Magnetism in MnxGe1-x semiconductors mediated by impurity band carriers

We present a comprehensive study of ferromagnetism and magnetotransport in Mn-doped germanium, grown with molecular-beam epitaxy. Ferromagnetism in MnxGe1-x (0<x<0.09) is characterized by two different ordering temperatures TC and TC* with TC TC*. The onset of global ferromagnetic order at TC coincides with the percolation threshold for (activated) charge transport. Magnetism between TC and TC* originates from "clustered dopants" associated with inhomogeneities. The ferromagnetic ordering temperature within the clusters is of order TC* while the coupling between the clusters is mediated by thermally activated carriers moving in an impurity band. The magnetoresistance exhibits nonmonotonic temperature and magnetic field dependence; both negative and positive magnetoresistance contributions are observed. The anomalous Hall effect between TC and TC* appears to be influenced heavily by the large magnetoresistance. The normal and anomalous Hall coefficients both diverge at low temperature. All these observations indicate that MnxGe1-x is most adequately described within an impurity band model where the ratio J t of the Mn hole exchange J and hole hopping t is large.