1 2010 Vol: 465(7300):901-904. DOI: 10.1038/nature09124

Real-space observation of a two-dimensional skyrmion crystal

Skyrmions are stable topological textures with particle-like properties [mdash] a mathematical concept that was originally used to describe nuclear particles but has since turned up at all scales. Last year, the presence of skyrmions in the magnetic compounds MnSi and Fe1-xCoxSi was confirmed with neutron-scattering experiments. Here, real-space images are presented of a two-dimensional skyrmion lattice in a thin film of the latter compound. The observed nanometre-scale spin topology might reveal new magneto-transport effects.

Mentions
Figures
Figure 1: Topological spin textures in the helical magnet Fe0.5Co0.5Si. a, b, Helical (a) and skyrmion (b) structures predicted by Monte Carlo simulation. c, Schematic of the spin configuration in a skyrmion. d–f, The experimentally observed real-space images of the spin texture, represented by the lateral magnetization distribution as obtained by TIE analysis of the Lorentz TEM data: helical structure at zero magnetic field (d), the skyrmion crystal (SkX) structure for a weak magnetic field (50 mT) applied normal to the thin plate (e) and a magnified view of e (f). The colour map and white arrows represent the magnetization direction at each point. Figure 2: Variations of spin texture with magnetic field and temperature in Fe0.5Co0.5Si. a–d, Magnetic-field dependence of the spin texture, in real-space Lorentz TEM (overfocus) images. e–h, FFT patterns corresponding to a–d. i–l, Temperature profiles of the distribution map of the lateral magnetization for a magnetic field of 50 mT. Magnetic fields were applied normal to the (001) thin film. The colour wheel represents the magnetization direction at every point. Figure 3: Phase diagrams of magnetic structure and spin textures in a thin film of Fe0.5Co0.5Si. a–c, Spin textures observed using Lorentz TEM obtained by Monte Carlo simulation. e–g, Spin textures after TEM. H, helical structure; SkX, skyrmion crystal structure; FM, ferromagnetic structure. d, h, Observed (d) and calculated (h) phase diagrams in the B–T plane. The magnetic field was applied perpendicular to the image plane. In h, B and T are normalized using the arbitrary constants BC and TC. The colour bars in the phase diagrams indicate the skyrmion density per 10−12 m2 (d) and per d2 (h), d being the helical spin wavelength. Dashed lines show the phase boundaries between the SkX, H and FM phases. Stars in d and h indicate (T, B) conditions for the images shown in a–c and e–g, respectively.
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References
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    • . . . The complex spin configurations are of great recent interest4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23 and are relevant to nontrivial physical phenomena such as the topological Hall effect24, 25, 26 . . .
    • . . . For example, MnSi is a helical magnet owing to the Dzyaloshinskii–Moriya interaction and has an unusual temperature–pressure phase diagram10, 11, 12, 14, 15, 16, 17 . . .
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    • . . . In other, less conventional, cases, spins can sometimes form highly nontrivial structures called spin textures4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23 . . .
    • . . . The complex spin configurations are of great recent interest4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23 and are relevant to nontrivial physical phenomena such as the topological Hall effect24, 25, 26 . . .
    • . . . For example, MnSi is a helical magnet owing to the Dzyaloshinskii–Moriya interaction and has an unusual temperature–pressure phase diagram10, 11, 12, 14, 15, 16, 17 . . .
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    • . . . In other, less conventional, cases, spins can sometimes form highly nontrivial structures called spin textures4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23 . . .
    • . . . The complex spin configurations are of great recent interest4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23 and are relevant to nontrivial physical phenomena such as the topological Hall effect24, 25, 26 . . .
    • . . . For example, MnSi is a helical magnet owing to the Dzyaloshinskii–Moriya interaction and has an unusual temperature–pressure phase diagram10, 11, 12, 14, 15, 16, 17 . . .
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    • . . . In other, less conventional, cases, spins can sometimes form highly nontrivial structures called spin textures4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23 . . .
    • . . . The complex spin configurations are of great recent interest4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23 and are relevant to nontrivial physical phenomena such as the topological Hall effect24, 25, 26 . . .
  14. Pfleiderer, C. Partial order in the non-Fermi-liquid phase of MnSi Nature 427, 227-231 (2004) .
    • . . . In other, less conventional, cases, spins can sometimes form highly nontrivial structures called spin textures4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23 . . .
    • . . . The complex spin configurations are of great recent interest4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23 and are relevant to nontrivial physical phenomena such as the topological Hall effect24, 25, 26 . . .
