Fig. 1: Structure, magnetism, and symmetry in the compensated antiferromagnet CoNb3S6.
a Layered CoNb3S6 with chiral lattice, where blue shading indicates tetrahedra formed by Co atoms in adjacent layers. b Nodal plane enforced by screw symmetry in the paramagnetic (PM) state (illustration). Black lines, black dots, red surfaces, and red line indicate the boundary of the Brillouin zone, time-reversal invariant momenta at kz = π/c, two Kramers-paired Fermi surfaces (FSs), and the intersection of these Fermi surfaces with the nodal plane. c Non-coplanar all-in-all-out (AIAO) magnetic order of cobalt ions (yellow spheres). Two magnetic domains are related by time reversal symmetry22,23. d Magnetic field (B) - temperature (T) phase diagram of CoNb3S6 obtained from magnetization M(T) at various B. A single-domain AIAO or AOAI state (inset) can be selected by field-cooling (FC) the sample in positive or negative B, respectively. Dashed and solid arrows indicate the sample history during the cooling run and measurement run, respectively. TN is the Néel temperature, and the magnetic field is parallel to the c-axis. e Proximate, non-symmorphic spin-space group symmetries in the AIAO state: For the three spin-only rotations by 180∘ around the red and black axes, the spin direction rotates while its position (in real space) remains fixed. This is followed by a spin translation along a/2 − b/2, indicated by red dashed arrows paired with the red rotation axis.
