Sign change of anomalous Hall effect and anomalous Nernst effect in the Weyl semimetal CeAlSi

Abstract

We report the anomalous Hall effect (AHE) and the anomalous Nernst effect (ANE) data for the noncollinear Weyl semimetal CeAlSi. The anomalous Hall conductivity (${\ensuremath{\sigma}}_{ij}^{A}$) was measured for two different orientations of the magnetic field ($B$), namely ${\ensuremath{\sigma}}_{yz}^{A}$ for $B||a$ and ${\ensuremath{\sigma}}_{xy}^{A}$ for $B||c$, where $a$ and $c$ denote the crystallographic axes. We find that ${\ensuremath{\sigma}}_{xy}^{A}$ and ${\ensuremath{\sigma}}_{yz}^{A}$ are of opposite sign and both are large below the Curie temperature (${T}_{\mathrm{C}}$). In the paramagnetic phase, ${\ensuremath{\sigma}}_{xy}^{A}$ rises even more and goes through a maximum at $T\ensuremath{\approx}170\phantom{\rule{0.28em}{0ex}}\mathrm{K}$, whereas the absolute value of ${\ensuremath{\sigma}}_{yz}^{A}$ decreases with increasing temperature. The origin of the sign difference between ${\ensuremath{\sigma}}_{xy}^{A}$ and ${\ensuremath{\sigma}}_{yz}^{A}$ was attributed to the reconstruction of the band structure under the variation of the spin orientation. Further, in a system where humps in the AHE are present and scalar spin chirality is zero, we show that the $\mathbf{k}$-space topology plays an important role to determine the transport properties at both low and high temperatures. We also observed the anomalous contribution in the Nernst conductivity (${\ensuremath{\alpha}}_{xy}^{A}$) measured for $B||c$. ${\ensuremath{\alpha}}_{xy}^{A}/T$ turns out to be sizeable in the magnetic phase and above ${T}_{\mathrm{C}}$ slowly decreases with temperature. We were able to recreate the temperature dependencies of ${\ensuremath{\sigma}}_{xy}^{A}$ and ${\ensuremath{\alpha}}_{xy}^{A}/T$ in the paramagnetic phase using a single band toy model assuming a nonzero Berry curvature in the vicinity of the Weyl node. A decisive factor appears to be a small energy distance between the Fermi level and a Weyl point.