Chirality-Dependent Hall Effect and Antisymmetric Magnetoresistance in a Magnetic Weyl Semimetal

Weyl semimetals host a variety of exotic effects that have no counterpart in conventional materials, such as the chiral anomaly and magnetic monopole in momentum space. These effects give rise to unusual transport properties, including a negative magnetoresistance and a planar Hall effect, etc. Here, we report a new type of Hall and magnetoresistance effect in a magnetic Weyl semimetal. Unlike antisymmetric (with respect to either magnetic field or magnetization) Hall and symmetric magnetoresistance in conventional materials, the discovered magnetoresistance and Hall effect are antisymmetric in both magnetic field and magnetization. We show that the Berry curvature, the tilt of the Weyl node, and the chiral anomaly synergically produce these phenomena. Our results reveal a unique property of Weyl semimetals with broken time reversal symmetry.

Figure 1

Chirality-dependent in-plane Hall effect at $T=20\mathrm{K}$. (a) Hall resistivity for magnetic field at $\theta =0°$ and 80°. The inset depicts the direction of current and the magnetic field. (b) Hall resistivity below $B_c$ after subtracting AHE. The difference between these two lines is inconsistent with OHE, implying an extra Hall resistivity. (c) Hall resistivity after subtracting OHE and AHE, denoted as ${\rho }_{yx}^{\chi }$. It is linear and antisymmetric in the magnetic field and changes its sign when the magnetization reverses polarity. The antisymmetry also suggests that symmetric magnetoresistance due to contact misalignment is negligible.

Figure 2

Extraction of the chirality-dependent Hall effect at $T=20\mathrm{K}$ for magnetic field in the $xz$ plane. (a) Hall resistivity after subtracting AHE at $\theta =\pm 50°$. To remove overlapped data between $\pm B_c$, the data between $-9$ to 0 T are plotted for sweeping up, while the data between 0 to 9 T are plotted for sweeping down. The inset depicts the magnetic field direction. When the angle is changed from positive to negative ($+\theta$ to $-\theta$), the in-plane magnetic field is reversed ($+B_{\parallel }$ to $-B_{\parallel }$) while the magnetization keeps its sign, resulting in ${\rho }_{yx}^{\chi }$ in the opposite field without altering OHE and AHE. (b),(c) The extracted OHE and ${\rho }_{yx}^{\chi }$, respectively. Both show a linear dependence at low fields. (d) Angular dependence of the Hall coefficient of OHE. The solid line is a fit to $\cos \theta$. (e) Angular dependence of the Hall coefficient of ${\rho }_{yx}^{\chi }$. The solid line is a fit to $\sin \theta$.

Figure 3

Antisymmetric linear MR at $T=20\mathrm{K}$ for magnetic field in the $yz$ plane. (a) MR at $\theta =0°$ and $\pm 70°$. The jump at $B_c$ is most likely induced by AHE due to non-ideal voltage contacts. (b) Close-up of MR below the coercive field. Solid and dashed lines represent the positive and negative magnetization, respectively. The slope depends on the polarity of magnetization. (c),(d) Extracted ordinary and chirality-dependent MR, respectively. (e) Ordinary MR as a function of the perpendicular magnetic field $B_{\perp }$. (f) Chirality-dependent MR as a function of the in-plane magnetic field $B_{\parallel }$.

Figure 4

Angular dependence of the chirality-dependent resistivity tensor for $B=9\mathrm{T}$ in the $xz$ and $yz$ planes. (a) ${\rho }_{yx}$ with field in the $xz$ plane. The discontinuities are caused by the sudden flip of the magnetization across the parallel position ($\theta =\pm 90°$). The difference between two discontinuities is a manifest of ${\rho }_{yx}^{\chi }$. (b) ${\rho }_{yx}^{\chi }$ extracted from (a) in polar coordinates. Red and blue represent positive and negative values, respectively. The polarity of $B_x$ and $M_z$ is labeled for four quadrants, highlighting the antisymmetric relations indicated by Eq. (1). (c) ${\rho }_{xy}$ with field in the $yz$ plane. No substantial asymmetry observed. (d) ${\rho }_{yx}^{\chi }$ extracted from (c) in polar coordinates. Compared with the case of $B\parallel xz$, it is significantly suppressed. (e) ${\rho }_{xx}$ for $B\parallel xz$. (f) ${\rho }_{xx}^{\chi }$ obtained from (e). It is essentially zero except for the spikes at $\theta =\pm 90°$, which is an artifact due to the discontinuities. (g) ${\rho }_{xx}$ for $B\parallel yz$. The asymmetry and the difference between two discontinuities are evidence. The resistivity value is different from that in (e) as two different electrodes were used due to failure of an electrode. (h) ${\rho }_{xx}^{\chi }$ obtained from (g) in polar coordinates, showing the same antisymmetry relations with ${\rho }_{yx}^{\chi }$.