Large anomalous Hall angle accompanying the sign change of anomalous Hall conductance in the topological half-Heusler compound HoPtBi

Controlling the anomalous Hall effect (AHE) in magnetic topological materials is an important property. Because of the close relationship between anomalous Hall conductance (AHC) and topological band (strong Berry curvature), AHC can be effectively tuned by magnetic field combined with strong spin-orbit interaction and special band structure. In this work, we observed a magnetic field driving the nonmonotonic magnetic field dependence of anomalous Hall resistivity and the sign change in magnetic-field-induced Weyl semimetal HoPtBi. The tunable ranges of the AHC and the anomalous Hall angle are $-75\sim 73{\mathrm{\Omega }}^{–1}\mathrm{c}{\mathrm{m}}^{–1}$ and $-12.3\sim 9.1\%$, respectively. Anisotropic measurements identified the magnetic field is the key factor in controlling the additional Hall term sign. Further analysis indicated that it originated from the field-induced shift of the Weyl points via exchange splitting of bands near the Fermi level. The large tunable effect of the magnetic field on the electronic band structure provides a path to tune the topological properties in this system. These findings suggest that HoPtBi is a good platform for tuning the Berry phase and AHC with the magnetic field.

Figure 1

(a) The crystal structure of HoPtBi with the space group F-43m (216). (b) Brillouin zone and (c) band structure of HoPtBi along the X-Γ-X-W-Γ-W-K-Γ-K-L-Γ-L high symmetry line. (d) Single crystal XRD pattern of the (111) plane. The inset is the typical shape of the HoPtBi single crystal. (e) The thermal magnetization of HoPtBi from 2 to 300 K at an external magnetic field $B$ = 0.05 T. The inset represents the fitting of the whole paramagnetic region of the thermal magnetization curve by Curie-Weiss law: the extension of the fitting curve intersects the negative $x$ axis, AFM exchange interaction is dominant. (f) Temperature dependence of resistivity curves for sample #1 with current I// [1–10].

Figure 2

AHE for sample #1. Magnetoresisitance (a) and Hall resistivity (b) for sample #1. The inset of (a) is the configuration of the magnetic field $B$//[111] and current $I$ //[1–10]. (c) Magnetization as a function of $B$ at different $T$ with $B$//[111]. (d) The extracting progress of the anomalous Hall resistivity at 2 K. The lower figure shows Hall resistivity at 2 and 20 K. The upper one shows the additional term $\mathrm{\Delta }{\rho }_{xy}^A$ at 2 K. The total curve can be divided into three regions I, II, and III. The additional term $\mathrm{\Delta }{\rho }_{xy}^A$ at 2 K was obtained by subtracting the linear Hall resistivity at 20 K. (e) The additional term $\mathrm{\Delta }{\rho }_{xy}^A$ for sample #1 at $T<20$ K.

Figure 3

Hall resistivity ${\rho }_{xy}$ and magnetoresistance ${\rho }_{xx}$ at different temperatures for three samples with different configurations of $B$ and $I$. (a) and (d) are the magnetoresistance ${\rho }_{xx}$ and Hall resistivity ${\rho }_{xy}$, respectively, with $B$//[110] and $I$//[1–10]. The inset of (b) shows the Hall resistivity at a low magnetic field. (c) and (d) are magnetoresistance ${\rho }_{xx}$ and Hall resistivity ${\rho }_{xy}$ for sample #3, respectively, with B//[001] and I//[1–10]. (e) and (f) are the results for sample #4 with B//[001] and I//[100].

Figure 4

The extracting progress of the anomalous Hall resistivity for sample #4. (a) Hall resistivity for sample #4 in the $2-50\mathrm{K}$ range. The dashed lines are a guide for the eye. (b) The anomalous Hall resistivity for sample #4 at $T$ = 2 K. (c) The anomalous Hall resistivity contains two terms,${\rho }_{xy}^A$, and additional term, $\mathrm{\Delta }{\rho }_{xy}^A, T<20\mathrm{K}$. (d) The additional term $\mathrm{\Delta }{\rho }_{xy}^A$ for sample #4.

Figure 5

(a) The additional Hall conductance $\mathrm{\Delta }{\sigma }_{xy}^A$ and (b) the corresponding AHA for samples #1 – #4 at 2 K. All data are obtained from the peak of $\mathrm{\Delta }{\rho }_{xy}^A.$ II represents the data gotten from the II region (low magnetic field), and III represents the data from the III region (high magnetic field). (c) The sketches of the mechanism of the AHC and the sign change for HoPtBi. The upper panel: in the absence of an external magnetic field, AHC tends to zero. The lower panel: under various magnetic field directions, the $t$ formed Weyl points shift around $E_{\mathrm{F}}$ and induced the AHC sign change.