Spin-wave excitations in the ferromagnetic-metallic and in the charge, orbital and spin ordered states in Nd${}_{1-x}$Sr${}_x$MnO${}_3$ with x$\approx$0.5

Inelastic neutron scattering experiments have been performed on single crystals of Nd${}_{1-x}$Sr${}_x$MnO${}_3$ with x$\approx$0.5. Colossal magnetoresistance (CMR) in the manganites arises from the interplay between a ferromagnetic metallic and antiferromagnetic charge and orbital ordered insulating state. Therefore, it appears important to compare these phases concerning their underlying magnetic interaction parameters. Our investigations of the spin-wave disperion in the AFM ordered state of Nd${}_{0.5}$Sr${}_{0.5}$MnO${}_3$ exhibits a strongly anisotropic stiffness. The sign of the anisotropy is characteristic for the site-centered model for charge and orbital ordering in half-doped manganites. Within this model, linear spin-wave theory yields a perfect description of the experimental dispersion. Furthermore, magnetic excitations in the ferromagnetic metallic state of Nd${}_{1-x}$Sr${}_x$MnO${}_3$ with x=0.49 and x=0.50 exhibit nearly the same magnon dispersion which can be described with a Heisenberg model including nearest-neighbor interactions.