Anomalous Hall resistivity and possible topological Hall effect in the EuAl$_4$ antiferromagnet

We report the observation of anomalous Hall resistivity in single crystals of EuAl$_4$, a centrosymmetric tetragonal compound, which exhibits coexisting antiferromagnetic (AFM) and charge-density-wave (CDW) orders with onset at $T_mathrm{N} sim 15.6$ K and $T_mathrm{CDW} sim 140$ K, respectively. In the AFM state, when the magnetic field is applied along the $c$-axis direction, EuAl$_4$ undergoes a series of metamagnetic transitions. Within this field range, we observe a clear hump-like anomaly in the Hall resistivity, representing part of the anomalous Hall resistivity. By considering different scenarios, we conclude that such a hump-like 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, 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.