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. To reveal the full details of the quantum evolution, we use Majorana's parametrization of a general state in the (2j + 1)-dimensional Hilbert space in terms of 2j Majorana points. We show that the intricate motion of the Majorana points may be described by a classical Hamiltonian which is of the same form, but of quite different origin, as that which appears in the spin-coherent-state path integral. 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. (paper)