| This work contains studies of two classes of perovskite transition metal oxides. The first class is the layered perovskite cuprates and the related nickelate. The second class is the three dimensional perovskite manganites. Both model and ab initio calculations are carried out for the two classes of systems. The dissertation is therefore divided into the following four parts.; The first part is about the 3-band Hubbard model. The model is commonly used for describing the electronic properties of the important CuO2 layers in the crystals of high-Tc superconducting cuprates, such as doped La2CuO4 and YBa2Cu3O 7. The straightforward perturbation expansion on the model taking tpd/ϵpd (∼0.36 for the cuprates) as the small parameter does not converge. In this work, I show that there exist canonical transformations on the model Hamiltonian such that the perturbation expansion based on the transformed Hamiltonians converges.; In the second part, crystal Hartree-Fock calculations are carried out for La2NiO4 and La2CuO4. The results predict correctly that these two materials are antiferromagnetic insulators, in contrast to the wrong predictions made by the density functional calculations using the local spin density approximation (LSDA). The spin form factors of the materials are also calculated. The results agree with previous theoretical works using an embedded cluster model. The calculated spin form factor of La2CuO4 is consistent with the few experimental data currently available, while the results for La2NiO4 show a large discrepancy between theory and experiment. We question the accuracy of the experimental results of La2NiO4 and call for more experiments to settle the issue.; In the third part, crystal Hartree-Fock calculations are carried out for LaMnO3. Our main focus is on the magnetic and orbital orderings, the effect of the crystal distortion from the cubic perovskite structure, and the analysis of the projected density of states. In addition, we also find unexpected charge associated with the Mn ions. The effective spin Hamiltonian obtained by mapping the energies of different magnetically ordered states is consistent with experimental data of the spin wave dispersion, while it is qualitatively different from that of a LSDA calculation which was also claimed to be consistent with the experiment. We show that the current experimental accuracy is not enough to distinguish these two theories.; In the fourth part, I report a study on possible extensions of the double-exchange (DE) model for the doped manganites in the hope of understanding the recently observed softening of the spin wave dispersion near the Brillouin zone edge. I also argue that most models in the literature are flawed by assuming uncoupled normal mode vibrations of the MnO6 octahedral clusters in the crystal. As a first trial, I consider several possible electron-phonon couplings based on the single-band DE model. The results show that the spin wave states are robust and the spin wave dispersion gets very slightly hardened in the presence of the electron-phonon couplings. This suggests that the observed softening of the spin wave dispersion may be beyond the scope of the single-band DE model. |
