Topological aspects of multi-$\bm{k}$ antiferromagnetism in cubic rare-earth compounds.

We advertise rare-earth intermetallics with high-symmetry crystal structures and competing interactions as a possible materials platform hosting spin structures with non-trivial topological properties. Focussing on the series of cubic $R$Cu compounds, where $R$ = Ho, Er, Tm, the bulk properties of these systems display exceptionally rich magnetic phase diagrams hosting an abundance of different phase pockets characteristic of antiferromagnetic order in the presence of delicately balanced interactions. The electrical transport properties exhibit large anomalous contributions suggestive of topologically nontrivial winding in the electronic and magnetic structures. Neutron diffraction identifies spontaneous long-range magnetic order in terms of commensurate and incommensurate variations of $(\pi\pi0)$ antiferromagnetism with the possibility for various multi-$\bm{k}$ configurations. Motivated by general trends in these materials, we discuss the possible existence of topologically nontrivial winding in real and reciprocal space in the class of $R$Cu compounds including antiferromagnetic skyrmion lattices. Putatively bringing together different limits of non-trivial topological winding in the same material, the combination of properties in $R$Cu systems promises access to advanced functionalities.