Competing spin phases in geometrically frustrated magnetic molecules

We identify a class of zero-dimensional classical and quantum Heisenberg spin systems exhibiting anomalous behavior in an external magnetic field B similar to that found for the geometrically frustrated kagome lattice of classical spins. Our calculations for the Isotropic Heisenberg model show the emergence of a pronounced minimum in the differential susceptibility dM/dB at B_sat/3 as the temperature T is raised from 0 K for structures based on corner-sharing triangles, specifically the octahedron, cuboctahedron, and icosidodecahedron. As the first experimental evidence we note that the giant Keplerate magnetic molecule {Mo₇₂Fe₃₀} (Fe³⁺ ions on the 30 vertices of an icosidodecahedron) exhibits this behavior. For low T when B ≈ B^sat/3 two competing families of spin configurations exist of which one behaves magnetically "stiff" leading to a reduction of dM/dB.