  To study the rare-earth doping effect on the phonon heat transport of
La-based cuprates and shed light on the mechanism of phonon scattering, both
$ab$-plane and c-axis thermal conductivities ($\kappa_{ab}$ and $\kappa_c$) are
measured for La$_{2-y}$Eu$_y$CuO$_4$ ($y$ = 0, 0.02 and 0.2) and
La$_{1.88-y}$Eu$_y$Sr$_{0.12}$CuO$_4$ ($y$ = 0 and 0.2) single crystals. It is
found that the phonon peak (at 20 -- 25 K) in $\kappa_{ab}(T)$ of
La$_{2-y}$Eu$_y$CuO$_4$ shows an anomalous Eu-doping dependence: it completely
disappears for $y$ = 0.02, which is discussed to be due to the local lattice
distortions around Eu dopants, and reappears for $y$ = 0.2 with much smaller
peak magnitude compared to $y$ = 0 sample. In contrast to the strong
suppression of the phonon peak in Eu-doped La$_2$CuO$_4$, Eu-doping to
La$_{1.88}$Sr$_{0.12}$CuO$_4$ enhances the low-$T$ phonon heat transport that
results in the reappearance of the phonon peak in this charge-carrier-doped
system. The data clearly show that the establishment of static stripe phase
rather than the structural change is responsible for the reappearance of phonon
peak.
