Mechanism for non-Heisenberg-exchange coupling between ferromagnetic layers.

We consider a free-electron model of exchange coupling between transition-metal ferromagnetic films separated by a paramagnetic metal spacer. The minority-spin energy bands in the ferromagnets are matched to those of the paramagnetic spacer. The majority-spin electrons experience a repulsive potential arising from the lack of corresponding states in the spacer. The height of the potential barrier is equal to the exchange-energy gap in the ferromagnets. We show how the model, applicable to a trilayer film such as Fe/Cr/Fe or Co/Ru/Co, generates an infinite sum of terms with coefficients A 12 ,B 12 ,... in the coupling energy, extending beyond the Heisenberg-like A 12 term of bilinear coupling between the moments of the ferromagnets