Static and Dynamical Properties of the Ferromagnetic Kondo Model with Direct Antiferromagnetic Coupling Between the localized $t_{2g}$ Electrons

The phase diagram of the Kondo lattice Hamiltonian with ferromagnetic Hund's coupling in the limit where the spin of the localized $t_{2g}$ electrons is classical is analyzed in one dimension as a function of temperature, electronic density, and a direct antiferromagnetic coupling $J'$ between the localized spins. Studying static and dynamical properties, a behavior that qualitatively resembles experimental results for manganites occurs for $J'$ smaller than 0.11 in units of the $e_g$ hopping amplitude. In particular a coexistence of ferromagnetic and antiferromagnetic excitations is observed at low-hole density in agreement with neutron scattering experiments on $\rm{La_{2-2x}Sr_{1+2x}Mn_2O_7}$ with$x=0.4$. This effect is caused by the recently reported tendency to phase separation between hole-rich ferromagnetic and hole-undoped antiferromagnetic domains in electronic models for manganites. As $J'$ increases metal-insulator transitions are detected by monitoring the optical conductivity and the density of states. The magnetic correlations reveal the existence of spiral phases without long-range order but with fairly large correlation lengths. Indications of charge ordering effects appear in the analysis of charge correlations.