Magnon heat conductivity and mean free paths in two-leg spin ladders: A model-independent determination

Abstract

The magnon thermal conductivity ${\ensuremath{\kappa}}_{\mathrm{mag}}$ of the spin ladders in ${\mathrm{Sr}}_{14}{\mathrm{Cu}}_{24\ensuremath{-}x}{\mathrm{Zn}}_{x}{\mathrm{O}}_{41}$ has been investigated at low doping levels $x=0$, 0.125, 0.25, 0.5, and 0.75. The Zn-impurities generate nonmagnetic defects which define an upper limit for ${l}_{\mathrm{mag}}$ and, therefore, allow a clear-cut relation between ${l}_{\mathrm{mag}}$ and ${\ensuremath{\kappa}}_{\mathrm{mag}}$ to be established independently of any model. Over a large temperature range we observe a progressive suppression of ${\ensuremath{\kappa}}_{\mathrm{mag}}$ with increasing Zn-content and find in particular that with respect to pure ${\mathrm{Sr}}_{14}{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}$ ${\ensuremath{\kappa}}_{\mathrm{mag}}$ is strongly suppressed even in the case of tiny impurity densities where ${l}_{\mathrm{mag}}\ensuremath{\lesssim}374\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}$. This shows unambiguously that large ${l}_{\mathrm{mag}}\ensuremath{\approx}3000\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}$ which have been reported for ${\mathrm{Sr}}_{14}{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}$ and ${\mathrm{La}}_{5}{\mathrm{Ca}}_{9}{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}$ on basis of a kinetic model are in the correct order of magnitude.