# Thermodynamics and spin mapping of quantum excitations in a Heisenberg spin heptamer

## TL;DR

This paper provides an exact analytical study of thermodynamics and spin excitations in spin-1/2 and spin-3/2 heptamers, applying the findings to understand quantum excitations in the pyrochlore lattice material MgCr2O4.

## Contribution

It introduces a spin mapping method for small spin systems to analyze complex quantum spin excitations in materials.

## Key findings

- Closed-form thermodynamic properties derived
- Spin excitations characterized via exact diagonalization
- Spin mapping clarifies neutron scattering results in MgCr2O4

## Abstract

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 {cluster-like excitations of quantum spin heptamer} in the three-dimensional pyrochlore lattice material MgCr$_2$O$_4$. Using a spin mapping of the spin-1/2 heptamer excitations, the calculated structure factors of the spin-3/2 heptamer are be determined, which provides clarification for the spin excitations in MgCr$_2$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.