Berry's Phase for Large Spins in External Fields

It is shown that even for large spins $J$ the fundamental difference between integer and half-integer spins persists. In a quasiclassical description this difference enters via Berry's connection. This general phenomenon is derived and illustrated for large spins confined to a plane by crystal electric fields. Physical realizations are rare-earth nickel borocarbides. Magnetic moments for half-integer spin $({\mathrm{Dy}}^{3+},J=15/2\mathrm{})$ and magnetic susceptibilities for integer spin $({\mathrm{Ho}}^{3+},J=8\mathrm{})$ are calculated. Experiments are proposed to furnish evidence for the predicted fundamental difference.