We consider the $t-J$ model for doped manganites, and show that double exchange for correlated $e_g$ electrons favors in the ferromagnetic metallic phase an orbital liquid (i.e., orbital-disordered) state. Therefore the spin-wave stiffness is isotropic, and increases with hole doping x, providing a direct measure of the kinetic energy $\propto x$ of strongly correlated $e_g$ electrons. The superexchange interactions, which stabilize orbital order at low doping, are frustrated in the orbital liquid and only reduce the stiffness constant, leading to a quantitative explanation of the magnon dispersion.

• Received 13 July 2001

DOI:https://doi.org/10.1103/PhysRevB.65.052414