Extraordinary Hall effect in Fe-Cr giant magnetoresistive multilayers

Abstract

We show that for giant magnetoresistive Fe-Cr multilayer samples, the scaling law for the extraordinary Hall constant, $R_S\sim {\rho }^n$ gives unrealistically large values of $n(n=2.8\mathrm{}–3.3)$ if we use the resistivity $\rho$ at an external field $B=0\mathrm{}$ as done by previous investigators. With B perpendicular to the film plane, the transverse magnetoresistance saturates at $B\approx 3$ 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 $B\approx 3$ T. Therefore, we use $\rho =\rho (B=3\mathrm{}\mathrm{T})$ in $R_S\sim {\rho }^n$ and obtain $n=1.96\mathrm{}\pm 0.02,$ which implies that the side-jump mechanism $n=2\mathrm{}$ is the dominant scattering process. We emphasize that our interpretation of $R_S\left(\rho \right)$ 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.