Scaling law and its universality in the anomalous Hall effect of giant-magnetoresistiveFe∕Crmultilayers

Abstract

We have investigated the Hall effect and transverse magnetoresistance extensively in two series of ion-beam-sputtered $\mathrm{Fe}∕\mathrm{Cr}$ multilayers composed of 10 and 30 iron-chromium $(\mathrm{Fe}∕\mathrm{Cr})$ bilayers, respectively, with Cr-layer thickness varying from $6\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}14\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}$ in both of them. It is shown that the scaling law ${R}_{s}\ensuremath{\sim}{\ensuremath{\rho}}^{2}$ for the extraordinary Hall coefficient ${R}_{s}$ and the electrical resistivity $\ensuremath{\rho}$ holds surprisingly well even in these multilayers of moderately high magnetoresistance of 29% (ten bilayers) and 33% (30 bilayers). The most important finding is that the scaling law for ${R}_{s}$ in these multilayers is independent of the magnitude of the giant magnetoresistance and it remains valid for any given value of the magnetic field which undoubtedly suggests the universality of the scaling law.