Search for ferromagnetism in doped semiconductors in the absence of transition metal ions

In contrast to semiconductors doped with transition metal magnetic elements (e.g., Ga_1-x Mn_x As), which become ferromagnetic at temperatures below ∼ 102 K, semiconductors doped with nonmagnetic ions (e.g., silicon doped with phosphorous) have not shown evidence of ferromagnetism down to millikelvin temperatures. This is despite the fact that for low densities the system is expected to be well modeled by the Hubbard model, which is predicted to have a ferromagnetic ground state at T=0 on two-dimensional (2D) or three-dimensional bipartite lattices in the limit of strong correlation near half-filling. We examine the impurity band formed by hydrogenic centers in semiconductors at low densities, and show that it is described by a generalized Hubbard model which has, in addition to strong electron-electron interaction and disorder, an intrinsic electron-hole asymmetry. With the help of mean-field methods as well as exact diagonalization of clusters around half filling, we can establish the existence of a ferromagnetic ground state, at least on the nanoscale, which is more robust than that found in the standard Hubbard model. This ferromagnetism is most clearly seen in a regime inaccessible to bulk systems but attainable in quantum dots and 2D heterostructures. If observed, this would be the first experimental realization of a system exhibiting Nagaoka ferromagnetism. We present extensive numerical results for small systems that demonstrate the occurrence of high-spin ground states in both periodic and positionally disordered 2D systems. We examine how properties of real doped semiconductors, such as positional disorder and electron-hole asymmetry, affect the ground state spin of small 2D systems, and use the results to infer properties at longer length scales.