  Kagome lattice materials are an important platform for highly frustrated
magnetism as well as for a plethora of phenomena resulting from flat bands,
Dirac cones and van Hove singularities in their electronic structures. We study
the little known metallic magnet CrRhAs, which belongs to a vast family of
materials that include $3d$, $4f$ and $5f$ magnetic elements, as well as
numerous nonmagnetic metals and insulators. Using noncollinear spin density
functional calculations (mostly spin spirals), we extract a model magnetic
Hamiltonian for CrRhAs. While it is dominated by an antiferromagnetic second
nearest neighbor coupling in the kagome plane, the metallic nature of the
compound leads to numerous nonzero longer range couplings and to important ring
exchange terms. We analyze this Hamiltonian and find unusual ground states
which are dominated by nearly isolated antiferromagnetic triangles that adopt
120$^\circ$ order either with positive or with negative vector chirality. We
discuss the connection to the few known experimental facts about CrRhAs.
Finally, we give a brief survey of other interesting magnetic members of this
family of kagome compounds.
