$g$-wave altermagnetic order parameter in hematite

Abstract: Altermagnets combine the vanishing net magnetization of antiferromagnets with momentum-dependent spin splitting. Magnon band splitting provides a direct probe of altermagnetic order and may enable chirality-selective magnon transport, yet the momentum-space symmetry of this splitting has not been determined quantitatively. Here we use inelastic neutron scattering to map the momentum dependence of altermagnetic magnon splitting in hematite ($α$-Fe$_2$O$_3$). The splitting vanishes along nodal directions and reaches maxima off the nodes, revealing the $g$-wave symmetry of the altermagnetic order parameter. These results agree with linear spin-wave theory calculations based on the altermagnetic model, which further identify the nondegenerate branches as magnons of opposite chirality and trace the splitting to symmetry-inequivalent long-range exchange interactions. Our results provide the first quantitative determination of the momentum-space symmetry of altermagnetic chiral magnons. These findings, together with hematite's high magnetic ordering temperature and low magnon damping, establish it as a promising platform for low-dissipation, symmetry-selective magnonic applications.