Non-Abelian Berry transport, spin coherent states, and Majorana points

We consider the adiabatic evolution of Kramers degenerate pairs of spin states in a half-integer spin molecular magnet as the molecule is slowly rotated, for which it is possible to encounter non-Abelian Berry's phase. To understand the full details of the adiabatic quantum evolution, we invoke Majorana's parametrization of a general spin-$j$ state in terms of the $2j$ Majorana points. As an illustration we consider molecular magnets of the $j=9/2$ Mn4 family and compute the frequency with which the magnetization varies. This frequency is generally different from the frequency of the rotation.