Spin wave dispersion of ultra-low damping hematite ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>α</mml:mi><mml:mo>−</mml:mo><mml:msub><mml:mi mathvariant="normal">Fe</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:math> ) at GHz frequencies

Low magnetic damping and high group velocity of spin waves (SWs) or magnons are two crucial parameters for functional magnonic devices. Magnonics research on signal processing wave-based computation at GHz frequencies focused the artificial ferrimagnetic garnet ${\mathrm{Y}}_{3}{\mathrm{Fe}}_{5}{\mathrm{O}}_{12}$ (YIG) so far. We report wave spectroscopy studies performed natural mineral hematite ($\ensuremath{\alpha}{\text{-Fe}}_{2}{\text{O}}_{3}$), which is a canted antiferromagnet. By means broadband inelastic light scattering, we determine coefficient $1.1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$ magnon velocities few 10 km/s, respectively, room temperature. Covering large regime vectors up to $k\ensuremath{\approx}24\phantom{\rule{0.16em}{0ex}}\mathrm{rad}/\textmu{}\mathrm{m}$, find exchange stiffness length be relatively short only about 1 \AA{}. In small field 30 mT, decay SWs estimated 1.1 cm similar best YIG. Still, scattering provides surprisingly broad partly asymmetric resonance peaks. Their characteristic shape induced by velocities, low damping, distribution incident angles inside laser beam. Our results promote as an alternative sustainable basis devices with fast speeds losses based stable mineral.