Artificial Spin Ice: Frustration and Magnetic Monopoles

Artificial spin ice, consisting of two-dimensional arrangements of dipolar coupled single-domain nanomagnets created via electron beam lithography, have come into the focus of the scientific community since they provide an ideal arena to study the effects of frustration. It is not only possible to fine tune the system geometry in terms of the shape and size of the nanomagnets, the lattice geometry and the lattice parameter, but also to use a variety of microscope techniques to study the magnetic configurations and their behaviour on the application of an external stimulus.

Particularly of interest in recent years is the artificial spin ice consisting of single domain nanomagnets arranged on a square lattice, with the nanomagnets elongated so that the moments can point in one of two directions [1]. The artificial spin ice take their name from the rare earth titanate pyrocholores [2] that form spin ice crystals, where the role of the Ising spins is taken by the moments of the nanomagnets and the anisotropy arising from the crystal field is replaced by the shape anisotropy associated with each nanomagnet. Our work has concentrated on a related system, the artificial kagome spin ice, with the elongated nanomagnets arranged on the kagome lattice and forming an array of hexagonal rings (lower section of Fig. 1a and Fig. 1b). In order to determine the magnetic configurations, we employ synchrotron x-ray photoemission electron microscopy, which provides an unequivocal picture of the magnetic configurations.

Selecting finite building blocks comprising one, two and three hexagonal rings [3], allows the full characterization of the energy levels using a dipolar calculation and identification of the lowest energy states. On attempting to apply an ‘effective thermal anneal’ via demagnetisation, it was found that the percentage of low energy states decreases as the number of rings increases, indicating that it will be impossible to achieve the ground state in an infinite array using such a partially deterministic demagnetisation protocol. We are therefore currently exploring the possibilities to access the low energy states in such a frustrated system via thermal annealing. For this purpose it is a goal to be able to pattern our artificial spin ice structures in films that have moment fluctuations at temperatures relatively close to room temperature. This would bring us closer to a direct comparison between such an artificially created spin ice system and the bulk spin ice, allowing us to observe the role of frustration in a dynamic system.

Our more recent observations demonstrate the existence of emergent magnetic monopoles in a quasi-infinite nanomagnet array [4]. In an applied magnetic field, monopole-antimonopole pairs nucleate and separate in an avalanche-type manner along one-dimensional Dirac strings consisting of overturned dipoles (see Fig. 1a and c), and the behaviour can be quantitatively explained by Monte Carlo simulations [4, 5, 6]. With careful modification of the shape of particular islands it is possible to control both where the nucleation of monopole-antimonopole pair occurs and where the monopoles are brought to a stop ([6] and supplementary information in Ref. [4]). This work on artificial spin systems opens the way to making use of the multiple states in coupled nanomagnet systems [7, 8] and to the controlled manipulation of magnetic charges that may lead to novel spintronic devices.


  1. R.F. Wang, C. Nisoli, R. S. Freitas, J. Li, W. McConville, B J.Cooley, M.S. Lund, N. Samarth, C. Leighton, V.H. Crespi, and P. Schiffer, Nature 439, 303 (2006)
  2. M.J. Harris, S.T. Bramwell, D.F. McMorrow, T. Zeiske, and K.W. Godfrey, Phys. Rev. Letts. 79, 2554 (1997)
  3. E. Mengotti, L.J. Heyderman, A. Fraile Rodríguez, A. Bisig, L. Le Guyader, F. Nolting, and H.B. Braun, Phys. Rev. B 78, 144402 (2008)
  4. E. Mengotti, L.J. Heyderman, A. Fraile Rodríguez, F. Nolting, R.V. Hügli, H.B. Braun Nature Physics 7, 68 (2011). See also: Laura Heyderman, Frithjof Nolting and Hans-Benjamin Braun, Monopole aus Nanomagneten (Monopoles from Magnets), Spektrum der Wissenschaft, March 2011
  5. R.V. Hügli, G. Duff, B. O’Conchuir, E. Mengotti, L.J. Heyderman, A. Fraile Rodríguez, F. Nolting, and H. B. Braun, J. Appl. Phys. 111, 07E103 (2012)
  6. R.V. Hügli, G. Duff, B. O'Conchuir, E. Mengotti, A. Fraile Rodríguez, F. Nolting, L.J. Heyderman, and H.B. Braun, Proceedings of the Royal Society (Accepted 2012)
  7. E. Mengotti, L.J. Heyderman, A. Bisig, A. Fraile Rodríguez, L. Le Guyader, F. Nolting, and H. B. Braun, J. Appl. Phys. 105, 113113 (2009)
  8. L.J. Heyderman, T. Jung, E. Mengotti, A. Bisig, A. Fraile Rodríguez, F. Nolting, H.B. Braun, T. Schrefl United States Patent US 8,085,578 B2, 27.12.2011


Prof. Dr. Laura Heyderman

Mesoscopic Systems
ETH Zürich - Paul Scherrer Institut
5232 Villigen PSI

+41 56 310 2613
+41 56 310 2646