Magnetic and orbital ordering in cuprates and manganites

The mechanisms of magnetic and orbital interactions due to double exchange (DE) and superexchange (SE) in transition metal oxides with degenerate e_g orbitals are presented. Specifically, we study the effective spin-orbital models derived for the d^9 ions as in KCuF_3, and for the d^4 ions as in LaMnO_3, for spins S=1/2 and S=2, respectively. Such models are characterized by three types of elementary excitations: spin waves, orbital waves, and spin-and-orbital waves. The SE interactions between Cu^{2+} (d^9) ions are inherently frustrated, which leads to a new mechanism of spin liquid which operates in three dimensions. The SE between Mn^{3+} (d^4) ions explains the A-type antiferromagnetic order in LaMnO_3 which coexists with the orbital order. In contrast, the ferromagnetic metallic phase and isotropic spin waves observed in doped manganites are explained by DE for degenerate e_g orbitals. It is shown that although a hole does not couple to spin excitations in ferromagnetic planes of LaMnO_3, the orbital excitations change the energy scale for the coherent hole propagation and cause a large redistribution of spectral weight. Finally, we point out some open problems in the present understanding of doped manganites.