Transport and thermodynamic properties of quasi-two-dimensional purple bronzes ${A}_{0.9}$Mo${}_{6}$O${}_{17}$ ($A=\mathrm{Na}$, K)

Transport and thermodynamic properties of quasi-two-dimensional purple bronzes $A_{0.9}$ Mo $_{6}$ O $_{17}$ ( $A = Na$ , K)

Xiaofeng Xu, A. F. Bangura, C. Q. Niu, M. Greenblatt, Song Yue, C. Panagopoulos, and N. E. Hussey

Phys. Rev. B 85, 195101 – Published 2 May 2012

Abstract

We report a comparative study of the specific heat, electrical resistivity, and thermal conductivity of the quasi-two-dimensional purple bronzes Na $_{0.9}$ Mo $_{6}$ O $_{17}$ and K $_{0.9}$ Mo $_{6}$ O $_{17}$ , with special emphasis on the behavior near their respective charge-density-wave transition temperatures $T_{P}$ . The contrasting behavior of both the transport and the thermodynamic properties near $T_{P}$ is argued to arise predominantly from the different levels of intrinsic disorder in the two systems. A significant proportion of the enhancement of the thermal conductivity above $T_{P}$ in Na $_{0.9}$ Mo $_{6}$ O $_{17}$ , and to a lesser extent in K $_{0.9}$ Mo $_{6}$ O $_{17}$ , is attributed to the emergence of phason excitations.

Received 14 November 2011

DOI:https://doi.org/10.1103/PhysRevB.85.195101

Authors & Affiliations

Xiaofeng Xu^1,2,3, A. F. Bangura^2,4, C. Q. Niu¹, M. Greenblatt⁵, Song Yue⁶, C. Panagopoulos³, and N. E. Hussey²

¹Department of Physics, Hangzhou Normal University, Hangzhou 310036, China
²H. H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, BS8 1TL, United Kingdom
³Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, 637371 Singapore
⁴RIKEN(The Institute of Physical and Chemical Research), Wako, Saitama 351-0198, Japan
⁵Department of Chemistry and Chemical Biology, Rutgers University, Piscataway, New Jersey 08854, USA
⁶Department of Physics, Jinan University, Guangzhou, China

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Vol. 85, Iss. 19 — 15 May 2012

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Figure 1
The zero-field in-plane (left axis) and interplane (right axis) resistivity of Na $_{0.9}$ Mo $_{6}$ O $_{17}$ (top panel) and K $_{0.9}$ Mo $_{6}$ O $_{17}$ (bottom panel) as a function of temperature between 4.2 and 300 K. The large anisotropy is evident from their different $y$ -axis scales.Reuse & Permissions
Figure 2
Panels (a) and (b) plot ( $d \ln ρ_{a b}) / d T$ and ( $d \ln ρ_{c}) / d T$ , respectively, to identify the temperature and the width of the CDW transition. In addition to the main CDW transition at $T_{P}$ , there exist extra structures at low temperature, pointed out by the color-coded arrows, which may be linked to other subdominant CDW/SDW transitions.Reuse & Permissions
Figure 3
The red two-tone squares in (a) represent the temperature dependence of the total thermal conductivity of Na $_{0.9}$ Mo $_{6}$ O $_{17}$ , as measured directly from the experiments. The blue open circles give the electronic part as determined from their electrical conductivity and the Wiedemann-Franz law, leaving the residual part $κ_{T} - κ_{e}$ , as indicated by the black open squares and replotted in panel (b) accordingly, correspond to the contributions from all other excitations. The red solid line in panel (b) indicates the fits to the phonon Boltzmann transport theory (see text). The phonon thermal conductivity $κ_{p h}$ , indicated by the blue dotted line, evolves as $\sim 1 / T$ at high temperature. A well-defined excess to $κ_{p h}$ , as plotted in the inset, is clearly evident around and above $T_{P}$ .Reuse & Permissions
Figure 4
Analogous to Fig. 3, the total thermal conductivity $κ_{T}$ of K $_{0.9}$ Mo $_{6}$ O $_{17}$ as measured from the experiments is decomposed into the electronic part $κ_{e}$ and the residual part $κ_{T} - κ_{e}$ in panel (a). Again, the phonon Boltzmann transport theory was applied to fit the low- $T$ $κ_{T} - κ_{e}$ data, as indicated by the red solid curve in panel (b). A well-defined excess to the phonon thermal conductivity $κ_{p h}$ , which is characteristic of $\sim 1 / T$ decay at high temperature and shown by the blue dashed line, is plotted in the inset and evidently seen around and above $T_{P}$ .Reuse & Permissions
Figure 5
(a): The temperature dependence of the specific heat in both zero field (black square) and 14-T magnetic field (red triangle) of Na $_{0.9}$ Mo $_{6}$ O $_{17}$ . Evidently, an applied magnetic field has little effect on its overall heat capacity. (b): The low-temperature zero-field $C_{P} / T$ data plotted as a linear function of $T^{2}$ to allow the normal electronic and acoustic phonon contributions to the specific heat to be delineated. The fitting gives $γ = 3.57$ mJ/K $^{2}$ mol, $β = 1.05$ mJ/K $^{4}$ mol.Reuse & Permissions
Figure 6
Similar to Fig. 5, panel (a) shows the temperature dependence of the specific heat in both zero field (black square) and 14-T magnetic field (red triangle) of K $_{0.9}$ Mo $_{6}$ O $_{17}$ . As noted, an applied magnetic field has little effect on the total heat capacity. Panel (b) separates the normal electronic and acoustic phonon contributions by fitting $C_{P} / T$ of $H = 0$ T data as a linear function of $T^{2}$ at very low temperatures. The resultant fitting parameters are $γ = 0.65$ mJ/K $^{2}$ mol, $β = 3.30$ mJ/K $^{4}$ mol.Reuse & Permissions

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Transport and thermodynamic properties of quasi-two-dimensional purple bronzes $A_{0.9}$ Mo $_{6}$ O $_{17}$ ( $A = Na$ , K)

Xiaofeng Xu, A. F. Bangura, C. Q. Niu, M. Greenblatt, Song Yue, C. Panagopoulos, and N. E. Hussey

Phys. Rev. B 85, 195101 – Published 2 May 2012

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Physical Review B

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Transport and thermodynamic properties of quasi-two-dimensional purple bronzes A0.9Mo6O17 (A=Na, K)

Xiaofeng Xu, A. F. Bangura, C. Q. Niu, M. Greenblatt, Song Yue, C. Panagopoulos, and N. E. Hussey

Phys. Rev. B 85, 195101 – Published 2 May 2012

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Transport and thermodynamic properties of quasi-two-dimensional purple bronzes $A_{0.9}$ Mo $_{6}$ O $_{17}$ ( $A = Na$ , K)