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We report on systematic temperature- and magnetic field-dependent studies ofthe EuGa$_4$ binary compound, which crystallizes in a centrosymmetrictetragonal BaAl$_4$-type structure with space group $I4/mmm$. The electronicproperties of EuGa$_4$ single crystals, with an antiferromagnetic (AFM)transition at $T_\mathrm{N} \sim 16.4$ K, were characterized via electricalresistivity and magnetization measurements. A giant nonsaturatingmagnetoresistance was observed at low temperatures, reaching $\sim 7 \times10^4$ % at 2 K in a magnetic field of 9 T. In the AFM state, EuGa$_4$ undergoesa series of metamagnetic transitions in an applied magnetic field, clearlymanifested in its field-dependent electrical resistivity. Below $T_\mathrm{N}$,in the $\sim$4-7 T field range, we observe also a clear hump-like anomaly inthe Hall resistivity which is part of the anomalous Hall resistivity. Weattribute such a hump-like feature to the topological Hall effect, usuallyoccurring in noncentrosymmetric materials known to host topological spintextures (as e.g., magnetic skyrmions). Therefore, the family of materials witha tetragonal BaAl$_4$-type structure, to which EuGa$_4$ and EuAl$_4$ belong,seems to comprise suitable candidates on which one can study the interplayamong correlated-electron phenomena (such as charge-density wave or exoticmagnetism) with topological spin textures and topologically nontrivial bands.

Giant magnetoresistance and topological Hall effect in the EuGa4 antiferromagnet