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Low-temperature phonon thermal conductivity of single-crystalline Nd 2 Cu O 4 : Effects of sample size and surface roughness

2008; American Physical Society; Volume: 77; Issue: 13 Linguagem: Inglês

10.1103/physrevb.77.134501

1550-235X

S. Y. Li, J.-B. Bonnemaison, A. Payeur, P. Fournier, C. H. Wang, Xianhui Chen, Louis Taillefer,

Advanced Condensed Matter Physics

The effect of sample size and surface roughness on the phonon thermal conductivity ${\ensuremath{\kappa}}_{p}$ of ${\mathrm{Nd}}_{2}\mathrm{Cu}{\mathrm{O}}_{4}$ single crystals was studied down to $50\phantom{\rule{0.3em}{0ex}}\mathrm{mK}$. At $0.5\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, ${\ensuremath{\kappa}}_{p}$ is proportional to $\sqrt{A}$, where $A$ is the cross-sectional area of the sample. This demonstrates that ${\ensuremath{\kappa}}_{p}$ is dominated by boundary scattering below $0.5\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ or so. However, the expected ${T}^{3}$ dependence of ${\ensuremath{\kappa}}_{p}$ is not observed down to $50\phantom{\rule{0.3em}{0ex}}\mathrm{mK}$. Upon roughing the surfaces, the ${T}^{3}$ dependence is restored, showing that departures from ${T}^{3}$ are due to specular reflection of phonons off the mirrorlike sample surfaces. We propose an empirical power law fit to ${\ensuremath{\kappa}}_{p}\ensuremath{\sim}{T}^{\ensuremath{\alpha}}$ (where $\ensuremath{\alpha}<3$) in cuprate single crystals. Using this method, we show that recent thermal conductivity studies of Zn doping in $\mathrm{Y}{\mathrm{Ba}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{y}$ reaffirm the universal heat conductivity of $d$-wave quasiparticles at $T\ensuremath{\rightarrow}0$.