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We report a study on the thermal conductivity (\kappa) of Tb_2Ti_2O_7 singlecrystals at low temperatures. It is found that in zero field this material hasan extremely low phonon thermal conductivity in a broad temperature range. Themean free path of phonons is even smaller than that of amorphous materials andis 3--4 orders of magnitude smaller than the sample size at 0.3 K. The strongspin fluctuation of the spin-liquid state is discussed to be the reason of thestrong phonon scattering. The magnetic-field dependence of \kappa andcomparison with Y_2Ti_2O_7 and TbYTi_2O_7 confirm the magnetic origin of thisphonon-glass-like behavior.

Magnetically originated phonon-glass-like behavior in Tb_2Ti_2O_7 single crystal