Low temperature phase diagram for the pyrochlore compound Tb2Ti2O7

The pyrochlore material Tb2Ti2O7, although possessing a negative paramagnetic Curie temperature witnessing the presence of antiferromagnetic exchange interactions, shows no long range magnetic order of Tb3+ moments down to 0.05 K. The reason for this behaviour is not thoroughly understood up to now. We present here a model based on the presence of a distortion from trigonal symmetry at low temperature, making this material a two-singlet system. Application of a 4-site mean field theory allows us to construct the phase diagram for this system and to understand how, in the presence of a distortion, Tb2Ti2O7 can remain in a paramagnetic spin liquid phase down to T = 0. Although the existence of a static distortion at low temperature in these materials is not yet convincingly assessed, we believe that our model can give useful hints towards an understanding of this interesting material.