Dimensional crossover of a frustrated distorted kagome Heisenberg Model:   Application to FeCrAs
  Motivated by recent experimental work on FeCrAs, we study the magnetic properties of classical spin models on the hexagonal Fe$_2$P/ZrNiAl structure (space group $P{\bar{6}}2m$). When both transition metal/rare earth sites carry magnetic moments, one has alternating distorted kagome and triangular lattice layers. Each point of the triangular lattice lies at the centre of a distorted hexagon and actually corresponds to three isolated magnetic atoms: a "trimer". We show that a simple model consisting of antiferromagnetically correlated Heisenberg spins on the frustrated distorted kagome lattice coupling either ferromagnetically or antiferromagnetically to Heisenberg spins at the average position of a trimer, leads to a rich phase diagram, including the possible selection of a $(1/3,1/3,0)$ magnetic order as may have been seen in FeCrAs. 
Travis E. Redpath, John M. Hopkinson, Alton A. Leibel and Hae-Young   Kee
cond-mat.str-el