The non-trivial magnetic and electronic phases occurring in topological magnets are often entangled, thus leading to a variety of exotic physical properties. Recently, the BaAl$_4$-type compounds have been extensively investigated to elucidate the topological features appearing in their real- and momentum spaces. In particular, the topological Hall effect and the spin textures, typical of the centrosymmetric Eu(Al,Ga)$_4$ family, have stimulated extensive experimental and theoretical research. In this topical review, we discuss the latest findings regarding the Eu(Al,Ga)$_4$ topological antiferromagnets and related materials, arising from a vast array of experimental techniques. We show that Eu(Al,Ga)$_4$ represents a suitable platform to explore the interplay between lattice-, charge-, and spin degrees of freedom, and associated emergent phenomena. Finally, we address some key questions open to future investigation.
Categories: cond-mat.str-el cond-mat.mtrl-sci