Fig. 4. Magnetic competition driven thermal evolution of anomalous Hall conductivity.

a Schematic magnetic phase diagram as a function of temperature and spin structures of Co₃Sn₂S₂, i.e. the FM and the in-plane AFM structures. The arrows mark the transition temperatures T_C1 ≃ 177 K, T_C2 ≃ 172 K and $T_{\mathrm{C}}^{*}$ ≃ 90 K. b The temperature dependence of the FM volume fraction and the in-plane anomalous Hall conductivity σ_xy. The error bars of the FM fraction represent the s.d. of the fit parameters. c The correlation plot of σ_xy vs fraction of the ferromagnetically ordered region. The solid straight line is drawn between a hypothetical situation of the minimum (zero) and the maximum values of σ_xy and the FM fraction. Data shown in solid circles are taken from ref. ¹⁰. d The dependence of σ_xy on the chemical potential, calculated for the out-of-plane FM and the in-plane AFM structures. The inset shows the calculated Berry curvature distribution in the BZ at the Ferromagnetic phase.