Microscopic model for Tb-based pyrochlore magnets

There have been extensive experimental investigations of the magnetic structures and excitations of Tb-based pyrochlores, Tb2B2O7 (B=Ti, Sn, Ge). Tb2Ti2O7 is a candidate for quantum spin ice, while Tb2Sn2O7 and Tb2Ge2O7 have long-range ordered spin ice state coexistent with strong spin fluctuations. However, a microscopic model of these materials is still lacking. In this talk, I will discuss our efforts to derive a pseudo spin-1/2 model of Tb-based pyrochlores via a projection operator approach. We find the virtual crystal field excitations between the two lower doublets result in significant renormalization of the classical Ising interactions and generate symmetry-allowed three-body interactions that play a crucial role in the selection of ground state. We find the electric quadrupole-quadrupole interactions also give rise significant quantum fluctuations.