Spin order on pyrochlore lattices studied by the Self - Consistent Cluster Approach

In this paper we present a study of magnetic order of quantum Heisenberg spins on pyrochlore type lattices: a lattice of corner sharing tetrahedra. We use the Cluster Variation Approximation with the tetrahedron as basic cluster. We find that in case of anti-ferromagnetic nearest–neighbour exchange there is no long–range spin order at any finite temperature for any spin s. For ferromagnetic exchange and s = 1/2 the spin system remains in a non-magnetic phase for all temperatures, while for s > 1/2 there is a finite order temperature. We derive the ground state phase diagram as a function of exchange anisotropy and tetragonal anisotropy and find regions of re–entrant behaviour. Magnetic fields can induce one or more magnetic transitions. Schottky–like anomalies appear in the specific heat, with on top signs of re–entrant behaviour. The limits of this Cluster Variation Approximations are discussed. PACS: 75.10, 75.30E, 75.30H. (Submit to Phys. Rev. B )