Fig. 2.

Spontaneous Hall effect of ${\mathrm{C}\mathrm{e}}_3{\mathrm{B}\mathrm{i}}_4{\mathrm{P}\mathrm{d}}_3$. (A) Temperature-dependent direct current (DC) Hall resistivity ${\rho }_{xy}$ in zero external magnetic field, showing a pronounced spontaneous Hall effect below 3 K. Data were taken without prior application of magnetic fields. (B) Spontaneous DC Hall conductivity ${\sigma }_{xy}$ in units of the 3D conductivity quantum vs. longitudinal conductivity ${\sigma }_{xx}$, with temperature as implicit parameter, for the DC response of the sample in A (bottom and left axes, black) and for the $1\omega$ response in an AC experiment on a sample from a different batch (top and right axes, red), both in zero magnetic field. In the Kondo coherent regime (gray shading), ${\sigma }_{xy}$ is linear in ${\sigma }_{xx}$. (C) Temperature-dependent nuclear and electronic contributions to the muon spin relaxation rate obtained from ZF $\mu$SR measurements. The electronic contribution is extremely small and temperature-independent within the error bars, ruling out TRS breaking with state-of-the-art accuracy. Magnetization and specific heat measurements corroborate this finding (see SI Appendix, sections II B and C and Figs. S11 and S12. (D) Scaled $2\omega$ spontaneous Hall voltage vs. square of $1\omega$ driving electrical current in zero magnetic field for different temperatures and at 1.7 K for various magnetic fields. (E) Quantities analogous to D for the $0\omega$ spontaneous Hall voltage. (F) Scaled coefficients of square-in-current response ${\alpha }^{2\omega ,0\omega ,\mathrm{D}\mathrm{C}}$ from D and E and SI Appendix, Fig. S6, respectively (left axis) and linear-in-current response ${\rho }_{xy}^{1\omega ,\mathrm{D}\mathrm{C}}$ from B (right axis), as function of scaled temperature ($T_{\mathrm{H}}$ is the onset temperature of the spontaneous Hall signal). The absolute values of ${\alpha }^{max,i}$, ${\rho }_{xy}^{max,i}$, and $T_{\mathrm{H}}$ are listed in SI Appendix, Table S1.