Anomalous Hall resistivity and possible topological Hall effect in the ${\mathrm{EuAl}}_4$ antiferromagnet

We report the observation of anomalous Hall resistivity in single crystals of ${\mathrm{EuAl}}_4$, a centrosymmetric tetragonal compound, which exhibits coexisting antiferromagnetic (AFM) and charge-density-wave (CDW) orders with onset at $T_{\mathrm{N}}\sim 15.6\mathrm{K}$ and $T_{\mathrm{CDW}}\sim 140\mathrm{K}$, respectively. In the AFM state, when the magnetic field is applied along the $c$-axis direction, ${\mathrm{EuAl}}_4$ undergoes a series of metamagnetic transitions. Within this field range, we observe a clear humplike anomaly in the Hall resistivity, representing part of the anomalous Hall resistivity. By considering different scenarios, we conclude that such a humplike feature is most likely a manifestation of the topological Hall effect, normally occurring in noncentrosymmetric materials known to host nontrivial topological spin textures. In view of this, ${\mathrm{EuAl}}_4$ would represent a rare case where the topological Hall effect not only arises in a centrosymmetric structure, but it also coexists with CDW order.

Figure 1

Temperature dependence of (a) magnetic susceptibility $\chi (T,H)$ and (b) electrical resistivity ${\rho }_{xx}(T,H)$ of ${\mathrm{EuAl}}_4$, measured in various applied magnetic fields. The arrows in (a) denote the four different magnetic transitions. The insets show the 0.1-T inverse susceptibility $\chi {\left(T\right)}^{-1}$ (top) and the zero field ${\rho }_{xx}\left(T\right)$ up to $\sim 300\mathrm{K}$ (bottom). The solid line in the top inset is a fit to the Curie-Weiss law, whereas the arrow in the bottom inset marks the CDW transition occurring at $T_{\mathrm{CDW}}\sim 140\mathrm{K}$.

Figure 2

Field dependence of (a) magnetization $M(H,T)$, (b) electrical resistivity ${\rho }_{xx}(H,T)$, and (c) Hall resistivity ${\rho }_{xy}(H,T)$ of ${\mathrm{EuAl}}_4$, collected at various temperatures. The arrows in panels (a) and (b) mark the saturation field ($H_{\mathrm{c}4}$) and the three critical fields ($H_{\mathrm{c}1}$, $H_{\mathrm{c}2}$, and $H_{\mathrm{c}3}$) where ${\mathrm{EuAl}}_4$ undergoes metamagnetic transitions. The arrows in (c) denote the upper and lower field limit, where the humplike anomaly appears in the ${\rho }_{xy}(H,T)$ data. The inset in (a) shows the 2-K magnetization, with the magnetic field applied along the $c$ axis (solid line) or in the $ab$ plane (dashed line). The inset in (c) shows the 2-K ${\rho }_{xy}\left(H\right)$ resistivity data up to 9 T, with the solid line being a polynomial fit.

Figure 3

(a) Field dependence of the extracted ${\mathrm{EuAl}}_4$ Hall resistivity $\mathrm{\Delta }{\rho }_{xy}\left(H\right)$ at various temperatures (see text for the definition of $\mathrm{\Delta }{\rho }_{xy}$). (b) Magnetic phase diagram of an ${\mathrm{EuAl}}_4$ single crystal, with the field applied along the $c$ axis. The critical temperatures ($T_{\mathrm{N}1}$ to $T_{\mathrm{N}4}$) are determined from $\chi (T,H)$ (circles), while the critical fields are determined from $M(H,T)$ (squares) and ${\rho }_{xx}(H,T)$ (triangles). The background color in (b) represents the magnitude of $\mathrm{\Delta }{\rho }_{xy}\left(H\right)$ at various temperatures. The dashed lines are guides to the eyes. The error bars correspond to the field steps in the field-swept measurements.

Figure 4

Possible scenarios for extracting the topological contribution from the measured Hall resistivity of an ${\mathrm{EuAl}}_4$ single crystal. (a) Field-dependent Hall resistivity and magnetization. (b) Calculated ${\rho }_{xy}^{A^{\prime }}\left(H\right)$. To compare it with the measured ${\rho }_{xy}\left(H\right)$, a scaling factor was used for calculating ${\rho }_{xy}^{A^{\prime }}$ from ${\rho }_{xx}$ and $M$. (c) Simulated field-dependent ${\rho }_{xy}$. The ordinary term is assumed to follow ${\rho }_{xy}^O\propto H^{0.8}$. All the results refer to the data at 2 K.