Large Spins in External Fields
  Spectra and magnetic properties of large spins $J$, placed into a crystal electric field (CEF) of an arbitrary symmetry point group, are shown to change drastically when $J$ changes by 1/2 or 1. At a fixed field symmetry and configuration of its $N$ extrema situated at $p$-fold symmetry axis, physical characteristics of the spin depend periodically on $J$ with the period equal to $p$. The problem of the spectrum and eigenstates of the large spin $J$ is equivalent to analogous problem for a scalar charged particle confined to a sphere $S^2$ and placed into magnetic field of the monopole with the charge $J$. This analogy as well as strong difference between close values of $J$ stems from the Berry's phase occurring in the problem. For energies close to the extrema of the CEF, the problem can be formulated as Harper's equation on the sphere. The $2J+1$-dimensional space of states is splitted into smaller multiplets of classically degenerated states. These multiplets in turn are splitted into submultiplets of states transforming according to specific irreducible representations of the symmetry group determined by $J$ and $p$. We classify possible configurations and corresponding spectra. Experimental realizations of large spins in a symmetric environment are proposed and physical effects observable in these systems are analyzed. 
V.A.Kalatsky and V.L.Pokrovsky