Spectral Function Analysis on Spin Dynamics in Double-Exchange Systems with Randomness

Spin excitation spectrum is studied in the double-exchange model with randomness. Applying the spin wave approximation and the spectral function analysis, we examine excitation energy and linewidth using analytical as well as numerical methods. For small wave number $q \sim 0$, the excitation energy is cosine-like and the linewidth shows a $q$-linear behavior. This indicates that the spin excitation becomes incoherent or localized near $q = 0$. Crossover takes place to marginally-coherent regime where both the excitation energy and the linewidth are proportional to $q^2$. The incoherence is due to local fluctuations of the kinetic energy of electrons. Comparison with experimental results in colossal magnetoresistance manganites suggests that spatially-correlated or mesoscopic-scale fluctuations are more important in real compounds than local or atomic-scale ones.