Exploring the magnetic properties of the largest single molecule magnets.

The giant $\{ \mathrm{Mn}_{70} \}$ and $\{ \mathrm{Mn}_{84} \}$ wheels are the largest nuclearity single-molecule magnets synthesized to date and understanding their magnetic properties poses a challenge to theory. Starting from first principles calculations, we explore the magnetic properties and excitations in these wheels using effective spin Hamiltonians. We find that the unusual geometry of the superexchange pathways leads to weakly coupled $\{ \mathrm{Mn}_{7} \}$ subunits carrying an effective $S=2$ spin. The spectrum exhibits a hierarchy of energy scales and massive degeneracies, with the lowest energy excitations arising from Heisenberg-ring-like excitations of the $\{ \mathrm{Mn}_{7} \}$ subunits around the wheel, at energies consistent with the observed temperature dependence of the magnetic susceptibility. We further suggest an important role for weak longer-range couplings in selecting the precise spin ground-state of the $\mathrm{Mn}$ wheels out of the nearly degenerate ground-state band.