Effect of electron–phonon coupling on the double-exchange interaction

Abstract

A simple, exactly solvable three-site Mn–O–Mn model is studied to extend the Anderson–Hasegawa treatment of double exchange (DEX) to include the effects of the electron–lattice coupling. The treatment being an exact solution includes both the so-called static and dynamical Jahn–Teller effects, as appropriate for the magnetoresistive manganites. It is shown that the DEX interaction energy JDEX is considerably reduced, by about a factor of three for parameters relevant to La1−xCaxMnO3. The angle dependence of JDEX is also altered from the Anderson–Hasegawa tcos(θ/2) form. Interestingly, in the strong electron–lattice coupling limit, the angular dependence reduces to the Heisenberg form JDEX∼cosθ. An oxygen isotope exponent of α≈0.15–0.20 for the shift of the Curie temperature TC, consistent with experiments, is obtained and an isotope shift of about 1–2% for the ferromagnetic spin-wave stiffness is predicted for the first time.