Based on the Hamiltonian of small polarons with the strong nearest neighbor
repulsion, we have investigated the charge ordering phenomena observed in
half-doped manganites R_{1/2}A_{1/2}MnO_3. We have explored possible
consequences of the charge ordering phase in the half-doped manganites. First,
we have studied the renormalization of the sound velocity around TCO,
considering the acoustic phonons coupled to the electrons participating in the
charge ordering. Second, we have found a new antiferromagnetic phase induced by
the charge ordering, and discussed its role in connection with the specific
CE-type antiferromagnetic structure observed in half-doped manganites.Comment: 5 pages, 2 Postscript figures. To appear in Phys. Rev. B - Rapid
Comm. (01Jun97