Theory of non-Heisenberg exchange: Results for localized and itinerant magnets

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Abstract
A general formulation of intersite (layer) exchange coupling in bulk (multilayer) materials is proposed based on the treatment of the spin (layer) rotation as a perturbation in terms of the force theorem and multiple scattering theory. The expansion of the intersite (layer) exchange interaction energy gives expressions for the bilinear and biquadratic exchange. For metals, the approach is illustrated by linear muffin‐tin orbital calculations of exchange coupling constants in the ferromagnetic 3D‐metals and the fcc phase of bulk Fe. Long range oscillations of strongly volume dependent exchange coupling in fcc Fe appears to be the origin of the spin‐density‐wave instability in this metastable phase. The correctness of expressions for the limit of localized magnets is demonstrated by calculations for the antiferromagnetic insulator NiO. In contrast with other theories, this method can be used for both nonmagnetic and magnetic spacers in metallic multilayers, as is illustrated by calculations of the interfacial and interlayer exchange in Fe/Mn and Co/Mn.