This study examines the increasing complexity in the magnetic properties of small $n=3,4,5,\mathrm{and}6$ spin-$\frac{1}{2}$ quantum rings. Using an exact diagonalization of the isotropic Heisenberg Hamiltonian with nearest and next-nearest neighbor interactions, the energy eigenstates, magnetic specific heat capacity, magnetic susceptibility, and inelastic neutron scattering structure factors are determined for variable next-nearest neighbor interactions. Here, it is shown that the presence of spin exchange symmetry breaking, multiple ground states, and nonzero total spin ground states can greatly complicate the energy eigenstates and excitations for these systems. Overall, the energy eigenstates and structure factor intensities are presented in closed form, while the thermodynamic properties detail the effect of a crossing interaction in the rings. The goal of this work is to provide insight into the evolution of the magnetic properties and spin excitations within these systems.

• Received 2 May 2016
• Revised 5 August 2016

DOI:https://doi.org/10.1103/PhysRevB.94.054436