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Real-space observation of emergent magnetic monopoles and associated Dirac strings in artificial kagome spin ice


Magnetic monopoles have been predicted to occur as emergent fractional quasiparticles inside pyrochlore spin ice, a frustrated magnetic insulator. Experimental signatures of such emergent monopoles accompanied by Dirac strings have been detected by means of neutron scattering in reciprocal space in pyrochlore spin ice at sub-Kelvin temperatures, but their real-space observation has remained elusive. Here we report on direct, real-space observations of emergent monopoles and their associated Dirac strings in two-dimensional (2D) artificial kagome spin ice at room temperature using synchrotron X-ray photoemission electron microscopy. Magnetization reversal proceeds through the nucleation and avalanche-type dissociation of monopole–antimonopole pairs along 1D Dirac strings. This is in sharp contrast to conventional domain growth in 2D systems, providing a striking example of dimensional reduction due to frustration. The observed hysteresis, monopole densities and 1D Dirac-string avalanches are quantitatively explained by Monte Carlo simulations.

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Figure 1: Emergent monopoles and associated Dirac strings in artificial kagome spin ice.
Figure 2: Identification of monopoles during magnetization reversal.
Figure 3: Creation and separation of monopole–antimonopole pairs and growth of Dirac strings.
Figure 4: Hysteresis and avalanches—experimental results.
Figure 5: Hysteresis, avalanches and disorder—Monte-Carlo simulations.


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The authors would like to thank: M. Horisberger, E. Deckardt, A. Weber, C. David, A. Steger, L. Le Guyader, A. Kleibert, J. Raabe, D. Eastwood and D. Atkinson for their help. We also acknowledge helpful discussions with V. Lobaskin, W. Nahm and M. Sigrist. This work was supported by the Swiss National Science Foundation and the Science Foundation of Ireland (08/RFP/PHY1532 and 05/IN1/I853), and part of this work was carried out at the Swiss Light Source, Paul Scherrer Institute, Villigen, Switzerland. We also acknowledge receipt of an HEA Ireland equipment fund.

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Sample preparation: E.M.; measurements: E.M., A.F.R.; analysis and interpretation: E.M., L.J.H., H.B.B.; theory and simulations: R.V.H., H.B.B.; preparation of the manuscript: E.M., L.J.H., H.B.B.; supervision of the project: L.J.H., H.B.B., F.N. All authors discussed the results and implications, and commented on the manuscript at all stages.

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Correspondence to Laura J. Heyderman or Hans-Benjamin Braun.

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The authors declare no competing financial interests.

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Mengotti, E., Heyderman, L., Rodríguez, A. et al. Real-space observation of emergent magnetic monopoles and associated Dirac strings in artificial kagome spin ice. Nature Phys 7, 68–74 (2011).

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