Fig. 4: Electronic band structures of HoAuSn with several magnetic ground states.

Energy dispersed band structure with spin-orbit coupling along the high symmetry axes (left panels) and the shape of the Fermi surfaces of the highest valence band and the lowest conduction band in the first Brillouin zone (right panels). Yellow bullet-like electron pockets are located at the zone boundary while green hole pockets are at the zone center. a Non-magnetic (NM) state. b Antiferromagnetic (AFM) state. c Ferromagnetic (FM) state. The right schematics exhibit the Fermi surface cross sections of the hole and electron pockets in the (111) plane. The smallest, second smallest hole pockets, and electron pocket correspond to \({{{{{{\rm{\alpha }}}}}}}_{1}\), \({{{{{{\rm{\alpha }}}}}}}_{2}\), and \({{{{{\rm{\beta }}}}}}\) which are revealed by the quantum oscillation in Fig. 3d, respectively.