Zone Edge Softening and Relaxation in the Double Exchange Model

The $J\to \mathrm{\infty }$ double exchange model is formulated in terms of three auxiliary particles. A slow true bosonic magnon propagates by admixture with a fast fermionic pseudo-magnon. This process involves the absorption of a conduction electron which, for this half-metal, carries only charge degrees of freedom. The magnon dispersion becomes much weaker and the relaxation rate increases rapidly upon approaching the zone boundary. That the magnons relax for all wave vector values implies the existence of a low energy spin continuum.