Approximate quantum model of the Heisenberg molecular magnet Mo_72Fe_30

We derive the low temperature properties of the molecular magnet Mo_72Fe_30 where 30 Fe^3+ paramagnetic ions occupy the sites of an icosidodecahedron and interact via isotropic nearest-neighbor antiferromagnetic Heisenberg exchange. The key idea of our model is that the low-lying excitations form a sequence of ``rotational bands", i.e., for each such band the excitation energies depend quadratically on the total spin quantum number. Our theoretical predictions (M.L. & J.S.) for the temperature and field dependence of the magnetization are in excellent agreement with our recent measurements (R.M.). The lowest two rotational bands are predicted to be separated by an energy gap of 0.7 meV, and this should be observable in inelastic neutron scattering measurements. We also predict the occurrence of resonances at temperatures below 0.1 K in the proton NMR spin-lattice relaxation rate associated with level crossings.