Magnetoelastic Instability in Ring-Shaped Molecule Magnets with Next-Nearest Neighbor Coupling

In considering next-nearest neighbor (NNN) coupling, we numerically investigate the magnetoelastic instability in ring-shaped mesoscopic antiferromagnetic Heisenberg spin 1/2 systems with spin-phonon interaction. The results indicate that, for antiferromagnetic NNN coupling J(2), there may be a critical value J(2)(c), at which the ground state is dimerized for arbitrary lattice spring constant and beyond and below which the magnetoelastic instability behavior is different from each other. The values of J(2)(c) are irrelevant to the system size. For ferromagnetic NNN coupling, only continuous transition is present from dimerized phase to uniform phase as lattice spring constant is increased.