Generally, the magnetic moment order in Mott insulators and a phase that breaks the time-reversal symmetry appears. However, there are theoretical proposals for time reversal invariant phases where the order parameter breaks the O(3) symmetry in the spin space. These are spin-nematic or spin quadrupolar phases. This may occur when both ferromagnetic and antiferromagnetic exchanges are present in a model, together with frustration, which leads to the formation of bound pairs of magnon excitations. The condensation of these bound pairs is then the spin-nematic phase.
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