Fig. 4. Phase diagram and transport in magnetic field.

(A) Phase diagram plotted as a function of the W-layer carrier concentration x and the out-of-plane magnetic field h_W. The blue region denotes the HFL regime where the hybridization order parameter is finite. The color code before the green line shows the value of the in-plane AFM order parameter M^∥. The solid green line shows the first-order phase transition line. On the other hand, the magenta one shows the second-order transition from the canted AFM-xy to the FM-z. (B) Evolution of the variational parameter along the line cut at x = 0.52 as a function of h_W/t_W. (C) Intrinsic contribution to the anomalous Hall conductivity for three different values of the Zeeman field. The vertical dashed lines denote the critical filling where the first-order transition takes place. (D) Intrinsic AHE for different values of the filling x as a function of the Zeeman field. The vertical dashed line denotes the first-order transition between the magnetic and the HFL phase, while the solid one denotes the second-order transition from a canted AFM to the FM-z. Above this line, the AHE vanishes. The calculation has been performed at J_K/t_W = 1, J_H/t_W = 0.05 (bandwidth 9t_W).