We report a study on the thermal conductivity ($\kappa$) of Tb${}_2$Ti${}_2$O${}_7$ single crystals at low temperatures. It is found that in zero field this material has an extremely low phonon thermal conductivity in a broad temperature range. The mean free path of phonons is even smaller than that of amorphous materials and is 3–4 orders of magnitude smaller than the sample size at 0.3 K. The strong spin fluctuation of the spin-liquid state is discussed to be the reason of the strong phonon scattering. The magnetic-field dependence of $\kappa$ and comparison with Y${}_2$Ti${}_2$O${}_7$ and TbYTi${}_2$O${}_7$ confirm the magnetic origin of this phonon-glass-like behavior.

• Received 12 April 2013

DOI:https://doi.org/10.1103/PhysRevB.87.214408