Giant magnetoresistance and quantum phase transitions in strongly localized magnetic two-dimensional electron gases

The application of a small magnetic field $\left(B\approx 0.1\mathrm{T}\right)$ either parallel or perpendicular to a low-density $\left(\approx {10}^{11}{\mathrm{cm}}^{\mathrm{-}2}\right)$ magnetic two-dimensional electron gas (2DEG) creates a striking positive magnetoresistance of up to 700%. This is a spin effect, caused by the suppression of spin-dependent hopping paths between localized states with on-site correlation. At higher fields, a spin-related delocalization is observed. In the perpendicular field geometry, orbital effects combine with this delocalization and lead to quantum phase transitions between the spin-polarized insulating state and the $\nu =1\mathrm{}$ quantum Hall liquid.