Low temperature magnetic ordering of frustrated rare-earth pyrochlores

We study the low temperature magnetic ordering of rare-earth pyrochlores. The dominant magnetic interaction: nearest neighbour antiferromagnetic Heisenberg exchange, is frustrated with a macroscopic ground-state degeneracy. This degeneracy is lifted by weaker interactions, stabilising long-range order. First we study the dipolar governed gadolinium stannate with an external magnetic field. Factorising the Hamiltonian in terms of ten quadratics provides exact solutions to the over-constrained model with fields orientated along highly symmetrical directions. Next we study the isostructural gadolinium titanate: the much more complex magnetism is indexed by a different propagation-vector to gadolinium stannate due to further neighbour exchange interactions. This material is controversial: elastic neutron scattering and Mössbauer experiments have been using contradictory interpretations. We propose a new state which appears to resolve this inconsistency. Finally we model erbium titanate, which is approached differently due to the dominant crystal-field. Existing elastic neutron scattering data is reexamined and found inconsistent with the state currently discussed in the literature so we suggest an unusual multiple-q state. The spins are not orientated along the expected crystal-field direction: a consequence of frustration. Energetics are studied phenomenologically. We suggest that experimentally observed gapless spin-waves control transfer of spin density between different q-points of the proposed state