Analytical theory of pyrochlore cooperative paramagnets

The pyrochlore lattice is associated with several potential and actual spin liquid phases as a result of its strong geometric frustration. At finite temperature, these can exhibit an unusually broad crossover regime to a conventional paramagnet. Here, we study this regime analytically by showing how a single-tetrahedron Hamiltonian can extrapolate beyond the first term of a high-temperature expansion and yield insights into the buildup of correlations. We discuss how this unusual behavior is brought about by the structure of the eigenspaces of the coupling matrix. Further interesting behavior can appear for parameter values located near phase transitions: we find coexistence of (111) rods and (220) peaks in the structure factor, as observed in neutron-scattering experiments on Yb2Ti2O7