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 σxy and σₓₓ and resistivities ρxy and ρₓₓ in a series of metallic (Ga,Mn)As samples. Two universal scaling relations are obtained: σxy∝σₓₓ1.5, obtained from measurements at a fixed low temperature (2.0 K) on a series of samples with different Mn concentrations; and ρxy/m∝ρₓₓ², where m is normalized magnetization, obtained from the temperature variation of ρₓₓ and ρxy measured on each sample of the series. The former scaling relation is, however, found to break down for highly conducting (Ga,Mn)As samples (σₓₓ>100 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.