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

TL;DR

This study measures magnon thermal conductivity in spin ladders with Zn impurities, establishing a model-independent relation between mean free path and conductivity, and confirming the large mean free paths reported in prior kinetic models.

Contribution

It provides a model-independent method to determine magnon mean free paths from thermal conductivity measurements in doped spin ladders.

Findings

Magnon mean free paths are limited by nonmagnetic defects.

Thermal conductivity is strongly suppressed by Zn impurities.

Large mean free paths (~3000 Å) are consistent with previous reports.

Abstract

The magnon thermal conductivity $\kappa_{\mathrm{mag}}$ of the spin ladders in $\rm Sr_{14}Cu_{24-x}Zn_xO_{41}$ 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 $\kappa_{\mathrm{mag}}$ to be established independently of any model. Over a large temperature range we observe a progressive suppression of $\kappa_{\mathrm{mag}}$ with increasing Zn-content and find in particular that with respect to pure $\rm Sr_{14}Cu_{24}O_{41}$ $\kappa_{\mathrm{mag}}$ is strongly suppressed even in the case of tiny impurity densities where $l_{\mathrm{mag}}\lesssim 374$~{\AA}. This shows unambiguously that large $l_{\mathrm{mag}}\approx 3000$~{\AA} which have been reported for $\rm Sr_{14}Cu_{24}O_{41}$ and $\rm La_{5}Ca_9Cu_{24}O_{41}$ on basis of a kinetic model are in the correct order of magnitude.