Fig. 1: Noncollinear antiferromagnetic structures with non-zero vector chirality and the corresponding electronic structure of Mn3Sn.
a Mn3Sn bulk crystal structure, blue and magenta balls represent the Mn atoms in top and bottom magnetic kagome layers at z = 1/4 and 3/4, respectively. The yellow balls represent the Sn atoms. The noncollinear chiral antiferromagnetic textures are presented in one kagome layer, named b “direct'', c “inverse” and d 3-in-3-out magnetic states with their corresponding κ values. The square box here depicts how switching of κ can be achieved via simultaneous staggered rotations of S1 and S2. e The 2D projection of the hexagonal Brillouin zone (BZ) of Mn3Sn. Essential high symmetry points are marked here. f The band structures without considering the spin-orbit coupling (SOC). Note, for all 120° noncollinear states band structures remain identical unless the SOC is switched on. After considering the SOC effect, g–i shows the band structure for the magnetic states “direct'', “inverse” and 3-in-3-out, respectively. The nontrivial features near Ef are highlighted within the red circles. The thick green line in e and the corresponding band structure plots f–i highlights the k-path for the kz = 0 plane of the BZ.
