Abstract
Skyrmions are topologically protected field configurations with particle-like properties that play an important role in various fields of science. Recently, skyrmions have been observed to be stabilized by an external magnetic field in bulk magnets. Here, we describe a two-dimensional square lattice of skyrmions on the atomic length scale as the magnetic ground state of a hexagonal Fe film of one-atomic-layer thickness on the Ir(111) surface. Using spin-polarized scanning tunnelling microscopy we can directly image this non-collinear spin texture in real space on the atomic scale and demonstrate that it is incommensurate to the underlying atomic lattice. With the aid of first-principles calculations, we develop a spin model on a discrete lattice that identifies the interplay of Heisenberg exchange, the four-spin and the Dzyaloshinskii–Moriya interaction as the microscopic origin of this magnetic state.
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References
Skyrme, T. H. A non-linear field theory. Proc. R. Soc. Lond. A 260, 127–138 (1961).
Wright, D. C. & Mermin, N. D. Crystalline liquids—the blue phases. Rev. Mod. Phys. 61, 385–432 (1989).
Al’Khawaja, U. & Stoof, H. T. C. Skyrmions in a ferromagnetic Bose–Einstein condensate. Nature 411, 918–920 (2001).
Sondhi, S. L., Karlhede, A., Kivelson, S. A. & Rezayi, E. H. Skyrmions and the crossover from the integer to the fractional quantum Hall effect at small Zeeman energies. Phys. Rev. B 47, 16419–19426 (1993).
Brey, L., Fertig, A. H., Côté, R. & MacDonald, A. H. Skyrme crystal in a two-dimensional electron gas. Phys. Rev. Lett. 75, 2562–2565 (1995).
Abrikosov, A. A. Nobel lecture: Type-II superconductors and the vortex lattice. Rev. Mod. Phys. 76, 975–979 (2004).
Bogdanov, A. N. & Yablonskii, D. A. Thermodynamically stable ‘vortices’ in magnetically ordered crystals. The mixed state of magnets. Sov. Phys. JETP 68, 101–103 (1989).
Mühlbauer, S. et al. Skyrmion lattice in a chiral magnet. Science 323, 915–919 (2009).
Yu, X. Z. et al. Real space observation of a two-dimensional skyrmion crystal. Nature 465, 901–904 (2010).
Yu, X. et al. Near room-temperature formation of a skyrmion crystal in thin-films of the helimagnet FeGe. Nature Mater. 10, 106–109 (2010).
Pappas, C. et al. Chiral paramagnetic skyrmion-like phase in MnSi. Phys. Rev. Lett. 102, 197202 (2009).
Rößler, U. K., Bogdanov, A. N. & Pfleiderer, C. Spontaneous skyrmion ground states in magnetic metals. Nature 442, 797–801 (2006).
Bode, M. et al. Chiral magnetic order at surfaces driven by inversion asymmetry. Nature 447, 190–193 (2007).
Ferriani, P. et al. Atomic-scale spin spiral with a unique rotational sense: Mn monolayer on W(001). Phys. Rev. Lett. 101, 027201 (2008).
Binz, B. & Vishwanath, A. Theory of helical spin crystals: Phases, textures, and properties. Phys. Rev. B 74, 214408 (2006).
Han, J. H., Zang, J., Yang, Z., Park, J-H. & Nagaosa, N. Skyrmion lattice in a two-dimensional chiral magnet. Phys. Rev. B 82, 094429 (2010).
Pfleiderer, C. & Rössler, U. K. News & Views, Condensed matter physics: Let’s twist again. Nature 447, 157–158 (2007).
von Bergmann, K. et al. Observation of a complex nanoscale magnetic structure in a hexagonal Fe monolayer. Phys. Rev. Lett. 96, 167203 (2006).
Ye, J. et al. Berry phase theory of the anomalous Hall effect: Applications to colossal magnetoresistance manganites. Phys. Rev. Lett. 83, 3737–3740 (1999).
Ward, R. S. Stable topological skyrmions on the 2D lattice. Lett. Math. Phys. 35, 385–393 (1995).
Abanov, A. & Pokrovsky, V. L. Skyrmion in a real magnetic film. Phys. Rev. B 58, R8889–R8892 (1998).
Heinze, S. et al. Real-space imaging of two-dimensional magnetism on the atomic-scale. Science 288, 1805–1808 (2000).
Wortmann, D., Heinze, S., Kurz, Ph., Bihlmayer, G. & Blügel, S. Resolving complex atomic-scale spin structures by spin-polarized scanning tunneling microscopy. Phys. Rev. Lett. 86, 4132–4135 (2001).
MacDonald, A. H., Girvin, S. M. & Yoshioka, D. t/U expansion for the Hubbard model. Phys. Rev. B 37, 9753–9756 (1988).
Dzyaloshinskii, I. E. Thermodynamic theory of weak ferromagnetism in antiferromagnetic substances. Sov. Phys. JETP 5, 1259–1262 (1957).
Moriya, T. Anisotropic superexchange interaction and weak ferromagnetism. Phys. Rev. 120, 91–98 (1960).
Fert, A. & Levy, P. A. Role of anisotropic exchange interactions in determining the properties of spin glasses. Phys. Rev. Lett. 44, 1538–1541 (1980).
Heide, M., Bihlmayer, G., Mavropoulos, Ph., Bringer, A. & Blügel, S. Spin–orbit Driven Physics at Surfaces (Newsletter of the Psi-K Network, Vol. 78, 2006); www.psi-k.org/newsletters/News_78/Highlight_78.pdf.
Bode, M. et al. Magnetization-direction dependent local electronic structure probed by scanning tunneling spectroscopy. Phys. Rev. Lett. 89, 237205 (2002).
von Bergmann, K. et al. Complex magnetism of the Fe monolayer on Ir(111). New J. Phys. 9, 396 (2007).
Acknowledgements
S.H. thanks the Stifterverband für die Deutsche Wissenschaft for financial support. K.v.B., M.M., J.B., A.K. and R.W. thank the SFB668, the ERC Advanced Grant FURORE and the Landesexzellenzcluster Nanospintronics for financial support.
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S.H. and G.B. carried out the density functional theory calculations and STM simulations and devised the spin model. K.v.B., M.M., J.B. and A.K. carried out the STM measurements. K.v.B. and M.M. analysed and interpreted the experimental data. S.H., K.v.B., G.B. and S.B. wrote the paper. All authors discussed the experimental and theoretical data and contributed to preparing the paper. S.H., K.v.B., M.M. and G.B. contributed equally to this work.
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Heinze, S., von Bergmann, K., Menzel, M. et al. Spontaneous atomic-scale magnetic skyrmion lattice in two dimensions. Nature Phys 7, 713–718 (2011). https://doi.org/10.1038/nphys2045
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DOI: https://doi.org/10.1038/nphys2045
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