We have measured the thermal heat conductivity $\kappa$ of the compounds ${\mathrm{Sr}}_{14}{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}$ and ${\mathrm{Ca}}_9{\mathrm{La}}_5{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}$ containing doped and undoped spin ladders, respectively. We find a huge anisotropy of both, the size and the temperature dependence of $\kappa$ that we interpret in terms of a very large heat conductivity due to the magnetic excitations of the one-dimensional spin ladders. This magnon heat conductivity decreases with increasing hole doping of the ladders. Magnon heat transport is analyzed theoretically using a simple kinetic model. From this analysis we determine the spin gap and the temperature-dependent mean free path of the magnons, which measures about several thousand angstrom at low temperature. The relevance of several scattering channels for the magnon transport is discussed.

• Received 21 May 2001

DOI:https://doi.org/10.1103/PhysRevB.64.184305