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.Comment: 155 pages, 66 figure
