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We present an interpretation of zero field diffuse neutron scattering and ofhigh field magnetisation data at very low temperature in the frustratedpyrochlore system Tb2Ti2O7. This material has antiferromagnetic exchangeinteractions and it is expected to have Ising character at low temperature.Contrary to expectations, it shows no magnetic ordering down to 0.05\,K, beingthus labelled a "spin liquid". However, the ground state in Tb2Ti2O7 is not amere fluctuating moment paramagnet but, as demonstrated by very recentexperiments, a state where the electronic degrees of freedom are hybridisedwith the phononic variables in an unconventional way. We show here that, byapproximating this complex and still unraveled electron-phonon interaction by adynamic Jahn-Teller coupling, one can account rather well for the diffuseneutron scattering and the low temperature isothermal magnetisation. We discussthe shortcomings of this picture which arise mainly from the fact that thesinglet electronic mean field ground state of the model fails to reproduce theobserved strong intensity of the elastic and quasi-elastic neutron scattering.

Low temperature diffuse neutron scattering and magnetisation in single crystal Tb2Ti2O7