Large finite-size effect of giant magnetoresistance in magnetic granular thin films

We have observed a finite-size effect of giant magnetoresistance (GMR) and extraordinary Hall effect (EHE) in ${\mathrm{Co}}_{20}$ ${\mathrm{Ag}}_{80}$ and ${\mathrm{Fe}}_{20}$ ${\mathrm{Ag}}_{80}$ granular thin films of varying thickness. The GMR approaches zero as the thicknness approaches zero. The thickness dependence of GMR can be explained by a dimensional-confinement effect coupled with a large surface-induced spin-flipping cross section. The EHE exhibits a strong correlation with GMR, which is likely due to the surface-induced spin-orbit interaction.