Dynamics of the Phase Separated States in the Double Exchange Model

We present large-scale simulations of spin dynamics in the phase-separated states of the one-orbital double-exchange model. These inhomogeneous electronic states consisting of ferromagnetic conducting clusters embedded in an antiferromagnetic insulating background play a crucial role in the colossal magnetoresistance phenomenon. We compute the dynamical structure factor of these nanoscale textures using an efficient real-space formulation of coupled spin and electron dynamics. Dynamical signatures of the various underlying magnetic correlations are identified. At small hole doping, the structure factor exhibits a dominating signal of magnons from the background N\'eel order and localized modes from small metallic clusters. A low-energy continuum due to large-size ferromagnetic clusters emerges at higher doping levels. Implications for experiments on magnetoresistive manganites are also discussed.