Solution (source code)

= Solution

Roughness can produce a distribution of local switching fields and nonuniform reversal. The abrupt edges in the ideal <pseudo spin valve> loops then become rounded or sloping, the antiparallel plateau becomes less flat, and overlapping layer-reversal distributions can narrow or partly eliminate the clear high-resistance window. The middle panel of the original diagram illustrates only this broadening mechanism.

Correlated roughness on the two interfaces can also introduce <orange-peel coupling>, a magnetostatic coupling that favors parallel alignment. Such coupling shifts switching fields and can suppress independent reversal. Sufficiently severe roughness or pinholes can have a similar qualitative effect by directly coupling the ferromagnets.

Changes in amplitude require care. Some spin-dependent interface scattering contributes to <giant magnetoresistance>, so a small increase in roughness is not guaranteed to lower the signal monotonically. Intermixing, spin-flip scattering and an incompletely antiparallel state generally reduce useful contrast. The detailed width, displacement and height of $R(H)$ therefore depend on how the interfaces become rough, rather than on a single roughness number.