The anomalous Hall Effect and magnetoresistance in the layered ferromagnet Fe_{1/4}TaS_2: the inelastic regime

The large magnetic anisotropy in the layered ferromagnet Fe_{1/4}TaS_2 leads to very sharp reversals of the magnetization $bf M$ at the coercive field. We have exploited this feature to measure the anomalous Hall effect (AHE), focussing on the AHE conductivity $sigma^A_{xy}$ in the inelastic regime. At low temperature T (5-50 K), $sigma^A_{xy}$ is T-independent, consistent with the Berry-phase/Karplus-Luttinger theory. Above 50 K, we extract an inelastic AHE conductivity $sigma^{in}_{xy}$ that scales as the square of $Deltarho$ (the T dependent part of the resistivity $rho$). The term $sigma^{in}_{xy}$ clarifies the T dependence and sign-reversal of the AHE coefficient R_s(T). We discuss the possible ubiquity of $sigma^{in}_{xy}$ in ferromagnets, and ideas for interpreting its scaling with $(Deltarho)^2$. Measurements of the magnetoresistance (MR) reveal a rich pattern of behavior vs. T and field tilt-angle. We show that the 2 mechanisms, the anisotropic MR effect and field-suppression of magnons, account for the intricate MR behavior, including the bow-tie features caused by the sharp reversals in $bf M$.