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 kagomé 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. This makes the spin ordering on these lattices a highly nontrivial issue. Triangles-or tetrahedrabased lattices might be classified into two categories: One is the tightly coupled lattice consisting of edge-sharing triangles or tetrahedra, and the other is the loosely-coupled lattice consisting of corner -sharing triangles or tetrahedra. Examples of the former are the triangular lattice in two dimensions (2D) and the stacked-triangular lattice in three dimensions (3D), while those of the latter are the 2D kagomé lattice and the 3D pyrochlore lattice. In earlier studies, emphasis was put on the former category. 2, 3) These studies revealed a variety of interesting ordering phenomena not encountered in standard unfrustrated magnets, e.g., novel universality classes, exotic phase transition such as chiral transition and new type of topological phase transition etc.Recently, interest has been focused more on the latter category, i.e., the 2D kagomé and 3D pyrochlore AFs. [4][5][6] Due to the looser coupling among the frustrating units, these systems often remain paramagnetic down to very low temperatures without any magnetic ordering. Indeed, various theoretical studies on the 2D kagomé and 3D pyrochlore AFs have revealed that these systems 1

Ordering of the geometrically frustrated two-dimensional Heisenberg antiferromagnet on a pyrochlore slab is studied by Monte Carlo simulations. In contrast to the kagomé Heisenberg antiferromagnet, the model exhibits locally non-coplanar spin structures at low temperatures, bearing nontrivial chiral degrees of freedom. Under certain conditions, the model exhibits a novel KosterlitzThouless-type transition at a finite temperature associated with these chiral degrees of freedom.

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