Lattice Effects in the Colossal-Magnetoresistance Manganites

We study the combined influence of spin double exchange and Jahn-Teller lattice coupling to holes in the ${\mathrm{La}}_{1-x}{A}_x{\mathrm{MnO}}_3$ perovskites ( $A=\mathrm{C}\mathrm{a},\mathrm{S}\mathrm{r},\mathrm{B}\mathrm{a}$). Using a mean-field approximation for the double exchange and a variational Lang-Firsov approximation for the lattice degrees of freedom, we show that the lattice effects decrease the magnetic transition temperature, and also cause the maximal value of the transition temperature as a function of dopant concentration $x$ to depend on the Jahn-Teller coupling strength. We find a continuous rapid crossover from a large polaronic state to a quasi-self-trapped small polaron state accompanying the magnetic transition.