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

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