Searching for the Magnetic Interactions in the Rare Earth Pyrochlore Oxide Yb₂Ti₂O₇
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Various experiments on Yb₂Ti₂O₇ have shown evidence of strange magnetic behaviour at low temperatures. Specific heat measurements on powder samples of Yb₂Ti₂O₇ show evidence of a sharp peak, indicating the occurence of a first order phase transition. Meanwhile, neutron scattering, Mössbauer absorption, and μSR measurements find no evidence of long range order below the temperature of this phase transition, leaving the nature of the low temperature phase a mystery. Quantifying the magnetic interactions in this material should allow us to better understand the low temperature behaviour of this material. In this study, we fit a symmetry allowed nearest-neighbour bilinear exchange model to quasi-elastic neutron scattering data collected well above the temperature of the experimentally observed phase transition. This neutron scattering data shows evidence of rods of scattering intensity along the ⟨111⟩ crystallographic directions. Neutron scattering probes the correlations between magnetic moments in a material, so fitting an interaction model to the neutron scattering is equivalent to fitting the interactions to the magnetic correlations. These correlations are driven by the interactions between the magnetic moments, so the neutron scattering should give us direct access to the form of these interactions. Using this method we successfully identify an anisotropic nearest-neighbour bilinear exchange model that reproduces the experimentally observed quasi-elastic neutron scattering. With this model we then proceed to compute real space correlation functions, finding that the rods of neutron scattering arise from the presence of strong correlations along nearest-neighbour chains. We also compute the bulk susceptibility and local susceptibility, obtaining very good fits to experiment with no variation of the model determined from the neutron scattering. The success of these calculations provides a further independent confirmation of the success of our interaction model in describing the magnetic interactions in Yb₂Ti₂O₇. Finally, we present a brief summary of ongoing work based on our anisotropic exchange model, including mean field calculations to determine the low temperature ground state of this model and classical Monte Carlo simulations to study the phase transition present in this model. We also discuss potential further studies of this and other models.