Localization effects in ferromagnetic Ga$_{1-x}$Mn$_{x}$Sb random alloys*

We have investigated temperature and magnetic field dependence of resistance (R$_{xx})$ in MBE-grown ferromagnetic Ga$_{1-x}$Mn$_{x}$Sb films in which the ferromagnetism is mediated by holes [1]. Samples with higher carrier densities (6.7 x 10$^{19 }$cm$^{-3}$ and 1.3 x 10$^{20 }$cm$^{-3}$, with Curie temperatures, T$_{c}$, of 13 K and 24 K respectively) show metal-like behavior in the temperature dependence of R$_{xx}$. These samples exhibit small positive magnetoresistance (MR) up to 0.5 T between 1.6 K and 20 K, followed by negative MR up to 10 and 11 T (at 2.4 K), respectively. Samples with lower carrier densities (2.9 x 10$^{19 }$cm$^{-3}$ and 3.9 x 10$^{19 }$cm$^{-3}$, with T$_{c}$'s of 13 K and 24 K, respectively) show ``weak'' thermally activated behavior and negative MR between 1.6 K and 50K (but no positive MR at low fields). The latter samples exhibit low field positive MR between 35 mK and $\sim $ 400 mK, followed by negative MR up to 8 T. R$_{xx}$ increases with decreasing temperature for both samples at zero field, and the magnitude of the change increases with applied magnetic field. These results will be discussed in terms of localization behavior in this system. [1] Eginligil et al.,\textit{ in press} PhysicaE (2007)