Interpretation of thermal conductivity in LaFeAsO at low temperatures Pavitra Devi Lodhi, Netram Kaurav, A. K. Parchur, and K. K. Choudhary Citation: AIP Conference Proceedings 1665, 090025 (2015); doi: 10.1063/1.4918005 View online: http://dx.doi.org/10.1063/1.4918005 View Table of Contents: http://scitation.aip.org/content/aip/proceeding/aipcp/1665?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Pressure-induced superconductivity in LaFeAsO: The role of anionic height and magnetic ordering Appl. Phys. Lett. 105, 251902 (2014); 10.1063/1.4904954 Magnetism dependent phonon anomaly in LaFeAsO observed via inelastic x-ray scattering J. Appl. Phys. 113, 17E153 (2013); 10.1063/1.4800657 Upper critical field and thermally activated flux flow in LaFeAsO1− x F x J. Appl. Phys. 109, 07E162 (2011); 10.1063/1.3566069 In situ high energy x-ray synchrotron diffraction study of the synthesis and stoichiometry of LaFeAsO and La Fe As O 1 − x F y J. Appl. Phys. 105, 123912 (2009); 10.1063/1.3149773 Heteroepitaxial growth and optoelectronic properties of layered iron oxyarsenide, LaFeAsO Appl. Phys. Lett. 93, 162504 (2008); 10.1063/1.2996591
Interpretation of Thermal Conductivity in LaFeAsO at Low Temperatures Pavitra Devi Lodhi1, Netram Kaurav1,*, A. K. Parchur2 and K. K. Choudhary3 1
Department of Physics, Govt. Holkar Science college, A. B. Road, Indore-452001, India Department of Biological Engineering, Utah State University, Logan, UT-84322 U.S.A. 3 Department of Physics, National Defence Academy, Khadakwasla, Pune- 411 0231 India *E-mail:
[email protected] 2
Abstract. Thermal conductivity κ(T) of LaFeAsO is theoretically investigated below the spin density wave (SDW) anomaly. The lattice contribution to the thermal conductivity (κph) is discussed within the Debye-type relaxation rate approximation in terms of the acoustic phonon frequency and relaxation time below 150 K. The theory is formulated when heat transfer is limited by the scattering of phonons from defects, grain boundaries, charge carriers, and phonons. The lattice thermal conductivity dominates in LaFeAsO and is an artifact of strong phonon-impurity and -phonon scattering mechanism. Our result indicates that the maximum contribution comes from phonon scatters and various thermal scattering mechanisms provide a reasonable explanation for maximum appeared in κ (T). Keywords: Thermal Properties, Phonons, Superconductors. PACS: 65.40.-b; 63.20.kg; 63.20.-e
INTRODUCTION Much attention has been paid to the layered rareearth iron oxypnictides LnFePnO (Ln = La, Pr, Ce, Sm; and Pn = P and As) with the ZrCuSiAs tetragonal structure since superconductivity was discovered at Tc = 26 K in the iron-based LaFeAsO1−xFx (x = 0.05 – 0.12) [1-2]. The superconductivity was induced by partial substitution of oxygen by fluorine in the parent compound LaFeAsO. In all the FeAs-based parent compounds, there is a structural phase transition in the temperature range 100–200 K, and a spin-density wave (SDW) type antiferromagnetic (AFM) ordering associated with Fe ions accompanies the structural transition [3]. Various chemical doping approaches, or the application of high pressure, can suppress the structural transition and AFM order, and high-Tc superconductivity consequently appears. Very recently, the superconductivity has been realized by producing oxygen vacancies instead of F atoms doping [4 - 7], which can create more carriers in the charge reservoir layer, as considered necessary to tune the physical properties. Thus, the stacking of these layers and ionic states of constituent ions have decisive role in the transport and superconducting properties. Evolution of structural, electronic and thermal properties would be an important step toward
realizing the potential technological scenario apart from richness of physics of this material class. Our result indicates that the maximum contribution comes from phonon scatters and various thermal scattering mechanisms provide a reasonable explanation for maximum appeared in κ(T).
THE MODEL The thermal conductivity can be calculated from the Kubo formula [8]. It has contributions from both the phonons and the carriers. The lattice part in the continuum approximation is κ
ph
=
kB 2π 2 v s
kB h
3 θD/T
∫ 0
x 4e x
(e
x
−1
)
2
τ
ph
( ω ) dx . (1)
where the different symbols are their usual meaning. The relaxation time is proportional to the imaginary part of the phonon self-energy. In the weak interaction case, it has been calculated to the lowest order of the various interactions and is defined elsewhere [8]
τ −ph1 = τ −ph1 − d + τ −ph1 − e + τ −ph1 − gb + τ −ph1 − ph , (2) The electronic thermal conductivity of a metal for the low-temperature behavior for electron-impurity
Solid State Physics AIP Conf. Proc. 1665, 090025-1–090025-2; doi: 10.1063/1.4918005 © 2015 AIP Publishing LLC 978-0-7354-1310-8/$30.00
090025-1
contribution is [κele = L0T/ρ0], L0 being the Lorenz number and ρ0 is residual resistivity mainly due to impurity scattering. Henceforth, the total contribution to κ is [= κph + κele].
