Orbital ordering in undoped manganites via a generalized Peierls instability

Abstract

We study the ground-state orbital ordering of ${\text{LaMnO}}_{3}$, at weak electron-phonon coupling, when the spin state is A-type antiferromagnet. We determine the orbital ordering by extending to our Jahn-Teller system a recently developed Peierls instability framework for the Holstein model [S. Datta and S. Yarlagadda, Phys. Rev. B 75, 035124 (2007)]. By using two-dimensional dynamic response functions corresponding to a mixed Jahn-Teller mode, we establish that the ${Q}_{2}$ mode determines the orbital order.