  We have found a class of zero-dimensional geometrically frustrated Heisenberg
spin systems exhibiting anomalous behavior in an external magnetic field B
similar to that occuring in geometrically frustrated planar antiferromagnetic
lattices. Our calculations for both the classical and quantum isotropic
Heisenberg models show the emergence of a pronounced minimum in the
differential susceptibility dM/dB at B_sat/3 as the temperature T is raised
from 0K for structures based on corner-sharing triangles, specifically the
octahedron, cuboctahedron, and icosidodecahedron. Low temperature measurements
of magnetization M versus B for the giant Keplerate magnetic molecule Mo72Fe30
(Fe(3+) ions with spin s=5/2 on the 30 vertices of an icosidodecahedron) are
consistent with our calculational results. The minimum in dM/dB is due to the
fact that for low temperatures when B is approx. B_sat/3 there exist two
competing families of spin configurations of which one behaves magnetically
'stiff' leading to a reduction of the susceptibility.
