Dzyaloshinskii–Moriya Interaction in Spin 1/2 Antiferromagnetic Rings with Nearest Next Neighbor Coupling

We numerically investigate the magnetoelastic (ME) instability in spin 1/2 antiferromagnetic rings with nearest-next neighbor (NNN) coupling J₂ and Dzyaloshinskii–Moriya (DM) interaction D_z. It is found that, for a given D_z, there exists a critical J₂^c . As J₂=J₂^c , the ME instability is irrelative to the DM interaction and NNN coupling. These results may come from the competition between the DM interaction and NNN coupling. The DM interaction does not affect the critical behavior at the point of J₂=0.5, at which the systems always locate in the dimerized state.