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Emergent reduced dimensionality by vertex frustration in artificial spin ice

Nature Physics volume 12, pages 162165 (2016) | Download Citation


Reducing the dimensionality of a physical system can have a profound effect on its properties, as in the ordering of low-dimensional magnetic materials1, phonon dispersion in mercury chain salts2, sliding phases3, and the electronic states of graphene4. Here we explore the emergence of quasi-one-dimensional behaviour in two-dimensional artificial spin ice, a class of lithographically fabricated nanomagnet arrays used to study geometrical frustration5,6,7. We extend the implementation of artificial spin ice by fabricating a new array geometry, the so-called tetris lattice8. We demonstrate that the ground state of the tetris lattice consists of alternating ordered and disordered bands of nanomagnetic moments. The disordered bands can be mapped onto an emergent thermal one-dimensional Ising model. Furthermore, we show that the level of degeneracy associated with these bands dictates the susceptibility of island moments to thermally induced reversals, thus establishing that vertex frustration can reduce the relevant dimensionality of physical behaviour in a magnetic system.

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This work was funded by the US Department of Energy, Office of Basic Energy Sciences, Materials Science and Engineering Division under grant no. DE-SC0010778. The work of C.N. was carried out under the auspices of the US Department of Energy at LANL under contract no. DE-AC52-06NA253962. Work performed at the University of Minnesota (UMN) was supported by the National Science Foundation through the UMN MRSEC under award number DMR-1420013, as well as by EU Marie Curie IOF project no. 299376. The Advanced Light Source is supported by the Director, Office of Science, Office of Basic Energy Sciences, of the US Department of Energy under contract no. DE-AC02-05CH11231.

Author information


  1. Department of Physics and Frederick Seitz Materials Research Laboratory, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA

    • Ian Gilbert
    • , Yuyang Lao
    • , Isaac Carrasquillo
    •  & Peter Schiffer
  2. Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455, USA

    • Liam O’Brien
    • , Justin D. Watts
    • , Michael Manno
    •  & Chris Leighton
  3. Thin Film Magnetism Group, Department of Physics, Cavendish Laboratory, University of Cambridge, Cambridge CB30HE, UK

    • Liam O’Brien
  4. School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455, USA

    • Justin D. Watts
  5. Lawrence Berkeley National Laboratory (LBNL), Berkeley, California 94720, USA

    • Andreas Scholl
  6. Theoretical Division and Center for Nonlinear Studies, MS B258, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA

    • Cristiano Nisoli


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I.G., C.N. and P.S. designed this study. I.G. and Y.L. fabricated the lithographic patterns, and L.O’B., J.D.W., M.M. and C.L. optimized and deposited the wedged permalloy films. A.S., I.G. and Y.L. conducted the XMCD-PEEM measurements. I.C. assisted with data analysis. C.N. developed the theory describing the tetris lattice. I.G., C.N. and P.S. wrote the paper with input from all of the co-authors.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to Peter Schiffer.

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