  121. Makhfudz, I., Krueger, B. & Tchernyshyov, O. Inertia and chiral edge modes of a skyrmion magnetic bubble. Phys. Rev. Lett. 109, 217201 (2012).

    Google Scholar 

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

    Google Scholar 

  123. Iwasaki, J., Mochizuki, M. & Nagaosa, N. Electric-current-induced skyrmion dynamics in constricted geometries. Nature Nanotech. 8, 742–747 (2013).

    CAS  Google Scholar 

  124. Sampaio, J., Cros, V., Rohart, S., Thiaville, A. & Fert, A. Nucleation, stability and current-induced motion of isolated magnetic skyrmions in nanostructures. Nature Nanotech. 8, 839–844 (2013).

    CAS  Google Scholar 

  125. Onose, Y., Okamura, Y., Seki, S., Ishiwata, S. & Tokura, Y. Observation of magnetic excitations of skyrmion crystal in a helimagnetic insulator Cu2OSeO3 . Phys. Rev. Lett. 109, 037603 (2012).

    CAS  Google Scholar 

  126. Mochizuki, M. & Seki, S. Magnetoelectric resonances and predicted microwave diode effect of the skyrmion crystal in a multiferroic chiral-lattice magnet. Phys. Rev. B 87, 134403 (2013).

    Google Scholar 

  127. Okamura, Y. et al. Microwave magnetoelectric effect via skyrmion resonance modes in a helimagnetic multiferroic. Nature Commun. 4, 2391 (2013).

    CAS  Google Scholar 

  128. Liu, Y.-H. & Li, Y.-Q. A mechanism to pin skyrmions in chiral magnets. J. Phys. Condens. Matter 25, 076005 (2013).

    Google Scholar 

  129. Rosch, A. Moving with the current. Nature Nanotech. 8, 160–161 (2013).

    CAS  Google Scholar 

  130. Blatter, G., Feigel'man, M. V., Geshkenbein, V. B. & Larkin, A. I. Vortices in high-temperature superconductors. Rev. Mod. Phys. 66, 1125–1388 (1994).

    CAS  Google Scholar 

  131. Du, H. et al. Magnetic vortex with skyrmionic core in a thin nanodisk of chiral magnets. EPL 101, 37001 (2013).

    Google Scholar 

  132. Du, H. et al. Field-driven evolution of chiral spin textures in a thin helimagnet nanodisk. Phys. Rev. B 87, 014401 (2013).

    Google Scholar 

  133. Schmitt, A. L., Higgins, J. M., Szczech, J. R. & Jin, S. Synthesis and applications of metal silicide nanowires. J. Mater. Chem. 20, 223–235 (2010).

    CAS  Google Scholar 

  134. Yu, X. Z. et al. Observation of the magnetic skyrmion lattice in a MnSi nanowire by Lorentz TEM. Nano Lett. 13, 3755–3759 (2013).

    CAS  Google Scholar 

  135. Ogasawara, T., Iwata, N., Murakami, Y., Okamoto, H. & Tokura, Y. Submicron-scale spatial feature of ultrafast photoinduced magnetization reversal in TbFeCo thin film. Appl. Phys. Lett. 94, 162507 (2009).

    Google Scholar 

  136. Finazzi, M. et al. Laser-induced magnetic nanostructures with tunable topological properties. Phys. Rev. Lett. 110, 177205 (2013).

    CAS  Google Scholar 

  137. Sun, L. et al. Creating an artificial two-dimensional skyrmion crystal by nanopatterning. Phys. Rev. Lett. 110, 167201 (2013).

    CAS  Google Scholar 

  138. Tchoe, Y. & Han, J. H. Skyrmion generation by current. Phys. Rev. B 85, 174416 (2012).

    Google Scholar 

  139. Felser, C. Skyrmions. Angew. Chem. Int. Ed. 52, 1631–1634 (2013).

    CAS  Google Scholar 

  140. Ezawa, M. Compact merons and skyrmions in thin chiral magnetic films. Phys. Rev. B 83, 100408 (2011).

    Google Scholar 

  141. Lin, S.-Z., Reichhardt, C., Batista, C. D. & Saxena, A. Driven skyrmions and dynamical transitions in chiral magnets. Phys. Rev. Lett. 110, 207202 (2013).

    Google Scholar 

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Acknowledgements

We acknowledge N. Kanazawa, M. Ishida, Y. Onose and X.Z. Yu for their help in preparing the manuscript. This work was supported by Grant-in-Aids for Scientific Research (Nos. 24224009) from the Ministry of Education, Culture, Sports, Science and Technology (MEXT) of Japan, Strategic International Cooperative Program (Joint Research Type) from Japan Science and Technology Agency, and by Funding Program for World-Leading Innovative R&D on Science and Technology (FIRST Program).

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Correspondence to Naoto Nagaosa.

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Nagaosa, N., Tokura, Y. Topological properties and dynamics of magnetic skyrmions. Nature Nanotech 8, 899–911 (2013). https://doi.org/10.1038/nnano.2013.243

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