Quantum rotational band model for the Heisenberg molecular magnet{Mo72Fe30}

Abstract

We derive the low-temperature properties of the molecular magnet{Mo72Fe30}, where 30 Fe3+ paramagnetic ionsoccupy the sites of an icosidodecahedron and interact viaisotropic nearest-neighbour antiferromagnetic Heisenbergexchange. The key idea of our model (J. S. & M. L.) is that thelow-lying excitations form a sequence of "rotational bands",i.e., for each such band the excitation energies dependquadratically on the total spin quantum number. For temperaturesbelow 50 mK we predict that the magnetisation is described by astaircase with 75 equidistant steps as the magnetic field isincreased up to a critical value and saturated for higherfields. For higher temperatures thermal broadening effects washout the staircase and yield a linear ramp below the criticalfield, and this has been confirmed by our measurements(R. M.). We demonstrate that the lowest two rotational bands areseparated by an energy gap of 0.7 meV, and this could be testedby EPR and inelastic neutron scattering measurements. We alsopredict the occurrence of resonances at temperatures below 0.1 Kin the proton NMR spin-lattice relaxation rate associated withlevel crossings. As rotational bands characterize the spectraof many magnetic molecules, our method opens a new road towards adescription of their low-temperature behaviour which is nototherwise accessible.