The spin liquid state of the Tb2Ti2O7 pyrochlore antiferromagnet:: a puzzling state of affairs

The pyrochlore antiferromagnet Tb2Ti2O7 has proven to be an enigma to experimentalists and theorists working on frustrated magnetic systems. The experimentally determined energy level structure suggests a local <111> Ising antiferromagnet at low temperatures, T less than or similar to 10 K. An appropriate model then predicts a long-range ordered Q = 0 state below approximately 2 K. However, muon spin resonance (muSR) experiments reveal a paramagnetic structure down to tens of millikelvins. The importance of fluctuations out of the ground state effective Ising doublet has been recently understood, for the measured paramagnetic correlations cannot be described without including the higher crystal field states. However, these fluctuations treated within the random phase approximation (RPA) fail to account for the lack of ordering in this system below 2 K. In this work, we briefly review the experimental evidence for the collective paramagnetic state of Tb2Ti2O7. The basic theoretical picture for this system is discussed, where results from classical spin models are used to motivate the investigation of quantum effects to lowest order via the RPA. Avenues for future experimental and theoretical work on Tb2Ti2O7 are presented.