Heat Transport in Spin Chains with Weak Spin-Phonon Coupling

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The heat transport in a system of S=1/2 large-J Heisenberg spin chains, describing closely Sr₂CuO₃ and SrCuO₂ cuprates, is studied theoretically at T≪ J by considering interactions of the bosonized spin excitations with optical phonons and defects. Treating rigorously the multi-boson processes, we derive a microscopic spin-phonon scattering rate that adheres to an intuitive picture of phonons acting as thermally populated defects for the fast spin excitations. The mean-free path of the latter exhibits a distinctive T-dependence reflecting a critical nature of spin chains and gives a close description of experiments. By the naturalness criterion of realistically small spin-phonon interaction, our approach stands out from previous considerations that require large coupling constants to explain the data and thus imply a spin-Peierls transition, absent in real materials.