Fig. 1: Crystal and magnetic structures of Bi₂CuO₄ and conceptual illustration of antiferromagnetic trichroism.

a, b Three-dimensional (a) and Y-axis (b) views of crystal and magnetic structures of Bi₂CuO₄. The [110], \([\bar{1}10]\), and [001] axes are referred to as X, Y, and Z, respectively. Green, brown, and gray balls represent Cu, O, and Bi atoms, respectively. A unit cell (gray dotted lines) contains four Cu ions labeled as Cu1–Cu4. Square-planar CuO₄ units stack in a twisted manner along the Z axis. Magenta arrows denote Cu spins, which are ferromagnetically aligned along the Z axis while antiferromagnetically aligned in the XY plane. A small displacement (0.08 Å) of a Cu atom from the plane of O₄ square along the Z axis is denoted by gray arrows in (b). c, Four antiferromagnetic domains (L_+X, L_−X, L_+Y, and L_−Y domains). They are distinguished in terms of the orientation of Néel vector L (thick magenta arrows) and the corresponding magnetic toroidal moment T (thick green arrows). d Conceptual illustration of antiferromagnetic trichroism. Absorption coefficient of light propagating along the +X axis (orange wave) takes three discrete magnitudes, depending on the direction of L, which is conceptually denoted by three colors (blue, red, and white). See text for details.