= Double-exchange mechanism
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= Double exchange
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Double exchange couples localized magnetic moments through actual carrier hopping between sites of different valence. Strong local <Hund's coupling> makes hopping energetically easier when neighboring core spins align, lowering the carrier <kinetic energy>. In the classical strong-coupling limit, a common effective hopping is $t_{\rm eff}=t\cos(\theta/2)$ for relative spin angle $\theta$; aligned cores maximize its magnitude. Unlike insulating <superexchange>, this mechanism directly connects carrier motion and magnetic alignment.<Interaction between the d-Shells in the Transition Metals. II. Ferromagnetic Compounds of Manganese with Perovskite Structure by Clarence Zener>[1951 abstract: the observed connection between conduction and ferromagnetism in manganese perovskites motivates the double-exchange mechanism]{ref}
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