Hierarchy of Exchange Interactions in a Disordered Magnetic System

A simple and very physical model to explain the magnetic properties of heavily doped, $n$-type semiconductors below the metal-nonmetal transition is proposed. Based on the wide distribution of exchange interactions between donors, this model establishes a hierarchy of exchange interactions accounting for the existence of the low-lying energy levels which determine the magnetization of the donor system at low temperature, and explain the absence of a transition to an ordered antiferromagnetic state.