Fig. 1: Berry curvature quadrupole in MiBi2Te4.
a Schematic diagrams of the band structure (the outline) and Berry curvature (color scale) of a generic magnetic material with non-zero Berry curvature quadrupoles. The + and – refer to the sign of Berry curvature. b Electric field induced change of Berry curvature (color scale) relative to the equilibrium state. Due to the Berry curvature distribution of the quadrupole, a field-induced dipole will appear, which contributes to the higher-order nonlinear anomalous Hall effect. The + and – refer to the sign of Berry curvature. c Schematic crystal structure of layered MiBi2Te4. The red arrows in Mn layers indicate the spin direction of Mn atoms.
