Independent magnon states on magnetic polytopes

For many spin systems with constant isotropic antiferromagnetic nextneighbour Heisenberg coupling the minimal energies Emin(S) form a rotational band, i. e. depend approximately quadratically on the total spin quantum number S, a property which is also known as Landé interval rule. However, we find that for certain coupling topologies, including recently synthesised icosidodecahedral structures this rule is violated for high total spins. Instead the minimal energies are a linear function of total spin. This anomaly results in a corresponding jump of the magnetisation curve which otherwise would be a regular staircase.