Carrier-controlled anomalous Hall effect in an intrinsic ferromagnetic semiconductor

The intrinsic ferromagnetic semiconductor GdN offers a unique opportunity to separate the anomalous and ordinary contributions to the Hall effect, and to investigate the strength of the anomalous Hall effect (AHE) as a function of carrier concentration and relaxation time. The data show an AHE that is inversely proportional to the carrier concentration n in a single spin channel. There is no dependence at all on the relaxation time τ, rather than the usual τ¹ or τ² dependencies predicted by conventional mechanisms. However, the n and τ dependencies are identical to those of the ordinary Hall effect, which suggests a semiclassical wave-packet description of an intrinsic AHE contribution that ultimately provides a quantitative agreement with the data.