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In their comment \cite{Sun} on our study of phonon heat transport inNd$_2$CuO$_4$ \cite{Li}, Sun and Ando estimate that the phonon mean free pathat low temperature is roughly half the width of the single crystal used in ourstudy, from which they argue that phonon scattering cannot be dominated bysample boundaries. Here we show that their use of specific heat data onNd$_2$CuO$_4$, which contains a large magnetic contribution at low temperaturethat is difficult to reliably extract, leads to an underestimate of the meanfree path by a factor two compared to an estimate based on the specific heatdata of the non-magnetic isostructural analog Pr$_2$CuO$_4$. This removes theapparent contradiction raised by Sun and Ando.

physical review. b, condensed matter and materials physics

Reply to "Comment on `Low-temperature phonon thermal conductivity of  single-crystalline Nd$_2$CuO$_4$: Effects of sample size and surface  roughness' " by Sun et al