  We derive the low temperature properties of the molecular magnet Mo72Fe30,
where 30 Fe(3+) paramagnetic ions occupy the sites of an icosidodecahedron and
interact via isotropic nearest-neighbour antiferromagnetic Heisenberg exchange.
The key idea of our model (J.S. & M.L.) 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. For
temperatures below 50 mK we predict that the magnetisation is described by a
staircase with 75 equidistant steps as the magnetic field is increased up to a
critical value and saturated for higher fields. For higher temperatures thermal
broadening effects wash out the staircase and yield a linear ramp below the
critical field, and this has been confirmed by our measurements (R.M.). We
demonstrate that the lowest two rotational bands are separated by an energy gap
of 0.7 meV, and this could be tested by EPR and 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. As rotational bands characterize the spectra of many magnetic
molecules our method opens a new road towards a description of their
low-temperature behaviour which is not otherwise accessible.
