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ABSTRACT: Geometric magnetic frustration provides a way to destabilize conventional magnetic order, allowing the development of exotic phases of matter such as Quantum Spin Liquids. The pyrochlore lattice is the canonical geometry for realizing strong frustration in three dimensions. There are a several fascinating materials hosting effective S=1/2 moments on the pyrochlore lattice; these often display strong quantum effects and lack magnetic long range order down to the lowest temperatures achievable. However, the geometry is not the only player in the development of exotic phases; anisotropy of the magnetic moments and exchange interactions is crucial to developing new phases, such as the quantum spin liquid predicted to arise in “quantum spin ice”, a phase which could host a full emergent electrodynamics (i.e., magnetic monopoles, electrons, and photons). A general model of anisotropic exchange on the pyrochlore lattice has been used to account for a variety of behavior in many pyrochlore materials. When the single-ion anisotropy is XY like, as in Yb2Ti2O7, Er2Ti2O7, and the new Co2+-based pyrochlore NaCaCo2F7, one can expect some XY exchange in the effective model, which can promote quantum dynamics. Furthermore, the known material examples each appear to live nearby phase boundaries in the effective model, which appears to contribute to their eventual ground state selection. After reviewing the general model for XY pyrochlores, I will present recent results in Yb2Ti2O7 (possibly quantum spin ice) and NaCaCo2F7 (frozen spins with strong quantum fluctuations).
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