Orbital ordering in La0.5Sr1.5MnO4: Density functional and exact diagonalization studies

Abstract

The nature of orbital ordering and type of the Jahn-Teller (JT) distortion in the doped manganite La${}_{0.5}$Sr${}_{1.5}$MnO${}_{4}$ has been a topic of long standing debate, with both experiments and theory supporting opposite views. With the help of ab initio density functional and exact diagonalization studies we have investigated the energetics of the cooperative JT distortion and orbital ordering in this system. The density functional calculations yield a ${x}^{2}\ensuremath{-}1/{y}^{2}\ensuremath{-}1$ (rod-type) orbital order as well as a Jahn-Teller distortion where the octahedral axes on the plane are elongated along the chain direction and compressed perpendicular to it in the $ab$ plane (type I). The essential physics of the problem is captured by a single zigzag chain model, which was studied with a tight-binding Hamiltonian and exact diagonalization on a finite chain, which help unravel the reason for the rod-type orbital order. The main conclusions from the latter studies are that: (i) The Coulomb correlation effects are relatively unimportant due to the low electron density in the ${e}_{g}$ states, (ii) the kinetic energy term (hopping along the ferromagnetic zigzag chain) favors the rod-type orbital order, and (iii) a significant noncubic crystal field, proposed earlier and found here from our DFT calculations, helps stabilize the rod-type orbital order even further.