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We present a theoretical framework for evaluating effective interactionsbetween localized spins mediated by itinerant electrons in double-exchangemodels. Performing the expansion with respect to the spin-dependent part of theelectron hopping terms, we show a systematic way of constructing the effectivespin model in the large Hund's coupling limit. As a benchmark, we examine theaccuracy of this method by comparing the results with the numerical solutionsfor the spin-ice type model on a pyrochlore lattice. We also discuss anextension of the method to the double-exchange models with Heisenberg and $XY$localized spins.

A strong coupling theory for electron-mediated interactions in double-exchange models