Fig. 4. The effect of the out-of-plane and in-plane magnetic field on the tetrahedral triple-Q ordering in Co_1/3TaS₂.

a, b A time-reversal pair of the tetrahedral spin configuration, having ${\chi }_{ijk}$ opposite to each other. The blue and orange arrows in a depict the generic canting of the tetrahedral ordering in Co_1/3TaS₂ by an out-of-plane magnetic field. c Comparison between the measured ${\sigma }_{xy}^{\mathrm{AHE}}$ (orange) and M_z (red) under the out-of-plane field at 3 K. d Comparison between the measured ${\sigma }_{xy}^{\mathrm{AHE}}$ (orange) at 3 K and ${\chi }_{ijk}$ (red) calculated from the M_z data in c. e Intensities of the three magnetic Bragg peaks in Fig. 2c under an external magnetic field along the a* direction. Error bars in e represent the standard deviation of the measured intensity.