  We study the role of diamagnetic effects on the transport properties of
metallic magnetic multilayers to elucidate whether they can explain the Giant
Magnetoresistance (GMR) effect observed in those systems. Realistic Fermi
surface topologies in layered ferromagnets are taken into account, with the
possibilities of different types of orbits depending on the electron spin. Both
configurations, with ferromagnetic and anti-ferromagnetic couplings between
magnetic layers, are considered and the transmission coefficient for scattering
at the interface boundary is modelled to include magnetic and roughness
contributions. We assume that scattering processes conserve the electron spin,
due to large spin diffusion lengths in multilayer samples. Scattering from the
spacer mixes different orbit topologies in a way similar to magnetic
`breakdown' phenomena. For antiferromagnetic coupling, majority and minority
spins are interchanged from one magnetic layer to the next. Cyclotron orbits
are also traveled in opposite directions, producing a compensation-like effect
that yields a huge GMR, particularly for closed orbits. For open orbits, one
may get the `inverse' magnetoresistance effect along particular directions.
