Fig. 5. Crystal Hall conductivity in the chiral crystal of CoNb₃S₆ antiferromagnet.

(A) Calculated magnetization isosurfaces in the CoNb₃S₆ antiferromagnet exhibit low symmetry and illustrate the global chiral symmetry breaking. (B) The crystal of the CoNb₃S₆ antiferromagnet ("L, " with a left-handed chirality) and its mirror m image ("R, " with a right-handed chirality). Note that the mirror m maps the two chiralities onto each other by redistributing the nonmagnetic S atoms while preserving the magnetic atom positions and orientations of the collinear antiferromagnetic moments. (C) The calculated crystal Hall conductivity (left axis) changes sign when the crystal chirality is reversed from left- to right-handed. The right axis corresponds to the calculated dependence of the electron filling on energy. (D) Band structure detail of antiferromagnetic CoNb₃S₆ without (black line) and with (red line) spin-orbit coupling. We show fraction of the LHA path in Brillouin zone.