Weak Antiferromagnetic Order in Anisotropic Quantum Pyrochlores

We study the ground state properties of an anisotropic, quasi-2D version of the quantum (S=1/2) pyrochlore antiferromagnet. In the presence of Dzyaloshinsky-Moriya interactions, in addition to the Heisenberg exchanges, it is shown that two types of ordered magnetic states are generally possible: non coplanar "chiral," and coplanar antiferromagnetic order. The magnetic moments in all cases are determined by the Dzyaloshinsky-Moriya interactions and in this sense the antiferromagnetic order is "weak."