We show that for giant magnetoresistive Fe-Cr multilayer samples, the scaling law for the extraordinary Hall constant, ${R}_{S}\ensuremath{\sim}{\ensuremath{\rho}}^{n}$ gives unrealistically large values of $n(n=2.8--3.3)$ if we use the resistivity $\ensuremath{\rho}$ at an external field $B=0$ as done by previous investigators. With B perpendicular to the film plane, the transverse magnetoresistance saturates at $B\ensuremath{\approx}3$ T in the 4.2--300 K temperature range. This indicates that the Fe layers, although antiferromagnetically coupled at $B=0,$ are ferromagnetically aligned only above $B\ensuremath{\approx}3$ T. Therefore, we use $\ensuremath{\rho}=\ensuremath{\rho}(B=3\mathrm{T})$ in ${R}_{S}\ensuremath{\sim}{\ensuremath{\rho}}^{n}$ and obtain $n=1.96\ifmmode\pm\else\textpm\fi{}0.02,$ which implies that the side-jump mechanism $n=2$ is the dominant scattering process. We emphasize that our interpretation of ${R}_{S}(\ensuremath{\rho})$ not only evolves from a proper understanding of the magnetic state of the multilayer system but also yields physically meaningful values of the exponent n.
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