Thermal conductivity of doped La2CuO4 as an example for heat transport by optical phonons in complex materials

We investigate the phonon thermal conductivity κph of doped La2CuO4 based on out-of-plane thermal conductivity measurements. When room temperature is approached the temperature dependence of κph strongly deviates from the T -decrease which is usually expected for heat transport by acoustic phonons. Instead, κph decreases much weaker or even increases with rising temperature. Simple arguments suggest that such unusual temperature dependencies of κph are caused by heat transport via dispersive optical phonons. PACS. 66.70.+f Nonelectronic thermal conduction and heat-pulse propagation in solids; thermal waves – 74.72.Dn La-based cuprates – 44.10.+i Heat conduction The thermal conductivity κ is an interesting tool in order to probe dissipation and scattering of any propagating excitation in a solid. A recent example is κ of complex materials with low-dimensional spin structures where magnetic excitations provide an unusual transport channel of heat [1,2,3,4,5]. Such magnetic heat conduction can in general only be measured in parallel with the phononic heat transport of the underlying crystal lattice. A thorough understanding of the phonon thermal conductivity κph is therefore essential to identify and separate a magnetic contribution κmag. In early experiments on magnetic materials clear deviations from a low-temperature scaling as T , which as T → 0 is expected for κph, were assessed as one important indication of κmag [6,7,8]. Recently, experiments have been performed on materials where magnetic coupling and velocities of magnetic excitations are several orders of magnitude larger than in these early studies. Significant κmag is in these cases present at much higher temperatures where κph is expected to follow a T −1 behavior. Prominent examples are the spin-ladder system (Sr,Ca,La)14Cu24O41 and the two-dimensional antiferromagnetic La2CuO4, where pronounced peaks are observed in κ at high T [1,2,3,4,5]. These high-T anomalies reflect the dimensionality of the underlying magnetic structure, i.e., they are only observed when κ is measured along the direction of ladders or, in the case of La2CuO4, parallel to the magnetic planes. However, it is not a priori clear that such anomalies result from magnetic heat transport. Just as well, it is possible that dispersive optical modes provide a thermal transport channel which could generate an unusual high-T behavior of κph. Even the observed anisotropies could be explained in such a scenario, since low-dimensional magnetic structures often originate from lattice sub-structures with a similar low dimensionality. It is therefore essential to carefully investigate the origin of high T anomalies. A firm proof that indeed magnetic heat conduction is present, is for example obtained if the analysis of the additional contributions yields characteristic magnetic properties like the spin gap of the ladders or magnetic defect distances [1,2,5]. The actual relevance of heat conduction by optical phonons has, however, never been studied systematically. It is the purpose of this paper to initiate future work in this field by pointing out that optical phonons provide a substantial transport mechanism of heat in doped La2CuO4. Our estimation for the heat conductivity by optical phonons κopt is based on realistic values for the phonon energies and velocities in this material. We find that at room temperature κopt can amount to about 40% of the total phonon thermal conductivity κph. The experimental data which give reason for our considerations is the out-of-plane thermal conductivity κc of La1.8−xEu0.2SrxCuO4-single crystals with x = 0, 0.08, 0.15 and 0.2. Fig. 1 displays κc as a function of T . Prior to discussing the high-T behavior of κc in more detail, we briefly summarize the most important facets of the dopingand temperature dependence of κc which have been elaborately discussed in Ref. [9]. Details of the experiment are also described there. Unlike the in-planethermal conductivity κab of doped La2CuO4 which, depending on doping, consists of phononic, magnetic and 2 Please give a shorter version with: \authorrunning and \titlerunning prior to \maketitle 0 100 200 300 0 2 4 6 8 10 12 x = 0 x = 0.08 x = 0.15 x = 0.2 Temperature (K) κκ c (W m -1 K -1 ) La 1.8-x Eu 0.2 Sr x CuO 4 Fig. 1. Out-of-plane thermal conductivity κc of La1.8−xEu0.2SrxCuO4 (x = 0, 0.08, 0.15, 0.2) as a function of temperature. electronic contributions, κc is purely phononic for all Srcontents. This is concluded from the very low out-of-plane electrical conductivity and the negligible magnetic coupling along the c-axis [5,9,10,11]. A usual low-T phonon peak is present in κc for all doping levels. The gradual suppression of the peak upon Sr-doping is straightforwardly understood in terms of scattering by impurities which are induced by the Sr-ions. For x ≤ 0.15 a step-like decrease is present at TLT ≈ 130 K which may be seen more clearly in Fig. 2, where the high-T behavior of κc is shown separately for each compound. At TLT a structural phase transition occurs between the so-called LTO(LowTemperature-Orthorhombic, T ≥ TLT ) and LTT-phases (Low-Temperature-Tetragonal,T ≤ TLT ). Soft tilting modes of the CuO6-octahedra enhance the scattering of acoustic phonons in the LTO-phase, which generates the step at TLT . As revealed from Fig. 2, the T -dependence of κc in the LTO-phase apparently evolves from (x = 0, 0.08) an almost constant behavior with a slight decrease at high T into a clear increase with increasing T (x = 0.15, 0.2). This obviously conflicts with the expected decrease of κph (ideally following T). Strong deviations from the expected behavior could in principle arise from structural peculiarities of the LTO-phase. This can, however, be ruled out since in the case of x = 0.2 the LTT-, the LTOand in addition the so-called HTT-structures (High-TemperatureTetragonal) are successively passed through with rising T without any influence on the increase of κc. Furthermore, κph of the LTO-phase should never be equal to and never exceed κph of the LTT-phase, where additional phononscattering by the aforementioned soft tilting modes does not exist. Yet this is the case for x = 0.15 and x = 0.2. For x = 0 and x = 0.08, a similar situation is present concerning a hypothetical κph of the LTT-phase which is extrapolated into the LTO-phase (solid lines in Fig. 2). These extrapolations have been obtained by fitting κph of the LTT-phase with κ = a/T + b, b > 0 and extrapolating 50 100 150 200 250 300 1.5 2.0 2.5 2 3 4