Scaling approach to hopping magnetoresistivity in dilute magnetic semiconductors

Abstract

We suggest a mechanism causing large positive magnetoresistance (MR) in dilute magnetic semiconductors when hopping via nonmagnetic donor impurities dominates the conductivity. The effect is due to the increase in the characteristic width $\ensuremath{\sigma}$ of the donor energy distribution with increasing magnetic field $B$, caused by exchange interactions between magnetic Mn atoms and the electrons localized on nonmagnetic Cl donor impurities. Using general scaling arguments based solely on the dependencies of hopping rates on temperature and on the energies of hopping sites we show that this mechanism accounts quantitatively for our experimental data on MR in $n$-type Zn${}_{1\ensuremath{-}x}$Mn${}_{x}$Se:Cl. We suggest a method for extracting the dependence of $\ensuremath{\sigma}$ on magnetic field from the MR data. The mechanism explains the experimentally observed universal dependence of the MR effect on the ratio $B/T$ at different temperatures $T$ under the premise that transport is due to the nearest-neighbor or Mott hopping mechanism.