Magnon Heat Conductivity and Mean Free Paths in Two-Leg Spin Ladders: A Model-Independent Determination

Abstract

The magnon thermal conductivity $\hat{I}{º}_{\mathrm{mag}}$ of the spin ladders in $\mathrm{S}{\mathrm{r}}_{14}\mathrm{C}{\mathrm{u}}_{24-\mathrm{x}}\mathrm{Z}{\mathrm{n}}_{\mathrm{x}}{\mathrm{O}}_{41}$ 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 $\hat{I}{º}_{\mathrm{mag}}$ to be established independently of any model. Over a large temperature range we observe a progressive suppression of $\hat{I}{º}_{\mathrm{mag}}$ with increasing Zn-content and find in particular that with respect to pure $\mathrm{S}{\mathrm{r}}_{14}\mathrm{C}{\mathrm{u}}_{24}{\mathrm{O}}_{41}$ $\hat{I}{º}_{\mathrm{mag}}$ is strongly suppressed even in the case of tiny impurity densities where $l_{\mathrm{mag}}\lesssim 374$~Ã . This shows unambiguously that large $l_{\mathrm{mag}}\approx 3000$~Ã which have been reported for $\mathrm{S}{\mathrm{r}}_{14}\mathrm{C}{\mathrm{u}}_{24}{\mathrm{O}}_{41}$ and $\mathrm{L}{\mathrm{a}}_5\mathrm{C}{\mathrm{a}}_9\mathrm{C}{\mathrm{u}}_{24}{\mathrm{O}}_{41}$ on basis of a kinetic model are in the correct order of magnitude.