Extraordinary Hall effect in Fe-Cr giant magnetoresistive multilayers

We show that for giant magnetoresistive Fe-Cr multilayer samples, the scaling law for the extraordinary Hall constant, RS;r n gives unrealistically large values of n(n52.8–3.3) if we use the resistivity r at an external field B50 as done by previous investigators. With B perpendicular to the film plane, the transverse magnetoresistance saturates at B'3 T in the 4.2–300 K temperature range. This indicates that the Fe layers, although antiferromagnetically coupled at B50, are ferromagnetically aligned only above B'3 T. Therefore, we use r5r(B53 T) in RS;r n and obtain n51.9660.02, which implies that the side-jump mechanism n52 is the dominant scattering process. We emphasize that our interpretation of RS(r) 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.