Fragmentation in Frustrated Magnets: A Review
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Fragmentation in Frustrated Magnets: A Review Elsa Lhotel1 · Ludovic D. C. Jaubert2 · Peter C. W. Holdsworth3 Received: 20 January 2020 / Accepted: 29 August 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract Spin liquids are exotic phases of matter that often support emergent gauge fields and quasi-particle excitations. While spin liquids are commonly known for remaining disordered, their definition has been extended to include phases with broken symmetry corresponding to (partial) long-range order, such as chiral and nematic spin liquids for example. For Coulomb spin liquids, this ordering can be quantitatively understood via a Helmholtz decomposition between divergence-free and divergencefull terms. This phenomenon has been coined fragmentation, where spin degrees of freedom fragment into two components: the fluctuating disordered part and the ordered one. In this review, we will cover the theoretical and experimental aspects of this growing field, in particular its relation to magnetic monopoles in spin ice, its phase diagram and the possibility to observe it in solid-state crystal and artificial networks. Keywords Magnetic fragmentation · Spin liquids · Spin ice · Magnetic monopoles · Pyrochlore · Kagome
1 Introduction Spin liquids are unconventional phases of matter where frustration prevents magnetic order down to the lowest temperatures [1, 2], opening a window for new collective phenomena. But while the absence of order has the merit of summarising * Elsa Lhotel [email protected] Ludovic D. C. Jaubert ludovic.jaubert@u‑bordeaux.fr Peter C. W. Holdsworth peter.holdsworth@ens‑lyon.fr 1
Institut Néel, CNRS-Université Grenoble Alpes, 38042 Grenoble, France
2
CNRS, Université de Bordeaux, LOMA, UMR 5798, 33405 Talence, France
3
Université de Lyon, ENS de Lyon, Université Claude Bernard, CNRS, Laboratoire de Physique, 69342 Lyon, France
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Vol.:(0123456789)
Journal of Low Temperature Physics
Fig. 1 a Pyrochlore lattice cubic unit cell of a pyrochlore lattice. The centre of the tetrahedra forms a diamond lattice whose bipartite nature particularises up and down tetrahedra, with a red and blue sphere respectively. The diamond lattice forms the backbone for magnetic monopoles. b Dumbbell model. The magnetic dipoles are replaced by a needle carrying a dumbbell of charge-small red and blue spheres. 2-in 2-out tetrahedra (top) are charge neutral, 3-in 1-out and 3-out 1-in carry a single-charge monopole (centre), 4-in and 4-out carry a double monopole (bottom). Note that a monopole is a composition of several dumbbell charges allowing monopole fractionalisation. Reproduced from Ref. [3] (Color figure online)
their most noticeable property, and to be reasonably straightforward to identify experimentally, it is not really satisfactory to define something by what it is not. The caveat of a definition by negation is that it tends to group together concepts which can be fairly different, linked here by the thread of magnetic disorder. To improve the description, one
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