Fig. 4: B-fields dependence of the transverse third-harmonic voltage in MiBi2Te4.

a The out-of-plane B-fields dependence of the \({V}_{{xy}}^{3\omega }\) measured at different temperatures. b The calculated Berry curvature quadrupole \({{\mathcal{Q}}}_{{xxz}}\) as a function of the magnetic order parameter Δ. c–e The band splitting and distribution of Berry curvature quadrupole Ωz (color scale) at different magnetic order parameter Δ = 0 (c), Δ = 0.2 (d), and Δ = 0.7 (e), where the black dashed line indicates the chemical potential.