Orbital ordering and exchange interaction in the manganites

Abstract

The microscopic origin of the exchange interaction in manganites is studied by solving an electronic model Hamiltonian for the Mn-O-Mn triad. It is shown that the magnetic structure of La1-xCaxMnO3 is correctly described within an electronic Hamiltonian model, provided that the appropriate orientation of the Mn(eg) orbitals induced by the Jahn-Teller effect is taken into account. The Jahn-Teller distortions of the MnO6 octahedra control the orientation of the eg orbitals in the crystal, which in turn is shown to determine the sign of the magnetic exchange. Electron hopping involving the Mn(t2g) orbitals is found to be important in certain situations, for instance, it can cause a sign change in the exchange interaction, from ferromagnetic to antiferromagnetic, as a function of the Mn-O-Mn bond angle. All our results are obtained by exact diagonalization of the model Hamiltonian, either by direct diagonalization or by diagonalization using the Lanczos method, if the Hamiltonian is too big, and are rationalized using results of the fourth-order perturbation theory. The exchange interactions (signs and magnitudes) of the end members LaMnO3 and CaMnO3 as well as of the half-doped compound, La1/2Ca1/2MnO3, are all described correctly within the model.