Effect of Lattice Distortion on Charge Order in Manganites at Doping x=0.5

In the present paper, we continue our investigation on the antiferromagneticorigin of the charge order observed in the halt-doped manganese. By introducing aSu-Schrieffer-Heeger (SSH) type of perturbation interaction to the double-exchange Hamiltonian, wecalculate again its ground-state phase diagram at Glling x = 0.5 by the unrestricted real-spaceHartree-Fock approximation method. We find that, as the SSH electron-phonon interaction increases,the charge order parameter decreases to zero rapidly but the CE-type antiferromagnetic order becomesmore stable. In other words, the charge order is much more fragile than the CE-type or theNeel-type antiferromagnetic orders under the electron-phonon perturbation. These results support theproposed theory in the recent publications that the charge order in these systems is induced by theantiferromagnetic correlations.