Static and dynamical properties of the ferromagnetic Kondo model with direct antiferromagnetic coupling between the localizedt2gelectrons

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 $J^{\prime }$ between the localized spins. Studying static and dynamical properties, a behavior that qualitatively resembles experimental results for manganites occurs for $J^{\prime }$ 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 ${\mathrm{La}}_{2-2x}{\mathrm{Sr}}_{1+2x}{\mathrm{Mn}}_2{\mathrm{O}}_7$ with $x=0.4\mathrm{}$. 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 $J^{\prime }$ 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.