  We predict that large moments $J$, placed into a crystal field with the cubic
point symmetry group, differ by their spectrum and magnetic properties. E. g.,
properties of the odd-integer moments are different from those of the
even-integer. The effect is due to Berry'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 degeneration
of energy levels depend on a remainder $\{J/n\}$, where the divisor $n=4$ and 3
for 6-fold and 8-fold coordination respectively. %High symmetry results in a
finite magnetic moment for half-integer %and some integer moments, for example
odd $J$ at 6-fold coordination. Large moments in the cubic environment can be
realized by diluted alloys ${R}_{1-x}{R}_{x}'$Sb, where R=Lu, La, and R$'$=Tb,
Dy, Ho, Er.

Quantum Physics;Condensed Matter