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Spin Ice As a Coulomb Liquid: From Emergent Gauge Fields to Magnetic Monopoles

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Spin Ice

Part of the book series: Springer Series in Solid-State Sciences ((SSSOL,volume 197))

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Abstract

This chapter provides an introduction to the Coulomb phase of spin ice. After reviewing conventional notions of order and disorder, as well as the emergence of quasiparticles, we show how spin ice is special in that it exhibits an emergent gauge field with fractionalised excitations in the form of magnetic monopoles. This is a property of a topological magnetic phase, a Coulomb phase of the corresponding emergent gauge theory, which even harbours irrational magnetic charge and observable ‘Dirac strings’. We provide a broad overview of unusual and novel phenomena arising in spin ice, including the notion of residual entropy, the possibility of generating dimensional reduction to kagome ice via application of a magnetic field, the role of disorder, magnetoelectric phenomena, and various unusual phase transitions.

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Notes

  1. 1.

    As an aside, we note that projective equivalence has effectively also been used in the study of fractional Chern insulators [25,26,27] to obtain dispersionless bands with nonzero Chern number in which interacting electrons at appropriate filling then exhibit a fractional quantum Hall effect.

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Acknowledgements

I am very grateful to my numerous collaborators in the work discussed here. It is almost impossible to single out any individuals here, but it was with Claudio Castelnovo, Sergei Isakov and Shivaji Sondhi that much of the conceptual framework presented here was developed. I am also grateful to the editors of this volume, Ludovic Jaubert and Masafumi Udagawa, for much encouragement, support and patience. I also thank the former, along with Peter Holdsworth, for help with the figures, and Maximilian Schulz for comments on the manuscript.

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    Roderich Moessner

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  1. Department of Physics, Gakushuin University, Tokyo, Japan

    Masafumi Udagawa

  2. Laboratoire Ondes et Matière d’Aquitaine, Université de Bordeaux, CNRS, Bordeaux, France

    Ludovic Jaubert

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Moessner, R. (2021). Spin Ice As a Coulomb Liquid: From Emergent Gauge Fields to Magnetic Monopoles. In: Udagawa, M., Jaubert, L. (eds) Spin Ice. Springer Series in Solid-State Sciences, vol 197. Springer, Cham. https://doi.org/10.1007/978-3-030-70860-3_3

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