Magnetotransport induced by anomalous Hall effect

In a magnetic metal, the Hall resistance is generally taken to be the sum of the ordinary Hall resistance and the anomalous Hall resistance. Here it is shown that this empirical relation is no longer valid when either the ordinary Hall angle or the anomalous Hall angle is not small. Using the proper conductivity relation, we reveal an unexpected magnetoresistance (MR) induced by the anomalous Hall effect (AHE). A $B$-linear MR arises and the sign of the slope depends on the sign of the anomalous Hall angle, giving rise to a characteristic bowtie shape. The Hall resistance in a single-band system can exhibit a nonlinearity which is usually considered as a characteristic of a two-band system. A $B$-symmetric component appears in the Hall. These effects reflect the fundamental difference between the ordinary Hall effect and the AHE. Furthermore, we experimentally reproduce the unusual MR and Hall reported before in ${\mathrm{Co}}_3{\mathrm{Sn}}_2{\mathrm{S}}_2$ and show that these observations can be well explained by the proposed mechanism. MR often observed in quantum anomalous Hall insulators provides further confirmation of the picture. The effect may also account for the large MR observed in nonmagnetic three-dimensional topological Dirac semimetals.

Figure 1

Field dependence of MR and Hall calculated from Eqs. (4), (5), and Eq. (1). The coercive field is set at $\mu B=0.5$. (a), (d) $tan\vartheta =0.4$ when $tan\theta >0$. The black dashed lines indicate the Drude resistivity ${\rho }_0$, which is independent of $B$. (b),(e) $tan\vartheta =-0.4$ when $tan\theta >0$.. The black dashed lines are calculated from Eq. (1). The inset in (a) depicts the carrier velocity $\mathit{v}$ and the electric field $\mathit{E}$. Here, ${\mathit{v}}_0$ and ${\mathit{v}}_{\mathit{k}}$ are the band velocity with and without AHE, respectively. (c), (f) ${\rho }_{xx}$ and ${\rho }_{yx}$ in a large $tan\theta$ (field) range.

Figure 2

Field dependence of MR and Hall calculated from Eqs. (4) and (5) with $tan\vartheta$ linear in $B$. ${\alpha }_B=0.002$ is used, such that when a Zeeman field of 150 T is applied, the anomalous Hall angle is 0.3, close to that in ${\mathrm{Co}}_3{\mathrm{Sn}}_2{\mathrm{S}}_2$. (a) MR. Data in a large $tan\theta$ range are shown in the inset. A strong peak appears at $tan\theta tan\vartheta \approx -1$. (b) Hall. Data in a large $tan\theta$ range are shown in the inset. An abrupt sign reversal appears at $tan\theta tan\vartheta \approx -1$.

Figure 3

Field dependence of MR and Hall calculated from Eqs. (4) and (5) with ${\alpha }_B=-0.06$. (a) MR. (b) Hall.

Figure 4

Experimental data of MR and Hall for ${\mathrm{Co}}_3{\mathrm{Sn}}_2{\mathrm{S}}_2$. (a), (b) ${\rho }_{xx}$ and ${\rho }_{yx}$ of N01 at 10 K. A jump in ${\rho }_{xx}$ occurs at the coercive field. The orange area at negative fields is enclosed by ${\rho }_{yx}\left(B\right)$ and the one obtained by an inversion of ${\rho }_{yx}\left(B\right)$ through $(0,{\rho }_{yx}\left(0\right))$, highlighting the $B$-symmetric component of ${\rho }_{yx}$. (c), (d) ${\rho }_{xx}$ and ${\rho }_{yx}$ of B04 at 20 K. Tiny drops in ${\rho }_{yx}$ at the coercive field are discernible, in agreement with $tan\theta$ and $tan\vartheta$ being of the same sign.