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Experimental signature of the attractive Coulomb force between positive and negative magnetic monopoles in spin ice

Nature Physics volume 12, pages 661–666 (2016)Cite this article

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Abstract

A non-Ohmic current that grows exponentially with the square root of applied electric field is well known from thermionic field emission (the Schottky effect)1, electrolytes (the second Wien effect)2 and semiconductors (the Poole–Frenkel effect)3. It is a universal signature of the attractive Coulomb force between positive and negative electrical charges, which is revealed as the charges are driven in opposite directions by the force of an applied electric field. Here we apply thermal quenches4 to spin ice5,6,7,8,9,10,11 to prepare metastable populations of bound pairs of positive and negative emergent magnetic monopoles12,13,14,15,16 at millikelvin temperatures. We find that the application of a magnetic field results in a universal exponential-root field growth of magnetic current, thus confirming the microscopic Coulomb force between the magnetic monopole quasiparticles and establishing a magnetic analogue of the Poole–Frenkel effect. At temperatures above 300 mK, gradual restoration of kinetic monopole equilibria causes the non-Ohmic current to smoothly evolve into the high-field Wien effect2 for magnetic monopoles, as confirmed by comparison to a recent and rigorous theory of the Wien effect in spin ice17,18. Our results extend the universality of the exponential-root field form into magnetism and illustrate the power of emergent particle kinetics to describe far-from-equilibrium response in complex systems.

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Figure 1: Magnetricity in spin ice Dy2Ti2O7 at 65 mK arising from non-equilibrium populations of magnetic monopoles.
Figure 2: Ohmic and non-Ohmic monopole conductivity κ as a function of magnetic field.
Figure 3: High-field Wien effect for magnetic monopoles in spin ice, fitted using the theoretical charge12 and accounting for charge screening as in refs 17,18: data at >0.12 T are shown but not fitted (see Methods and Supplementary Information 1).
Figure 4: Far-from equilibrium magnetic monopole conductivity in spin ice: schematic of our main results for the short-time monopole conductivity as a function of temperature and magnetic field.

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Acknowledgements

C.P. acknowledges discussions and mathematical modelling help from C. Gignoux. S.T.B. thanks his collaborators on refs 17,18—V. Kaiser, R. Moessner and P. Holdsworth—for many useful discussions concerning the theory of the Wien effect in spin ice. S.R.G., D.P. and G.B. thank EPSRC for funding. We thank M. Ruminy for assistance with sample preparation. The crystal growth by K.M. was carried out under the Visiting Researchers Program of the Institute for Solid State Physics, the University of Tokyo.

Author information

Authors and Affiliations

  1. Institut Néel, C.N.R.S—Université Joseph Fourier, BP 166, 38042 Grenoble, France

    C. Paulsen & E. Lhotel

  2. School of Physics and Astronomy, Cardiff University, Cardiff CF24 3AA, UK

    S. R. Giblin

  3. Physics Department, Clarendon Laboratory, Oxford University, Oxford OX1 3PU, UK

    D. Prabhakaran

  4. Department of Physics, University of Warwick, Coventry CV4 7AL, UK

    G. Balakrishnan

  5. Kyushu Institute of Technology, Kitakyushu 804-8550, Japan

    K. Matsuhira

  6. London Centre for Nanotechnology, University College London, 17-19 Gordon Street, London WC1H 0AJ, UK

    S. T. Bramwell

  7. Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, UK

    S. T. Bramwell

Authors
  1. C. Paulsen
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  2. S. R. Giblin
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  3. E. Lhotel
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  7. S. T. Bramwell
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Contributions

Experiments were conceived, designed and performed by C.P., E.L. and S.R.G. The data were analysed by C.P., E.L., S.R.G. and S.T.B., who adapted the theory of ref. 18. Contributed materials and analysis tools were made by K.M., D.P. and G.B. The paper was written by S.T.B., C.P., E.L. and S.R.G.

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Correspondence to C. Paulsen.

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The authors declare no competing financial interests.

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Paulsen, C., Giblin, S., Lhotel, E. et al. Experimental signature of the attractive Coulomb force between positive and negative magnetic monopoles in spin ice. Nature Phys 12, 661–666 (2016). https://doi.org/10.1038/nphys3704

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