Interlayer exchange coupling

Interlayer exchange coupling is an interaction that favors particular relative orientations of magnetization in different magnetic layers. In a metallic multilayer, spacer electrons can mediate coupling even when a nonmagnetic layer separates the magnets.

A simple model writes energy per area as $E/A=-J{\hat{\mathbf{m}}}_1\cdot {\hat{\mathbf{m}}}_2$. Positive $J$ favors parallel alignment and negative $J$ favors antiparallel alignment. Spacer material and thickness affect the coupling; magnetic-field sweeps can reveal the field needed to overcome it. Correlated interface roughness can instead produce orange-peel coupling, so a preferred alignment alone does not uniquely establish exchange mediation. ^[ref]

Electrons reflected by two magnetic interfaces can mediate an interaction across a nonmagnetic metal spacer. The phase accumulated on traversing the spacer varies with its thickness, producing oscillatory contributions to $J(t)$ from Fermi surface spanning vectors. In the sign convention in the title, positive $J$ favours parallel moments and negative $J$ antiparallel moments. Multiple periods, interface phase shifts, disorder and finite temperature prevent a universal sign rule based on thickness alone.