In this study, we examine the thermodynamics and spin dynamics of spin-1/2 and spin-3/2 heptamers. Through an exact diagonalization of the isotropic Heisenberg Hamiltonian, we find the closed-form, analytical representations for thermodynamic properties, spin excitations, and neutron-scattering structure factors. Furthermore, we investigate the clusterlike excitations of quantum spin heptamer in the three-dimensional pyrochlore lattice material ${\mathrm{MgCr}}_2{\mathrm{O}}_4$. Using a spin mapping of the spin-1/2 heptamer excitations, the calculated structure factors of the spin-3/2 heptamer are to be determined, which provides clarification for the spin excitations in ${\mathrm{MgCr}}_2{\mathrm{O}}_4$. Overall, this study demonstrates the ability to use the spin mapping of structure factors for small spin systems to analyze more complex structures.

• Received 16 August 2018
• Revised 25 November 2018

DOI:https://doi.org/10.1103/PhysRevB.98.214434