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The Coulomb phase is a classical spin liquid arising in frustrated systems with "ice-rules" constraints, such as spin ice [1].
We present here an analytical picture of how magnetic loops emerge from this phase, both in 2 and 3 dimensions, and provide conducting channels for itinerant electrons coupled to the lattice spins via double exchange [2]. Minimizing the kinetic energy of these charges then leads to doping- and dimension-dependent rearrangements of the loop ensemble.
Even if partially lifted, the macroscopic degeneracy of the Coulomb phase resists to a low and finite density of electrons, thanks to a mechanism of segmentation of the very long loops. At intermediate doping, "loop crystals" are stabilized for some points of the phase diagram, and gradually melt into each other by varying the doping.
[1] Jaubert, Haque & Moessner, Physical Review Letters, 107, 177202 (2011) [2] Jaubert, Pitaecki, Haque & Moessner, arXiv:1201.0677 (2012). |
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