We propose a simple scaling of anomalous Hall conductivity ${\sigma }_{\mathrm{xy}}$ with sign by considering the contributions of the Fermi surface and Fermi sea. For the four ferromagnetic metals studied, polycrystalline Co, Ni, $\mathrm{C}{\mathrm{o}}_{27}\mathrm{N}{\mathrm{i}}_{73}$, and amorphous $\mathrm{C}{\mathrm{o}}_{40}\mathrm{F}{\mathrm{e}}_{40}{\mathrm{B}}_{20}, {\sigma }_{\mathrm{xy}}$ is dominated by the linear term in the conductivity ${\sigma }_{\mathrm{xx}}$, mainly attributed to the Fermi surface by skew scattering. Notably, the quadratic term (square of ${\sigma }_{\mathrm{xx}}$), attributed mainly to the Fermi sea, is of opposite sign to the linear term from the Fermi surface. The sum of the quadratic (Fermi-sea) term and the constant term can be larger than the linear (Fermi-surface) term for $\mathrm{C}{\mathrm{o}}_{27}\mathrm{N}{\mathrm{i}}_{73}$. Our scaling of the anomalous Hall effect is applicable to various materials, even largely deviating from conventional scaling.

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• Anomalous Hall effect
• Spintronics
• Ferromagnets
• Magnetic thin films