Orbital ordering in undoped manganites using Jahn-Teller interaction

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To understand the orbital ordering of LaMnO₃ in the ground state, we study it in the A-type spin antiferromagnetic state. We calculate the two-dimensional response functions associated with the Jahn-Teller Q₂ and Q₃ distortions and find that they diverge at the wavevector π,π). Furthermore, the Q₂ response function diverges faster which indicates that perhaps the ordering of the orbitals at low temperatures is dominated by the Q₂ distortion. We calculate the ground state energy for the cases when only one of the Q₂ and Q₃ modes is excited cooperatively and find that the Q₂ excited state yields lower energy.