Anisotropic Magnon Spin Transport in Ultra-thin Spinel Ferrite Thin Films -- Evidence for Anisotropy in Exchange Stiffness

We report measurements of magnon spin transport in a spinel ferrite, magnesium aluminum ferrite $mathrm{MgAl_{0.5}Fe_{1.5}O_4}$ (MAFO), which has a substantial in-plane four-fold magnetic anisotropy. We observe spin diffusion lengths $> 0.8$ $mathrm{mu m}$ at room temperature in 6 nm films, with spin diffusion length 30% longer along the easy axes compared to the hard axes. The sign of this difference is opposite to the effects just of anisotropy in the magnetic energy for a uniform magnetic state. We suggest instead that accounting for anisotropy in exchange stiffness is necessary to explain these results.