Thermal conductivity of pure and Mg-doped CuGeO 3 in the incommensurate phase

The thermal conductivity $\ensuremath{\kappa}$ of ${\mathrm{Cu}}_{1\ensuremath{-}x}{\mathrm{Mg}}_{x}{\mathrm{GeO}}_{3}$ is measured in magnetic fields up to 16 T. At the transition field ${H}_{c}$ to the high-field incommensurate (I) phase, $\ensuremath{\kappa}$ abruptly decreases. While $\ensuremath{\kappa}$ of the pure ${\mathrm{CuGeO}}_{3}$ is enhanced with the application of the higher magnetic field above ${H}_{c},$ such an enhancement disappears below N\'eel temperature in Mg-doped samples and $\ensuremath{\kappa}(H)$ shows an anomalous plateau feature. With the help of specific heat data, taken supplementally for the identical samples, the above features are well understood to show that phonons are strongly scattered by spin solitons and that $\ensuremath{\kappa}$ in the I phase is governed by their spatial distribution. In particular, the plateau feature in the doped samples suggests ``freezing'' of the solitons, in which antiferromagnetism must be playing an essential role.