Nonlinear temperature dependence of resistivity in single crystal ${\mathrm{Ag}}_5{\mathrm{Pb}}_2{\mathrm{O}}_6$

We measured electrical resistivity, specific heat and magnetic susceptibility of single crystals of highly conductive oxide ${\mathrm{Ag}}_5{\mathrm{Pb}}_2{\mathrm{O}}_6$, which has a layered structure containing a Kagome lattice. Both the out-of-plane and in-plane resistivity show $T^2$ dependence in an unusually wide range of temperatures up to room temperature. This behavior cannot be accounted for either by electron correlation or by electron-phonon scattering with high frequency optic phonons. In addition, a phase transition with a large diamagnetic signal was found in the ac susceptibility, which strongly suggests the existence of a superconducting phase below $48\mathrm{mK}$.

Figure 1

Crystal structure of ${\mathrm{Ag}}_5{\mathrm{Pb}}_2{\mathrm{O}}_6$.

Figure 2

Photos of single crystals of ${\mathrm{Ag}}_5{\mathrm{Pb}}_2{\mathrm{O}}_6$ taken with optical microscopes. The long axis of these crystals are along the $c$ axis. (a) Single crystals in a crucible which are obtained with basic reaction parameters described in the text. (b) Single crystals at the bottom of a crucible when we mixed ${\mathrm{AgNO}}_3$ and $\mathrm{Pb}{\left({\mathrm{NO}}_3\right)}_2$ with a ratio of $\mathrm{Ag}:\mathrm{Pb}=5:1$ and also chose a lower reaction temperature $\left(380°\mathrm{C}\right)$. The crystals grew dispersed from each other and the shapes became better with the aid of self-flux ${\mathrm{AgNO}}_3$. In this case ${\mathrm{AgNO}}_3$ little remained since most of unreacted ${\mathrm{AgNO}}_3$ had been evaporated or resolved into $\mathrm{Ag}$ metal. (c) A group of single crystals removed from the crucible in photo (b). We obtained a lot of crystals with a perfectly hexagonal-stick shape by adding self-flux ${\mathrm{AgNO}}_3$. (d) A cross section of a typical single crystal (not the largest). This hexagonal plane is in the $ab$ plane of ${\mathrm{Ag}}_5{\mathrm{Pb}}_2{\mathrm{O}}_6$.

Figure 3

Temperature dependence of the out-of-plane (open squares) and the in-plane resistivity (open triangles) down to $3\mathrm{K}$. Solid lines are the fitting with $\rho \left(T\right)={\rho }_0+A^{\prime }{T}^p$ with $p=2.13$ for ${\rho }_c$ and $p=2.11$ for ${\rho }_{ab}$. Dashed lines are the fitting assuming the existence of an Einstein-like optic phonon mode.

Figure 4

Specific heat of ${\mathrm{Ag}}_5{\mathrm{Pb}}_2{\mathrm{O}}_6$ down to $0.35\mathrm{K}$. These figures contain the results of several different samples. Inset: $C_P∕T$ plotted against $T^2$ below $3.3\mathrm{K}$. Solid line is the fitting $C_P\left(T\right)∕T={\gamma }_{\mathrm{e}}+{\beta }_{\mathrm{p}}{T}^2$ with ${\gamma }_{\mathrm{e}}=3.42\mathrm{mJ}∕{\mathrm{K}}^2\mathrm{mol}$ and ${\beta }_{\mathrm{p}}=3.91\mathrm{mJ}∕{\mathrm{K}}^4\mathrm{mol}$.

Figure 5

The ac magnetic susceptibility below $0.1\mathrm{K}$, measured with an ac magnetic field of amplitude $2.3\times {10}^{-2}\mathrm{Oe}$ and frequency $887\mathrm{Hz}$. A very large diamagnetic phase transition signal was found below $45\mathrm{mK}$, which suggests the existence of a superconducting (SC) phase. Inset: Phase diagram of ${\mathrm{Ag}}_5{\mathrm{Pb}}_2{\mathrm{O}}_6$ below $50\mathrm{mK}$. Closed squares are “$H_{\mathrm{c}}$” determined from the peaks of imaginary part ${\chi }_{\mathrm{ac}}^{″}$. The dashed line shows the classical parabolic law of superconductivity: $H_{\mathrm{c}}\left(T\right)=H_{\mathrm{c}0}\left[1-{\left(T∕T_{\mathrm{c}0}\right)}^2\right]$.