Orbital ordering and exchange interaction in the manganites - art. no. 094433

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 sh own that the magnetic structure of La1-xCaxMnO3 is correctly described with in an electronic Hamiltonian model, provided that the appropriate orientati on of the Mn(e(g)) orbitals induced by the Jahn-Teller effect is taken into account. The Jahn-Teller distortions of the MnO6 octahedra control the ori entation of the eg orbitals in the crystal, which in turn is shown to deter mine the sign of the magnetic exchange. Electron hopping involving the Mn(t (2g)) orbitals is found to be important in certain situations. for instance , it can cause a sign change in the exchange interaction, from ferromagneti c to antiferromagnetic, as a function of the Mn-O-Mn bond angle. All our re sults are obtained by exact diagonalization of the model Hamiltonian, eithe r by direct diagonalization or by diagonalization using the Lanczos method, if the Hamiltonian is too big, and are rationalized using results of the f ourth-order perturbation theory. The exchange interactions (signs and magni tudes) of the end members LaMnO3 and CaMnO3 as well as of the half-doped co mpound, La1/2Ca1/2MnO3, are all described correctly within the model.