Bound magnetic polaron hopping and giant magnetoresistance in magnetic semiconductors and nanostructures

A theory of bound magnetic polaron (BMP) hopping, driven by thermodynamic fluctuations of the local magnetization, has been developed. It is based on a two-site model of the BMP. The BMP hopping probability rate was calculated in the framework of the ``golden rule'' approach by using the Ginzburg-Landau effective Hamiltonian method. The theory explains the main features of the hopping resistivity observed in a variety of experiments in dilute magnetic semiconductors and magnetic nanocomposites, namely, (a) the negative giant magnetoresistance, the scale of which is governed by a magnetic polaron localization volume, and (b) the low-magnetic-field positive magnetoresistance which usually precedes the negative magnetoresistance. It is shown that the positive magnetoresistance is a signature of the fluctuation-driven bound magnetic polaron hopping. This effect is related to the vector nature of the magnetic order parameter affected by the presence of the localized-electron spin.