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Spin Ice pp 143–188Cite as

Modelling of Classical Spin Ice: Coulomb Gas Description of Thermodynamic and Dynamic Properties

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

Abstract

The Coulomb gas description of spin ice has revolutionized our understanding of these systems. Built on the remarkable self screening of the dipolar spin ice model, the emergence of magnetic monopole quasi-particles has allowed a depth of analytic and conceptual progress that is far beyond the spin description. After defining the magnetic Coulomb gas, or magnetolyte, we bench mark it against dipolar spin ice, before presenting a Debye-Hückel theory modified to take into account the underlying constraints of the spin degrees of freedom. The calculated specific heat compares favourably with simulation and experiment, with quantitative agreement at high and at low temperature. Moving to dynamical properties, we show how the temperature dependence of experimentally observed relaxation time scales is captured by monopole dynamics. We show that the magnetolyte exhibits non-Ohmic contributions to the monopole conductivity, the AC Wien effect, and we propose detailed protocols for its observation in experiments. Thermal and field quenches take the magnetolyte far from equilibrium, exposing a cornucopia of phenomena characteristic of reaction diffusion processes, dimer absorption and kinetically constrained models.

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Notes

  1. 1.

    The diffusion constant for a random walk on a diamond lattice is \(D=\frac{r_d^2}{6\tau _0}\) [24], which is modified to take into account both the spatial [24] and temporal [31] constraints of monopole hopping in the magnetolyte.

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Acknowledgements

The work presented in this article covers a cross section of collaborations by both authors. It is a pleasure to thank all our collaborators for these extensive and fruitful projects and in particular S.T. Banks, S.T. Bramwell, J.T. Chalker, T. Fennell, M.J.P. Gingras, V. Kaiser, L.D.C. Jaubert, and R. Moessner. We are grateful to M.J.P Gingras for providing us with the DSI specific heat data and to V. Kaiser for useful comments on the manuscript. This work was supported in part by EPSRC Grant No. EP/K028960/1 and EPSRC Grant No. EP/M007065/1 (CC) and by the Institut Universitaire de France (PCWH).

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Authors and Affiliations

  1. TCM group, Cavendish Laboratory, University of Cambridge, Cambridge, UK

    C. Castelnovo

  2. Université de Lyon, ENS de Lyon, Université Claude Bernard, CNRS, Laboratoire de Physique, F-69342, Lyon, France

    P. C. W. Holdsworth

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Correspondence to C. Castelnovo .

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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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Castelnovo, C., Holdsworth, P.C.W. (2021). Modelling of Classical Spin Ice: Coulomb Gas Description of Thermodynamic and Dynamic Properties. 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_7

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