In giant- and tunneling-magnetoresistance (FMR and TMR)systems, two ferromagnetic layers are coupled through a nonmagnetic spacer. In spite of the numerous theoretic
studies (and the award of a Nobel Prize), quantitative predictions on the strength of the interlayer exchange coupling (IEC) is still missing, largely due to the difficulties at handling the interlayer roughness. This deficiency becomes more urgent in recent years with the advance of technique in ion beam bombardment which enables tailoring of specific topography down to the nanoscale.
This thesis is devoted to clarifying the role of interface roughness in multilayer systems. As opposed to a disturbing potential energy, the deviation from a smooth profile becomes the subject of our perturbation theory. Rather than the detrimental role predicted by common mean-field theory, we find the interface roughness can in fact enhance the IEC via resonance states when its major Fourier conjugate satisfies certain conditions. In the case of GMR, these conditions involve matching with the Fermi momentum of the metallic spacer. Although there is no intrinsic momentum scale in TMR, the case is reminiscent of the famous Casimir effect in the optical system where the handling of interface roughness is also a pressing question. We elaborate on the similarities and how lessons can be borrowed between these two systems. Finally, we report another calculation of ours that shows the strength of IEC to oscillate with the width of ferromagnetic layers. Base on our predictions, our German collaborators will be able to achieve the stunt of enhancing the IEC by two folds and at another width nearly turning it off.

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