    • . . . For example, MnSi is a helical magnet owing to the Dzyaloshinskii–Moriya interaction and has an unusual temperature–pressure phase diagram10, 11, 12, 14, 15, 16, 17 . . .
    • . . . Neutron scattering shows that under pressure the direction of q in MnSi is disordered but its magnitude remains constant at |q| = 0.043 Å, resulting in non-Fermi-liquid-like transport properties14 . . .
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    • . . . In other, less conventional, cases, spins can sometimes form highly nontrivial structures called spin textures4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23 . . .
    • . . . The complex spin configurations are of great recent interest4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23 and are relevant to nontrivial physical phenomena such as the topological Hall effect24, 25, 26 . . .
    • . . . For example, MnSi is a helical magnet owing to the Dzyaloshinskii–Moriya interaction and has an unusual temperature–pressure phase diagram10, 11, 12, 14, 15, 16, 17 . . .
    • . . . The spontaneous skyrmion ground state was theoretically proposed as a candidate for the partially ordered state15, 16 . . .
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    • . . . In other, less conventional, cases, spins can sometimes form highly nontrivial structures called spin textures4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23 . . .
    • . . . The complex spin configurations are of great recent interest4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23 and are relevant to nontrivial physical phenomena such as the topological Hall effect24, 25, 26 . . .
    • . . . For example, MnSi is a helical magnet owing to the Dzyaloshinskii–Moriya interaction and has an unusual temperature–pressure phase diagram10, 11, 12, 14, 15, 16, 17 . . .
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    • . . . In other, less conventional, cases, spins can sometimes form highly nontrivial structures called spin textures4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23 . . .
    • . . . The crystallization of skyrmions as driven by thermal fluctuations has recently been confirmed in a narrow region of the temperature/magnetic field (T–B) phase diagram in neutron scattering studies of the three-dimensional helical magnets MnSi (ref. 17) and Fe1−xCoxSi (ref. 22) . . .
    • . . . The complex spin configurations are of great recent interest4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23 and are relevant to nontrivial physical phenomena such as the topological Hall effect24, 25, 26 . . .
    • . . . For example, MnSi is a helical magnet owing to the Dzyaloshinskii–Moriya interaction and has an unusual temperature–pressure phase diagram10, 11, 12, 14, 15, 16, 17 . . .
    • . . . Recent neutron scattering experiments on MnSi (ref. 17) and Fe1−xCoxSi (ref. 22) have identified the mysterious ‘A phase’ with the skyrmion lattice phase . . .
    • . . . Theoretical analysis and experimental results concluded that the skyrmion lattice is stabilized by thermal fluctuations in some limited region of the T–B plane near the critical temperature, whereas the conical state with the wavevector q parallel to the magnetic field is more stable over most of the phase diagram17. . . .
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    • . . . In other, less conventional, cases, spins can sometimes form highly nontrivial structures called spin textures4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23 . . .
    • . . . The complex spin configurations are of great recent interest4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23 and are relevant to nontrivial physical phenomena such as the topological Hall effect24, 25, 26 . . .
    • . . . Observation of the helical spin structure in Fe0.5Co0.5Si using Lorentz TEM, including magnetic-lattice defects such as edge dislocations, was first reported in ref. 18 . . .
    • . . . The Lorentz TEM observation of the zero-field state below the magnetic transition temperature (~40 K) clearly reveals the stripy pattern (Fig. 1d) of the lateral component of the magnetization, with a period of 90 nm, as previously reported18; this indicates the proper-screw spin propagating in the [100] or [010] direction . . .
    • . . . In the real-space image, however, knife-edge dislocations (such as that marked by an arrowhead in Fig. 2a) are often seen in the helical spin state, as pointed out in ref. 18 . . .
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    • . . . In other, less conventional, cases, spins can sometimes form highly nontrivial structures called spin textures4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23 . . .
    • . . . The complex spin configurations are of great recent interest4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23 and are relevant to nontrivial physical phenomena such as the topological Hall effect24, 25, 26 . . .
    • . . . In a bulk (three-dimensional) crystal, the SkX phase appears in a narrow window of the T–B plane, at around 10 mT and 35–40 K (ref. 19) . . .
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    • . . . In other, less conventional, cases, spins can sometimes form highly nontrivial structures called spin textures4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23 . . .
    • . . . The complex spin configurations are of great recent interest4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23 and are relevant to nontrivial physical phenomena such as the topological Hall effect24, 25, 26 . . .
