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 La_1-xAₓMnO₃ perovskites ( A0ex0ex=0ex0exCa,0ex0exSr,0ex0exBa). 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.