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Interplay between carrier and impurity concentrations in annealed Ga$_{1-x}$Mn$_{x}$As intrinsic anomalous Hall Effect

Investigating the scaling behavior of annealed Ga$_{1-x}$Mn$_{x}$As anomalous Hall coefficients, we note a universal crossover regime where the scaling behavior changes from quadratic to linear, attributed to the anomalous Hall Effect intrinsic and extrinsic origins, respectively. Furthermore, measured anomalous Hall conductivities when properly scaled by carrier concentration remain constant, equal to theoretically predicated values, spanning nearly a decade in conductivity as well as over 100 K in T$_{C}$. Both the qualitative and quantitative agreement confirms the validity of new equations of motion including the Berry phase contributions as well as tunablility of the intrinsic anomalous Hall Effect.