  21. Takeda, M. Nematic-to-smectic transition of magnetic texture in conical state J. Phys. Soc. Jpn. 78, 093704 (2009) .
    • . . . In other, less conventional, cases, spins can sometimes form highly nontrivial structures called spin textures4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23 . . .
    • . . . The complex spin configurations are of great recent interest4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23 and are relevant to nontrivial physical phenomena such as the topological Hall effect24, 25, 26 . . .
  22. Münzer, W. Skyrmion lattice in the doped semiconductor Fe1−xCoxSi Phys Rev. B 81, 041203(R) (2010) .
    • . . . In other, less conventional, cases, spins can sometimes form highly nontrivial structures called spin textures4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23 . . .
    • . . . The crystallization of skyrmions as driven by thermal fluctuations has recently been confirmed in a narrow region of the temperature/magnetic field (T–B) phase diagram in neutron scattering studies of the three-dimensional helical magnets MnSi (ref. 17) and Fe1−xCoxSi (ref. 22) . . .
    • . . . The complex spin configurations are of great recent interest4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23 and are relevant to nontrivial physical phenomena such as the topological Hall effect24, 25, 26 . . .
    • . . . Recent neutron scattering experiments on MnSi (ref. 17) and Fe1−xCoxSi (ref. 22) have identified the mysterious ‘A phase’ with the skyrmion lattice phase . . .
    • . . . In analogy to Bragg reflections observed in neutron scattering22, two peaks were found in the corresponding fast Fourier transform (FFT) pattern (Fig. 2e), confirming that the helical axis is along the [100] direction . . .
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    • . . . In other, less conventional, cases, spins can sometimes form highly nontrivial structures called spin textures4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23 . . .
    • . . . The complex spin configurations are of great recent interest4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23 and are relevant to nontrivial physical phenomena such as the topological Hall effect24, 25, 26 . . .
    • . . . In the context of the skyrmion, the thin film has the advantage that the conical state is not stabilized when the magnetic field is perpendicular to the plane23 . . .
    • . . . The ferromagnetic coupling between the layers effectively increases the spin stiffness in the real case, leading to a ‘heavier-spin’ object and, consequently, relatively weaker thermal fluctuations than in the 2D model23. . . .
  24. Onose, Y.; Takeshita, N.; Terakura, C.; Takagi, H.; Tokura, Y. Doping dependence of transport properties in Fe1-xCoxSi Phys. Rev. B 72, 224431 (2006) .
    • . . . The skyrmion configuration in a magnetic solid is anticipated to produce unconventional spin–electronic phenomena such as the topological Hall effect24, 25, 26 . . .
    • . . . The complex spin configurations are of great recent interest4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23 and are relevant to nontrivial physical phenomena such as the topological Hall effect24, 25, 26 . . .
  25. Lee, M.; Kang, W.; Onose, Y.; Tokura, Y.; Ong, N. P. Unusual Hall anomaly in MnSi under pressure Phys. Rev. Lett. 102, 186601 (2009) .
    • . . . The skyrmion configuration in a magnetic solid is anticipated to produce unconventional spin–electronic phenomena such as the topological Hall effect24, 25, 26 . . .
    • . . . The complex spin configurations are of great recent interest4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23 and are relevant to nontrivial physical phenomena such as the topological Hall effect24, 25, 26 . . .
  26. Neubauer, A. Topological Hall effect in the A phase of MnSi Phys. Rev. Lett. 102, 186602 (2009) .
    • . . . The skyrmion configuration in a magnetic solid is anticipated to produce unconventional spin–electronic phenomena such as the topological Hall effect24, 25, 26 . . .
    • . . . The complex spin configurations are of great recent interest4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23 and are relevant to nontrivial physical phenomena such as the topological Hall effect24, 25, 26 . . .
  27. Landau, L. D.; Lifshitz, E. M.; Pitaevskii, L. P. Electrodynamics of Continuous Media , 178-179 (2008) .
  28. Grundy, P. J.; Tebble, R. S. Lorentz electron microscopy Adv. Phys. 17, 153-242 (1968) .
    • . . . In this Letter, we report the real-space observation of the formation of the SkX in a thin film of B20-type Fe0.5Co0.5Si, the thickness of which is less than the helical wavelength, using Lorentz TEM28 with a high spatial resolution . . .
  29. Tonomura, A. Observation of individual vortices trapped along columnar defects in high-temperature superconductors Nature 412, 620-622 (2001) .
    • . . . The situation is similar to the magnetic flux in a superconductor29, in which the spins are parallel to the magnetic field in the core of each vortex. . . .
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