Thermal conductivity of ${\mathrm{YBa}}_2$${\mathrm{Cu}}_4$${\mathrm{O}}_8$ dominated by phonon-phonon interactions

The thermal conductivity κ of dense sintered ceramic ${\mathrm{YBa}}_2$${\mathrm{Cu}}_4$${\mathrm{O}}_8$ in the range 30–310 K has been measured. At 100 K, κ is 10 W ${\mathrm{m}}^{\mathrm{-}1}$ ${\mathrm{K}}^{\mathrm{-}1}$, approaching the in-plane κ of single crystals of other high-${\mathit{T}}_{\mathit{c}}$ materials. κ decreases rapidly with increasing T to 7.4 W ${\mathrm{m}}^{\mathrm{-}1}$ ${\mathrm{K}}^{\mathrm{-}1}$ at 300 K. Fitting standard models for κ(T) to the data we find that κ is limited mainly by phonon-phonon interactions. Depending on the model used, the best fit is found for effective values of ${\mathit{FTHETA}}_{\mathrm{Debye}}$ between 155 and 185 K, characteristic for the acoustic phonon branches, indicating that such phonons carry most of the heat. Finally, we suggest a possible way to test the electron-phonon model for the electrical and thermal conductivities in high-${\mathit{T}}_{\mathit{c}}$ materials.