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 cuprate family, such as Sr2CuO3, where the superexchange J is much larger than the Debye energy ΘD. 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 nonequilibrium 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 that 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 quasiballistic spin excitations and renders the thermal conductivity finite. Altogether, these effects yield the following spin-boson thermal conductivity behavior: κs T2 at low temperatures, κs T-1 at intermediate temperatures, and κs=const at higher temperatures T∼ΘD. The saturation at higher temperatures is of rather nontrivial origin and we provide a detailed discussion of it. 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.
|Journal||Physical Review B - Condensed Matter and Materials Physics|
|Publication status||Published - 1 Sep 2005|