Theory of oscillatory exchange coupling in magnetic multilayers

Magnetic multilayers, in which magnetic layers are separated by nonmagnetic spacer layers, exhibit several effects in which there has been significant recent interest: giant magnetoresistance (GMR), spin-transfer torques and oscillatory exchange coupling. The oscillatory exchange coupling is the coupling between the magnetic layers that oscillates in sign as a function of the spacer layer thickness. In magnetic multilayers, multiple reflection from the interfaces produces quantum well states, which are spin polarized because the reflection amplitudes are spin dependent. The quantum well states move in energy as the thickness of the spacer layer increases. When they cross the Fermi level, the energy gained or lost from filling them changes the relative energies of the configurations with parallel and antiparallel magnetizations.

Simple models show that there are oscillatory contributions to the exchange coupling due to critical points of the spacer layer Fermi surface. These critical points occur where two sheets of the Fermi surface are parallel at pairs of locations on the Fermi surface that differ by wave vector in the interface direction. The periods of the oscillatory coupling are set by critical spanning vectors of the Fermi surface of the spacer layer material. The strength of the coupling depends both on the geometry of the Fermi surface and on the reflection amplitudes for electrons scattering from the interfaces between the spacer layers and the magnetic layers.

The critical spanning vectors and spin-dependent reflection probabilities for Fe/Au/Fe(001), the system on which the most extensive measurements have been done. These results can be compared to measurements done in the Electron Physics Group.

Online: May 1996
Last Updated: February 2008

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