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It is shown, within the quantum-well theory of the exchange coupling J in magnetic multilayers, that the temperature dependence of J is governed not only by the spacer Fermi surface but also by the confining strength of the ferromagnetic layers. The confinement mechanism is first explored for an exactly solvable parabolic-band model and cases in which it leads to a very strong temperature dependence of J are identified. Finally, it is demonstrated, using fully realistic tight-binding bands,doi:10.1103/physrevb.53.r13306 pmid:9983173 fatcat:dpkx7px7tnajlm27uzgo7xcmpq