  $\mathrm{Mn}_3\mathrm{X}$ compounds in which the magnetic $\mathrm{Mn}$ atoms
form AB-stacked kagome lattices have received a tremendous amount of attention
since the observation of the anomalous Hall effect in
$\mathrm{Mn}_3\mathrm{Ge}$ and $\mathrm{Mn}_3\mathrm{Sn}$. Although the
magnetic ground state has been known for some time to be an inverse triangular
structure with an induced in-plane magnetic moment, there have been several
controversies about the minimal magnetic Hamiltonian. We present a general
symmetry-based model for these compounds that includes a previously unreported
interplane Dzyaloshinskii-Moriya interaction, as well as anisotropic exchange
interactions. The latter are shown to compete with the single-ion anisotropy
which strongly affects the ground state configurations and elementary spin-wave
excitations. Finally, we present the calculated elastic and inelastic neutron
scattering intensities and point to experimental assessment of the types of
magnetic anisotropy in these compounds that may be important.
