Frustration and absence of long range order on the corner sharing-tetrahedron lattice within mean field theory (abstract)

The metal atoms in the pyrochlore system of compounds (A2B2O7, where A and B are metals) form an infinite 3D network of corner sharing tetrahedra with cubic symmetry. For antiferromagnetic nearest neighbor interactions and only B atoms magnetic, there is a very high degree of frustration, and no long range order is predicted in the absence of further neighbor interactions. Mean field calculations for n-component classical vector spins, show that the wave vector dependent susceptibility diverges, at the same temperature Tc, for 2N normal modes of the system where N is the number of unit cells. In some cases further neighbor interactions will stabilize the q=0 or incommensurate modes. A comparison will be made with long range order known to exist in the pyrochlore form of FeF3.