Geometric frustration and low temperature properties of Ising pyrochlore magnets

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  • 1 February 1999
Abstract
The rare earth titanate pyrochlores, R_2 Ti_2 O_7, where R = Ho, Dy, or Yb, are very nearly ideal Ising models on a lattice of corner-sharing tetrahedra (the ``pyrochlore lattice''), and are interesting because of their peculiar lattice structure which can cause geometric frustration and unusual magnetic ordering. While earlier studies have considered a nearest neighbour Ising model, we find it necessary to use a more sophisticated model with a long-ranged dipole-dipole interaction as well as a nearest-neighbour antiferromagnetic superexchange. Depending on the relative values of these, three kinds of behaviour occur: an ordered, doubly degenerate ground state with a phase transition to a paramagnetic high temperature state; a glassy, but partially ordered ground state with large degeneracy but vanishing entropy per mole, and a sharp first order phase transition to a paramagnetic state; or a highly disordered ground state with finite entropy (governed mainly by a local ``ice rule'') with a broad crossover to the paramagnetic high temperature phase. The competing interactions thus make this unlike any ``ice model'' studied earlier. All three cases, predicted by our theory and simulations, are apparently realized in recent experiments of Ramirez et al.

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