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Magnetic Moment Fragmentation in Spin Ice and Artificial Spin Ice

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Magnetic systems where interactions and lattice geometry fail to produce conventional (e.g., ferromagnetic or antiferromagnetic) ordered states are referred to as being frustrated. This phenomenon often leads to an effectively reduced Hilbert space at low energy/temperature that has enhanced—or emergent—symmetries. A case in point is the so-called Coulomb phase [1,2] in dimer and ice models, where the magnetic configurations acquire an emergent gauge symmetry and dipolar correlations. In this talk I will introduce these concepts at a pedagogical level and illustrate their experimental signatures (for instance in the form of so-called pinch-point scattering patterns in the structure factor) in solid-state frustrated magnets and artificial arrays of magnetic nano-particles. I will then focus on model spin ice and artificial systems where the the emergent field can be separated into divergence full and divergence free parts, following a Helmholz decomposition [3]. As a consequence the configuration of magnetic moments naturally fragments into two distinct fields, one providing a dense pattern of `magnetic charges’, and the other providing a persistent fluctuating background. Driving the system into an ordered charge crystal phase leads only to partial ordering of the spins, with one components providing the Bragg peaks of the ordered state and the other a magnetic fluid with all the characteristics of an emergent Coulomb phase. Specific examples include a monopole crystal phase for spin ice and the charge ordered KII phase of artificial kagome ice [3]. Recent experiments have shown evidence of this fragmentation in three dimensions, in the frustrated pyrochlore magnet Nd2Zr2O7 [4], in artificial kagome ice [5] and in the layered quasi-two-dimensional magnet Dy3Mg2Sb3O14 [6], and I shall comment on these exciting developments.

[1] C. L. Henley, Annu. Rev. Condens. Matter Phys. 1, 179(2010);

V. Isakov, K. Gregor, R. Moessner, and S. L. Sondhi, Phys. Rev. Lett., 93, 167204 (2004);

[3] M. Brooks-Bartlett, S. Banks, L. Jaubert, A. Harman-Clarke, P. C. W. Holdsworth, Phys. Rev. X4, 011007 (2014);

[4] S. Petit et. al. , Nature Physics (2016), doi:10.1038/nphys3710;

[5] Benjamin Canals et. al. , Nature Communications (2016) 7, 11446;

[6] Joseph A. M. Paddison et al. Nature Communications (2016) 7, 13842.

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