Scaling Theory of Magnetoresistance and Carrier Localization in ${\mathrm{Ga}}_{1-x}{\mathrm{Mn}}_x\mathrm{As}$

We compare experimental resistivity data on ${\mathrm{Ga}}_{1-x}{\mathrm{Mn}}_x\mathrm{As}$ films with theoretical calculations using a scaling theory for strongly disordered ferromagnets. The characteristic features of the temperature dependent resistivity can be quantitatively understood through this approach as originating from the close vicinity of the metal-insulator transition. However, accounting for thermal fluctuations is crucial for a quantitative description of the magnetic field induced changes in resistance. While the noninteracting scaling theory is in reasonable agreement with the data, we find clear evidence for interaction effects at low temperatures.

Figure 1

Comparison between the experimental data and the theoretical results at magnetic fields $H=0$, 3, 6, and 9 T. Dots represent experimental data, solid lines are theoretical fits.

Figure 2

Temperature dependence of the magnetization in an external in-plane magnetic field ($H=50\mathrm{Oe}$) compared to our Monte Carlo results and assuming a RKKY, Mn-Mn interaction. The inset shows the effect of critical fluctuations.