CaMn${}_2$Sb${}_2:$ a fully frustrated classical magnetic system

We show by means of density functional calculations that CaMn${}_2$Sb${}_2$ is very close to a mean-field critical point known for the classical Heisenberg model on the honeycomb lattice. Three entirely different long range ordered magnetic phases become degenerate at this point: the Neel phase and two different spiral phases. We speculate that the unusual physical properties of this compound, observed in recent experiments, in particular the enigmatic intermediate temperature phase, are due to this proximity.