Selection rules for oscillations of the interlayer exchange coupling as a function of ferromagnet thickness

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Abstract
Using a torque formula, oscillations of the exchange coupling between two magnetic layers embedded in a nonmagnetic metal are calculated from the spin current across the structure. It is shown that each component of the spin current for a fixed value of the wave vector parallel to the layers exhibits quasiperiodic oscillations as a function of the ferromagnet thickness. Ideas of the theory of quasicrystals are used to derive a general expression relating the oscillation periods to the ferromagnetic Fermi surface in a subtle way. Simple rules are formulated to select from a large number of potential oscillation periods only those that have nonzero amplitudes. The general formalism is first illustrated for a single-orbital tight-binding band and then applied to obtain the oscillation periods in a Co/Cu(001) trilayer.

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