Carrier-Dependent Quadratic Scaling Of Anomalous Hall Conductivity In Ferromagnetic Semiconductor

We report an unconventional carrier-dependent anomalous Hall effect (AHE) with a quadratic scaling relation in epitaxial films of a ferromagnetic semiconductor (ZnCo)O with a high Co concentration. We show the co-existence of AHE together with the nonlinear ordinary Hall effect (NLHE) and the separation of NLHE by using a two-conducting channels model in the expression of Hall resistivity. We found that the NLHE depends strongly on both temperature and carrier density n and dominates at low temperature when n <1.0x10(20)cm(-3), indicating the very necessary of separation them from each other for a proper scaling of the AHE. The anomalous Hall resistivity is nearly independent on carrier density and longitudinal resistivity regardless the underlying transport mechanisms and thermal properties. Very interestingly, a quadratic scaling relation between anomalous Hall conductivity and longitudinal conductivity sigma(AHE)(xy) proportional to sigma(2)(xx) is obtained. The further analysis shows that sigma(AHE)(xy) proportional to n(2) with a frozen electron mobility. In addition, sign reversal of the AHE has been observed by reducing magnetization via growth controlling engineering. Our results reveal a carrier-dependent AHE in low conductivity regime and provide an experimental evidence for the itinerant ferromagnetism in ferromagnetic semiconductor (ZnCo)O.