Abstract
The spin-current method is used to calculate the oscillatory exchange energy that couples two semi-infinite ferromagnets with exchange-split parabolic bands which are joined by a nonmagnetic metallic spacer. A closed asymptotic formula extends the previous RKKY-type formula to the case in which the ferromagnets and spacer have different Fermi vectors. The predicted amplitude of oscillatory coupling increases steeply with Fermi vector or electron density in the spacer, as do the experimental trends reported by Parkin. Numerical computations relevant to iron support this closed formula and show that the amplitude of the biquadratic ( J 2 cos 2θ) and higher-order corrections to the conventional - J 1 cos θ form of energy is less than 2%.
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