Intermediate spin and certain small magnets

An isolated spin S can have only whole or half-integer values. It is shown that under certain circumstances a system composed of such spins can have low-lying excitations which correspond to a different value of the spin S-eff which is intermediate between these standard possibilities. A general demonstration valid in any dimension is given followed by a detailed examination of the simplest, zero-dimensional example, namely a small easy plane ferromagnet. Some experimental implications are worked out.