  In order to clarify why the experimental magnetization curve of the spherical
kagome cluster in {W72V30} at 0.5 K shows no sign of staircase behavior up to
50 T, we study the effects of Dzyaloshinsky-Moriya (DM) interactions and tilts
of the g tensors, both of which lead to the breaking of the total-S z
conservation, by using the exact diagonalization method. It is found that the D
vector component parallel to the radiation direction of the polyhedron cancels
out the staircase in a low magnetic field region efficiently. The tilts of the
g tensors are inherent to systems defined on the poly- hedrons and lead to
induced magnetic fields varying site by site. This induced magnetic field
affects the magnetization only at high magnetic fields. We also discuss two
existing experimental results on the basis of our calculated results.

Strongly Correlated Electrons