Ordering of the antiferromagnetic Heisenberg model on a pyrochlore slab

Ordering of the geometrically frustrated two-dimensional Heisenberg antiferromagnet on a pyrochlore slab is studied by Monte Carlo simulations. The model is expected to serve as a reference system of SrCrGaO compound studied extensively. In sharp contrast to the kagome Heisenberg antiferromagnet, the model exhibits locally non-coplanar spin structures at low temperatures, bearing nontrivial chiral degrees of freedom. We find that under certain conditions the model exhibits a novel Kosterlitz-Thouless-type transition at a finite temperature associated with these chiral degrees of freedom, Implications to experiments are discussed.