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This study examines the increasing complexity in the magnetic properties ofsmall $n$ = 3, 4, 5, 6 spin-1/2 quantum rings. Using an exact diagonalizationof the isotropic Heisenberg Hamiltonian with nearest and next-nearest neighborinteractions, the energy eigenstates, magnetic specific heat capacity, magneticsusceptibility, and inelastic neutron scattering structure factors aredetermined for variable next-nearest neighbor interactions. Here, it is shownthat the presence of a complex spin-mixing, multiple ground states, andnon-zero ground states greatly complicate the spin Hamiltonian. Overall, theenergy eigenstates and structure factor intensities are presented in closedform, while the thermodynamic properties detail the effect of a crossinginteraction in the rings. The goal of this work is to provide insight into theevolution of the magnetic properties and spin excitations within these systems.

Evolution of the thermodynamic properties and inelastic neutron scattering intensities for spin-1/2 antiferromagnetic quantum rings