Scaling relations between anomalous Hall and longitudinal transport coefficients in metallic (Ga,Mn)As films

We report a systematic study of the temperature dependence of the anomalous Hall and longitudinal conductivities σ_xy and σ_xx and resistivities ρ_xy and ρ_xx in a series of metallic (Ga,Mn)As samples. Two universal scaling relations are obtained: σ_xyσxx1.5, obtained from measurements at a fixed low temperature (2.0 K) on a series of samples with different Mn concentrations; and ρ_xy/mρxx2, where m is normalized magnetization, obtained from the temperature variation of ρ_xx and ρ_xy measured on each sample of the series. The former scaling relation is, however, found to break down for highly conducting (Ga,Mn)As samples (σ_xx100 Ω^-1 cm^-1). The latter scaling relation leads to a magnetization-dependent anomalous Hall coefficient, which we attribute to the emergence of magnetization fluctuations at high temperatures.