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

Abstract

We report a systematic study of the temperature dependence of the anomalous Hall and longitudinal conductivities sigma(xy) and sigma(xx) and resistivities rho(xy) and rho(xx) in a series of metallic (Ga,Mn)As samples. Two universal scaling relations are obtained: sigma(xy) proportional to sigma(1.5)(xx), obtained from measurements at a fixed low temperature (2.0 K) on a series of samples with different Mn concentrations; and rho(xy)/m proportional to rho(2)(xx), where m is normalized magnetization, obtained from the temperature variation of rho(xx) and rho(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 (sigma(xx) > 100 Omega(- 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.