Abstract
An analytical asymptotic approximation for the effective coupling between local moments in itinerant-electron systems is presented. On the basis of this result, the relation between the salient features of the coupling, namely, its sign, strength, and range, and specific features of the electronic structure of the system are established. We find that the coupling oscillates as a function of the interatomic distance with well-defined periods, which are determined by the extremal dimensions of the up- and down-spin Fermi surfaces of the materials along each crystalline direction. The amplitude and phase of the coupling are controlled by specific features of the electronic structure of the system, particularly the geometry of the Fermi surfaces for electrons with up- and down-spins. As regards the range of the coupling, it is expected to decay as ${1/R}_{\mathrm{ij}}^{3}$ at $T=0 \mathrm{K},$ and to exhibit an exponential damping at finite temperatures.
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