Amorphous Antiferromagnetism: The Cluster Approach in Doped Semiconductors

A simple method is outlined for the calculation of the paramagnetic spin susceptibility χ s appropriate t o a random spatial distribution of antiferromagnetically coupled spins. This method considers the microscopic sample to be a collection of decoupled clusters each containing three spins. It is specifically applied t o the n‐type silicon system with donor impurity concentrations in the range 10 17 donors,/cm 3 ≦ N D , ≦ 4 × 10 18 donors/cm 3 . The resulting theoretical susceptibilities were of the Curie‐Weiss form for temperatures T > 5 K, but exhibited steepening of the x s −1 vs. T curves a t low temperatures and high concentrations. Both of these features have been observed in amorphous antiferromagnetic systems.