RESULTS AND DISCUSSION The experimental data on polycrystalline LaFeAsO sample is used in this work was reported by Kihou et al. [7] and have shown SDW anomaly at around T = 150 K. We first qualitatively discuss the properties of thermal conductivity due to phonons (κph). In the calculation of temperature dependent of thermal conduction of LaFeAsO [9], we use the parameters which characterize the strengths of the phonon-defect, phonon-electron, and phonon- phonon scattering process as A = 4.9 x 10−7 K−3, B = 0.15 and C = 0.8 K−6 sec−1, respectively. The length of the sample is about 3 mm and vs = 4.76 x 105 cm sec−1. Fig. 1 shows our results for phonon thermal conductivity of LaFeAsO. It is found that the κph increases exponentially due the grain boundaries scattering as the temperature increases in the absence of the other scattering mechanism. Although κph experiences an exponential increase at low temperatures, the presence of the defect, and the electron scatterings set a limit on its growth, as a consequence the κph diminishes as the temperature increases further. At much higher temperature phononphonon scattering becomes more effective and decreased mean free path of phonon is responsible for decrease in thermal conductivity at higher temperature. The maximum position depends on the relative magnitudes of the phonon-electron, phonon-defect and phonon-phonon scattering processes. This brings us to point out that the phonon peak originates from the competition between the increase in the phonon population and decrease in phonon mean free path due to phonon-phonon scattering with increasing temperature. An estimate of electronic thermal conductivity (κele) can be obtained from the Wiedemann-Franz law with L = 2.45 x 10-8 W Ω K-2, the Lorenz number and is plotted in the inset of Fig. 1. It is meaningful to comment that the contribution of the electron-impurity towards thermal conductivity to the κph is about 1% in the temperature domain (0 < T < 150). Phonons are, then, the sole carriers of heat in this temperature domain. Further, all the contributions are clubbed together and temperature dependent of total thermal conductivity is shown in the inset of Fig. 1 along with experimental data [7]. The present analysis on thermal conductivity shows good agreement with the experimental results. In conclusion, our result indicates that the maximum contribution comes from phonon scatters
FIGURE 1. Variation of phononic thermal conductivity with temperature. Inset shows the variation of electronic and total thermal conductivity along with the exp. data [7].
and various thermal scattering mechanisms provide a reasonable explanation for maximum appeared in κ(T). The numerical analysis of heat transfer below 150 K shows similar results as revealed from experiments.
ACKNOWLEDGMENTS Financial assistance from Department of Science and Technology (DST), New Delhi, India is gratefully acknowledged.
REFERENCES 1. Y. Kamihara, T. Watanabe, M. Hirano and H. Hosono, J. Am. Chem. Soc. 130, 3296 (2008). 2. M. V. Sadovskii, Phys. Usp. 51, 1201 (2008). 3. Q. Huang, Y. Qiu, W. Bao, J. W. Lynn, M. A. Green, Y. Chen, T. Wu, G. Wu and X. H. Chen, Phys. Rev. Lett. 101, 257003 (2008). 4. Zhi-An Ren, Guang-Can Che, Xiao-Li Dong, Jie Yang, Wei Lu, Wei Yi, Xiao-Li Shen, Zheng-Cai Li, Li-Ling Sun, Fang Zhou and Zhong-Xian Zhao, Eurphys. Lett. 83, 17002 (2008). 5. H. Kito, H. Eisaki and A. Iyo, J. Phys. Soc. Jpn. 77, 063707 (2008). 6. N. Kaurav, Y. T. Chung, Y. K. Kuo, R. S. Liu, T. S. Chan, J. M. Chen, J.-F. Lee, H.-S. Sheu, X. L. Wang, S. X. Dou, S. I. Lee, Y. G. Shi, A. A. Belik, K. Yamaura, Appl. Phys. Lett. 94, 192507 (2009). 7. K. Kihou, C. H. Lee, K. Miyazawa, P. M. Shirage, A. Lyo, and H. Eisaki, J. Appl. Phys. 108, 033703 (2010). 8. J. Callaway, Quantum theory of the Solid State, London: Academic Press, 1991. 9. D. Varshney, K. K. Choudhary and R. K. Singh, New J. Phys. 5, 72.1 (2003).
090025-2
