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Low temperature diffuse neutron scattering and magnetisation in single crystal Tb2Ti2O7

We present an interpretation of zero field diffuse neutron scattering and of high field magnetisation data at very low temperature in the frustrated pyrochlore system Tb2Ti2O7. This material has antiferromagnetic exchange interactions and it is expected to have Ising character at low temperature. Contrary to expectations, it shows no magnetic ordering down to 0.05\,K, being thus labelled a "spin liquid". However, the ground state in Tb2Ti2O7 is not a mere fluctuating moment paramagnet but, as demonstrated by very recent experiments, a state where the electronic degrees of freedom are hybridised with the phononic variables in an unconventional way. We show here that, by approximating this complex and still unraveled electron-phonon interaction by a dynamic Jahn-Teller coupling, one can account rather well for the diffuse neutron scattering and the low temperature isothermal magnetisation. We discuss the shortcomings of this picture which arise mainly from the fact that the singlet electronic mean field ground state of the model fails to reproduce the observed strong intensity of the elastic and quasi-elastic neutron scattering.