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Spin ice and beyond: towards a general theory of magnetism on the pyrochlore lattice

The discovery and understanding of the classical spin liquid state in the “spin ices” Ho2Ti2O7 and Dy2Ti2O7 has been a landmark achievement in condensed matter physics. The fascinating properties of these materials stem from the “frustrated geometry” of the pyrochlore lattice- a network of corner sharing tetrahedra. This lattice is common to a large and growing family of rare earth oxide compounds, exhibiting very diverse behaviour, including the “order by disorder” system Er2Ti2O7, the “quantum spin ice” Yb2Ti2O7 and the spin-liquid candidate Tb2Ti2O7. Here we describe a unified framework in which to understand the magnetism of these materials. We find that much of the interesting physics may be traced back to the regions of the phase diagram where ordered phases with different symmetries meet. This includes the origin of the ground state selection in Er2Ti2O7 and the “dimensional reduction” observed in neutron scattering experiments on Yb2Ti2O7. Moreover, we are able to demonstrate the existence of a hitherto undiscovered spin liquid which may explain the nature of the algebraic correlations observed in Tb2Ti2O7.