We predict that large moments J, placed into a crystal field with the cubic
point symmetry group, differ in their spectrum and magnetic properties. E.
g., properties of the odd-integer moments are different from those of the e
ven-integer. The effect is due to Ferry's phases gained by the moment, when
it tunnels between minima of the external field. Two cases of the group O
are classified, namely, 6- and 8-fold coordinations. The spectrum and degen
eration of energy levels depend on a remainder (J/n), where the divisor n =
4 and 3 for the 6-fold and 8-fold coordination, respectively. Large spins
in the cubic environment of the 6- and 8-fold coordinations can be realized
by diluted alloys R1-xRx'Sb, where R = Lu, La, Y, and R' = Er, Sm, Ce, Dy,
Pm, Yb.