Doping dependence of the exchange energies in bilayer manganites: Role of orbital degrees of freedom

Recently, an intriguing doping dependence of the exchange energies in the bilayer manganites La_2-2xSr_1+2xMn₂O₇ has been observed in the neutron scattering experiments. The intralayer exchange changed only weakly with doping while the interlayer one drastically decreased. Here we propose a theory which accounts for these experimental findings. We argue that the observed striking doping dependence of the exchange energies can be attributed to the evaluation of the orbital level splitting with doping. The latter is handled by the interplay between Jahn-Teller effect (supporting an axial orbital) and the orbital anisotropy of the electronic band in the bilayer structure (promoting an in-plane orbital), which is monitored by the Coulomb repulsion. The presented theory, while being mean-field type, describes well the experimental data and also gives the estimates of the several interesting energy scales involved in the problem.