Rotational Band Structure of Low-Lying Excitations in Small Heisenberg Systems

We derive the low-temperature properties of the giant molecular magnet {Mo₇₂Fe₃₀}, where 30 Fe³⁺ paramagnetic ions occupy the sites of an icosidodecahedron and interact via isotropic nearest-neighbour 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. As rotational bands characterise the spectra of many magnetic molecules our method opens a new road towards a description of their low-temperature behaviour which is not accessible otherwise.