  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.
