Divergence between long- and short-wavelength magnon damping in spinel ferrites

The realization of practical, high-speed magnonic devices requires engineering magnetic materials with low dissipation over wide frequency ranges. While optical and microwave probes are used to infer the damping of low energy/long wavelength modes, the degree to which these $q\sim0$ properties translate into higher-energy, finite-momentum modes remains an important open question. Here, we utilize a combination of ferromagnetic resonance (FMR) and resonant inelastic x-ray scattering on spinel ferrites Li$_{0.5}$Al$_x$Fe$_{2.5-x}$O$_4$ to probe magnons in both the short- and long-wavelength limits. We observe that aluminum substitution both markedly reduces the magnon bandwidth and drastically shortens the high-$q$ magnon lifetimes, in sharp contrast to the ultralow magnon damping inferred from FMR. These findings demonstrate a disparity between how non-magnetic substituents impact magnon damping in the long- and short-wavelength limits, providing a new perspective for assessing candidate materials for magnonic devices.