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Liquid crystal order in the kagome lattice

The kagome lattice is an outstanding example of a frustrated magnet, a system in which the
magnetic moments cannot satisfactorily align to minimize the energy. Its
ground-state configuration has been a long-standing puzzle. Recent debate has
focused on the relative stability of a valence bond-crystal, and an isotropic
spin-liquid (where quantum fluctuations cause all ordering to disappear). Using
numerical techniques, we have shown [1] that there is an intermediate competing
order, where moments align along parallel lines, but are not ordered along the
lines themselves, much like a liquid crystal. This type of nematic order has so far been neglected in the characterization of frustrated magnets, but may in fact be very common: the
same broken symmetry, suggestive of the nematic phase, is seen in kagome-like materials volborthite and Zn-doped paratacamite.

Kagome lattice

Kagome Lattice

striped spin-liquid