Disorder driven maximum in the magnetoresistance of spin polaron systems

Ferromagnetic polarons are self trapped states of an electron in a locally spin polarised environment. They occur close to the magnetic $T_c$ in low carrier density local moment magnets when the electron-spin coupling is comparable to the hopping scale. In non disordered systems the primary signatures are a modest non-monotonicity in the temperature dependent resistivity $\rho(T)$, and a magnetoresistance that can be $\sim 20-30 \%$ at $T_c$, at fields that, in energy units, are $\sim 0.01 k_BT_c$. We find that structural disorder, in the form of pinning centers, promotes polaron formation, hugely increases the resistivity peak at $T_c$, and can enhance the magnetoresistance to $\sim 80\%$. The change in magnetoresistance with disorder is, however, non-monotonic. Too much disorder just creates an Anderson insulator - with the resistivity unresponsive to the magnetisation. This paper establishes the optimum disorder for maximising the magnetoresistance, suggests the physical process behind the unusual disorder dependence, and provides a magnetoresistance map - in terms of coupling and disorder - that locates some of the existing magnetic semiconductors within this framework.