Working with epitaxial films of Fe, we succeeded in independent control of different scattering processes in the anomalous Hall effect. The result appropriately accounted for the role of phonons, thereby clearly exposing the fundamental flaws of the standard plot of the anomalous Hall resistivity versus longitudinal resistivity. A new scaling has been thus established that allows an unambiguous identification of the intrinsic Berry curvature mechanism as well as the extrinsic skew scattering and side-jump mechanisms of the anomalous Hall effect.PACS numbers: 75.47.Np;72.15.Eb;73.50.Jt Shortly after the discovery of the Hall effect, in 1880 Edwin Hall further observed in ferromagnetic metals an additional large contribution besides the ordinary one, which is now called the anomalous Hall effect (AHE) -one of the most prominent phenomena existing in magnetic materials [1]. While the ordinary Hall effect has been well understood as a result of the Lorentz force deflecting the charge carriers, the mechanism of the AHE has remained controversial despite the long history of research, because its rich phenomenology defies the standard classification methodology, prompting conflicting reports claiming the dominance of various processes [2][3][4][5][6][7][8][9][10][11][12]. Recently it again attracts great attention because of its natural connection to the spin Hall effect and quantum spin Hall effect [13,14].In ferromagnets, the transverse resistivity has two contributions: one is ordinary and is proportional to the applied magnetic field; the other is anomalous and is normally proportional to the magnetization [8,9]. It is often written aswhere r 0 and r a are coefficients that characterize the strength of the ordinary and anomalous Hall resistivity ρ h and ρ ah , respectively.

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We derive a general scaling relation for the anomalous Hall effect in ferromagnetic metals involving multiple competing scattering mechanisms, described by a quadratic hypersurface in the space spanned by the partial resistivities. We also present experimental findings, which show strong deviation from previously found scaling forms when different scattering mechanisms compete in strength but can be nicely explained by our theory.

We investigate the unusual temperature dependence of the anomalous Hall effect in Ni. By varying the thickness of the MBE-grown Ni films, the longitudinal resistivity is uniquely tuned without resorting to doping impurities; consequently, the intrinsic and extrinsic contributions are cleanly separated out. In stark contrast to other ferromagnets such as Fe, the intrinsic contribution in Ni is found to be strongly temperature dependent with a value of 1100 (Ω · cm) −1 at low temperatures and 500 (Ω · cm) −1 at high temperatures. This pronounced temperature dependence, a cause of long-standing confusion concerning the physical origin of the AHE, is likely due to the small energy level splitting caused by the spin orbit coupling close to the Fermi surface. Our result helps pave the way for the general claim of the Berry-phase interpretation for the AHE.