Hexagonal versus perovskite phase of manganite<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>R</mml:mi><mml:mi mathvariant="normal">Mn</mml:mi><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow></mml:math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mo>(</mml:mo><mml:mi>R</mml:mi><mml:mo>=</mml:mo><mml:mi mathvariant="normal">Y</mml:mi><mml:mo>,</mml:mo><mml:mspace width="0.3em"/><mml:mi mathvariant="normal">Ho</mml:mi><mml:mo>,</mml:mo><mml:mspace width="0.3em"/><mml:mi mathvariant="normal">Er</mml:mi><mml:mo>,</mml:mo><mml:mspace width="0.3em"/><mml:mi mathvariant="normal">Tm</mml:mi><mml:mo>,</mml:mo><mml:mspace width="0.3em"/><mml:mi mathvariant="normal">Yb</mml:mi><mml:mo>,</mml:mo><mml:mspace width="0.3em"/><mml:mi mathvariant="normal">Lu</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>

The floating-zone method and high-pressure synthesis have been used to obtain the hexagonal and the perovskite $R\mathrm{Mn}{\mathrm{O}}_{3}$ $(R=\mathrm{Y},\phantom{\rule{0.3em}{0ex}}\mathrm{Ho},\phantom{\rule{0.3em}{0ex}}\mathrm{Er},\phantom{\rule{0.3em}{0ex}}\mathrm{Tm},\mathrm{Yb},\phantom{\rule{0.3em}{0ex}}\mathrm{Lu})$ compounds. We have refined the crystal structure and characterized the compounds with measurements of magnetic susceptibility $\ensuremath{\chi}(T)$ and thermal conductivity $\ensuremath{\kappa}(T)$. The systematic change of $\ensuremath{\kappa}(T)$ below ${T}_{N}$ found in all members of the hexagonal $R\mathrm{Mn}{\mathrm{O}}_{3}$ family shows that some spin-independent bond-length fluctuation plays an important role in the suppression of $\ensuremath{\kappa}(T)$ below ${T}_{N}$ as well as in the paramagnetic phase. The responsible soft vibrational mode is identified. In contrast, the perovskite $R\mathrm{Mn}{\mathrm{O}}_{3}$ shows a phonon-like $\ensuremath{\kappa}(T)$ below room temperature, but with an anomalously large critical scattering at ${T}_{N}$. A phase diagram of transition temperatures versus the ${R}^{3+}$-ion radius for both hexagonal and perovskite phases is also given.