Heat Transport in Spin Chains with Weak Spin-Phonon Coupling

Abstract

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 multiboson 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 meanfree 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 spinphonon 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.PACS numbers: 75.10. Jm, 75.50.Ee, 75.40.Gb, 72.20.Pa The one-dimensional (1D) spin chains are among the first strongly-interacting quantum many-body systems ever studied [1, 2] and they remain a fertile ground for new ideas [3] and for developments of advanced theoretical and numerical [4, 5] methods. A number of physical realizations of spin-chain materials [6-10] have allowed for an unprecedentedly comprehensive comparisons between theory, numerical approaches, and experimental data [11][12][13]. Current theoretical challenges for these systems include their dynamical, non-equilibrium, and transport properties [14][15][16][17][18][19][20]. The transport phenomena are particularly challenging as the couplings to phonons and impurities, perturbations that are extrinsic to the often integrable spin systems, become crucial [21][22][23][24][25][26].In this Letter, we address the problem of heat transport in 1D spin-chain systems by considering coupling of spins to optical phonons and impurities and having in mind a systematic experimental thermal conductivity study in the high-quality, single-crystalline, large-J spin-chain cuprates Sr 2 CuO 3 and SrCuO 2 that has been recently conducted [27][28][29][30]. Several attempts to develop a suitable formalism to describe this phenomenon have been made in the past [24][25][26]. However, these approaches either relied on unrealistic choices of parameters [24,26] or offered only qualitative insights [24,25].Below we attempt to bridge the gap between experiment and theory. We argue that the heat conductivity by spin excitations can be quantitatively described within the bosonization framework with the large-momentum scattering by optical phonons or impurities. For weak impurities, scattering grows stronger at lower temperature, a feature intimately related to a critical character of the S = 1/2 Heisenberg chains [26]. Taking into account multi-spin-boson processes, it follows naturally from our microscopic calculations that scattering by phonons bears a close similarity to that by weak impurities, except that the phonons are thermally populated and thus control heat transport at high T . This is also in acco...

Heat transport of cuprate-based low-dimensional quantum magnets with strong exchange coupling

“…30b is the fact that at T 100 K the mean free path becomes significantly smaller than that of both the 2-leg ladder and of the plane compounds. Since the temperature-induced reduction of l mag of the spin chain materials has clearly been assigned to spinonphonon scattering [39,40,64], this observation seems to imply that the spinon heat transport of the S = 1/2 Heisenberg chain is much more prone to scattering of phonons than the two-leg Heisenberg ladder and the 2D-HAF counterparts. It remains to be clarified to what extent this notion is related to the integrability of the Heisenberg chain model, whose ballistic transport properties potentially could exhibit a particular sensitivity to distortions such as those induced by the phonons.…”

“…However at lower temperature, the agreement between the experimental results and the theoretical l sp becomes less satisfactory (see [40] for details). Very recently, Chernyshev and Rozhkov reanalyzed the experimental data of Hlubek et al for both SrCuO 2 and Sr 2 CuO 3 with an alternative theoretical model which specifies l sp including realistic numerical values for the spin-phonon interaction [64]. Also in this case, the analysis relies for both compounds on just two types of scattering processes, viz.…”

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“…Working with ballistic QWs, in the following we will see that the CCT and the HCT are only affected by the scattering processes at the central island. While our approach is effective in working out the zero-temperature, fixed point properties of the junction, in general other effects, which we do not consider here, such as coupling with phonons, may become effective in determining the finite-temperature transport properties of our system [68] (see, e.g., [38 and 69] for a comprehensive discussion of several possible physical mechanisms affecting the thermal transport properties of an electronic system). In Fig.…”

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“…58 Previous studies of thermal transport in insulating magnetic materials indicated that the magnetic and thermal contributions to the thermal conductivity can be comparable. [59][60][61][62][63][64] Our main result in this work is to show that the spatially anisotropic magnetic states that can arise from strong spin-orbit coupling can dramatically affect the thermal transport, or have a rather small effect depending on the relative size of magnon and phonon thermal conductivities. In some cases, the thermal transport may help identify the symmetries of the magnetically ordered state if other measurements are difficult or problematic.…”