Spin-dependent electrical transport in ion-beam sputter deposited Fe-Cr multilayers

The temperature dependence of the electrical resistivity and magnetoresistance of Xe-ion-beam-sputtered Fe-Cr multilayers has been investigated. The electrical resistivity between 5 and 300 K in the fully ferromagnetic state, obtained by applying a field beyond the saturation field ${(H}_{\mathrm{sat}})$ necessary for the antiferromagnetic- (AF-) ferromagnetic (FM) field-induced transition, shows evidence of spin-disorder resistivity as in crystalline Fe and an s-d scattering contribution (as in $3d$ metals and alloys). The sublattice magnetization $m(T)$ in these multilayers has been calculated in terms of the planar and interlayer exchange energies. The additional spin-dependent scattering $\ensuremath{\Delta}\ensuremath{\rho}(T)=\ensuremath{\rho}{(T,H=0)}_{\mathrm{AF}}\ensuremath{-}\ensuremath{\rho}{(T,H=H}_{\mathrm{sat}}{)}_{\mathrm{FM}}$ in the AF state over a wide range of temperature is found to be proportional to the sublattice magnetization, both $\ensuremath{\Delta}\ensuremath{\rho}(T)$ and $m(T)$ reducing along with the antiferromagnetic fraction. At intermediate fields, the spin-dependent part of the electrical resistivity $[{\ensuremath{\rho}}_{s}(T)]$ fits well to the power law ${\ensuremath{\rho}}_{s}(T)=b\ensuremath{-}{\mathrm{cT}}^{\ensuremath{\alpha}}$ where c is a constant and b and \ensuremath{\alpha} are functions of H. At low fields $\ensuremath{\alpha}\ensuremath{\simeq}2$ and the intercept b decreases with H much the same way as the decrease of $\ensuremath{\Delta}\ensuremath{\rho}(T)$ with T. A phase diagram (T vs ${H}_{\mathrm{sat}})$ is obtained for the field-induced AF-to-FM transition. Comparisons are made between the present investigation and similar studies using dc-magnetron-sputtered and molecular-beam-epitaxy-grown Fe-Cr multilayers.