Effect of lattice distortion on charge order in manganites at doping x = 0.5

In the present paper, we continue our investigation on the antiferromagnetic origin of the charge order observed in the half-doped manganese. By introducing a Su-Schrieffer-Heeger (SSH) type of perturbation interaction to the double-exchange Hamiltonian, we calculate again its ground-state phase diagram at filling x = 0.5 by the unrestricted real-space Hartree-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 becomes more stable. In other words, the charge order is much more fragile than the CE-type or the Neel-type antiferromagnetic orders under the electron-phonon perturbation. These results support the proposed theory in the recent publications that the charge order in these systems is induced by the antiferromagnetic correlations.