Scaling Study of Disordered Antiferromagnetic Systems of Acceptors in p-Type Semiconductors

We consider the low temperature magnetic properties of a system of randomly-distributed interacting acceptor atoms in a p-type semiconductor. For the equivalent n-type system, where donor interactions are well described by a spin-1/2 Heisenberg model with a single antiferromagnetic exchange coupling that varies exponentially with donor separation, the classic work of Bhatt and Lee [Phys. Rev. Lett. 48, 344 (1982)] provides an iterative numerical procedure for discarding irrelevant high energy excitations of strongly interacting donor pairs while renormalizing the remaining donor couplings. Due to valence band degeneracy and spin-orbit coupling, acceptor interactions are known to be more complex. Recent computations thereof suggest a six-level energy spectrum characterized by five distinct coupling parameters and a nontrivial degeneracy structure. By employing an interaction model that respects this degeneracy structure, we extend the Bhatt-Lee renormalization procedure to the acceptor case, studying the evolution of the distribution of exchange couplings, and calculating magnetic susceptibility, as a function of decreasing temperature. Results are compared with that of spin-1/2 and spin-3/2 Heisenberg models.