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 Mn{sub x}Ge{sub 1-x} (0 < x < 0.09) is characterized by two different ordering temperatures T{sub c} and T*{sub c} with T{sub c}-T*{sub c}. The onset of global ferromagnetic order at T{sub c} coincides with the percolation threshold for (activated) charge transport. Magnetism between T{sub c} and T*{sub c} originates from 'clustered dopants' associated with inhomogeneities. The ferromagnetic ordering temperature within the clusters is of order T*{sub c} 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 T{sub c} and T*{sub c} 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 Mn{sub x}Ge{sub 1-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.