WIGNER CRYSTAL IN THE MANGANESE OXIDES R(1-X)A(X)MNO(3)

A path-integral approach for the double-exchange model with long-range Coulomb interaction [V-ij = V(o)a(o)/r(ij) with a(o) the lattice cons tant] is used to investigate the electronic phase transition in R(1-x) A(x)MnO(3) compounds. This method corresponds to the extended random-p hase approximation and can treat the metallic phase and charge-ordered phase of the system on an equal footing. We show that when the intera ction strength V-o is larger than a critical value, the uniform ferrom agnetic state becomes unstable near x = 0.5 and a Wigner-crystal state is energetically more favorable. This phase transition is first order . It is estimated that the interaction strength in the Mn oxides may b e larger than the critical value, yielding a possible interpretation o f the charge orderings observed in experiments.