Oscillations in the exchange coupling of ferromagnetic layers separated by a nonmagnetic metallic layer

A general theory of oscillations in the exchange coupling J between two transition metal ferromagnets separated by a nonmagnetic transition metal spacer is developed. Detailed calculations of J as a function of the spacer layer thickness are made for a specific model based on a simple cubic tight-binding band structure. For a suitable choice of band filling a good account is given of the main features observed in Co/Ru, Co/Cr and Fe/Cr layered structures. An analysis of the numerical accuracy required in computing J from a total energy difference is given and this throws some light on difficulties experienced by previous workers using this approach. A general expression for J is obtained for an arbitrary band and finite temperature in the limit of large spacer thickness. A close analogy between oscillations in the exchange coupling and de Haas-van Alphen oscillations is established and the relation to RKKY theory is also discussed. It is shown that the period, asymptotic decay and temperature dependence of the oscillations in J are determined by properties of the Fermi surface of the spacer layer.