Phys. Rev. B

We study the problem of heat transport in one-dimensional (1D) spin-chain systems weakly coupled to three-dimensional phonons and impurities. We consider the limit of fast spin excitations and slow phonons, applicable to a number of compounds of the cuprates family, such as Sr2CuO3, where the superexchange J is much larger than the Debye energy. In this case the Umklapp scattering among the spin excitations is strongly suppressed for all relevant temperatures. We argue that the leading scattering mechanism for the spin excitations at not too low temperatures is the normal (as opposed to the Umklapp) spin-phonon scattering in which the non-equilibrium momentum is transferred from the spin subsystem to phonons where it quickly relaxes through the phonon bath. Because of the lower dimensionality of the spin excitations it is only the momentum along the chains which is conserved in such a scattering. We find that this effect leads to a particular momentum- and temperature-dependence of the spin-phonon relaxation rate valid for the broad class of low-dimensional spin systems. Subsequently we demonstrate that the spin-phonon relaxation mechanism is insufficient for the low-energy, long-wavelength 1D spin-chain excitations, which make the thermal conductivity diverge. We complete our consideration by taking into account the impurity scattering, which in 1D cuts off the quasi-ballistic spin excitations and renders the thermal conductivity finite. Our results compare very well with the existing experimental data for Sr2CuO3. Using our microscopic insight into the problem we propose further experiments and predict an unusual impurity concentration dependence for a number of quantities.