Fine structure in magnetization of individual fluxoid states

Each time a vortex enters or exits a small superconductor, a different flux oid state develops which can be characterized by its vorticity, i.e., the n umber of fluxoids inside. We have studied magnetization response of such in dividual states and found clear signatures of first and second order transi tions within the states, which reveal the existence of distinct vortex phas es for a fixed number of fluxoids. We attribute the transitions to the merg er of individual vortices into a single giant vortex and switching between different arrays of vortices.