Quantum critical behavior in superconducting ${\mathrm{Na}}_x{\left({\mathrm{H}}_3\mathrm{O}\right)}_z\mathrm{Co}{\mathrm{O}}_2\bullet y{\mathrm{H}}_2\mathrm{O}$ observed in a high-field Co NMR experiment

Co nuclear magnetic resonance (NMR) measurements are performed on superconducting ${\mathrm{Na}}_x{\left({\mathrm{H}}_3\mathrm{O}\right)}_z\mathrm{Co}{\mathrm{O}}_2\bullet y{\mathrm{H}}_2\mathrm{O}$ with a bilayered hydrate structure. External fields are applied exactly parallel to the $\mathrm{Co}{\mathrm{O}}_2$ plane on a high-quality powdered sample, which is aligned in a strong magnetic field. When superconductivity is suppressed by external magnetic fields, the nuclear spin-lattice relaxation rate divided by temperature $(1∕T_{1}T)$ continues to increase down to $T_c\left(H\right)$, which is the superconducting transition temperature under a magnetic field $H$. From the analyses of the temperature variation, it was found that a sample with $T_c\sim 4.8\mathrm{K}$, which is the maximum $T_c$, possesses magnetic fluctuations with a quantum critical character. This suggests the intimate relationship between superconductivity and quantum critical fluctuations in the hydrate cobaltate. We determined $T_c\left(H\right)$ and constructed the $H_{c2}-T_c$ phase diagram from the present NMR measurements. The field dependence of $T_c\left(H\right)$ is discussed.

Figure 1

Co-NMR spectrum with external field applied perpendicular to the $c$ axis. The solid line and dotted line are the experimental result and simulated result, respectively. All the experimental results are reproduced by the simulation. The sharp peaks arising from ${}^{63}\mathrm{Cu}$ and ${}^{65}\mathrm{Cu}$ in the coil and ${}^{23}\mathrm{Na}$ in the sample are observed, which are marked by arrows. The peak marked by an asterisk is the impurity phase (see in text). The inset is the close view of the central peak ($m=1∕2\leftrightarrow -1∕2$ transition). A two-peak structure is observed.

Figure 2

(Color online) Field dependence of the central peak above and below $T_c\left(H\right)$. (a), (b), (c), (d), and (e) are measured around 2.5, 4, 7, 10, and $14\mathrm{T}$. Solid lines and dotted lines of each figure are NMR spectra obtained above and below $T_c$, respectively. Peak positions which are determined by fitting the data by two component Gaussian are indicated by down arrows.

Figure 3

(Color online) The temperature dependence of $1∕T_{1}T$ at various magnetic fields. The symbol for each magnetic field is displayed in the figure. The red solid curve is the fitting function described in the text. The arrows indicate $T_c\left(H\right)$, at which $1∕T_{1}T$ deviates from the normal-state temperature variation.

Figure 4

(Color online) The field dependence of SC transition temperature $T_c\left(H\right)$. Larger circles in the present data are determined both from $1∕T_{1}T$ and Knight shift measurements. The smaller circle is $T_c$ at $13\mathrm{T}$, which is determined only from the temperature dependence of $1∕T_{1}T$. $T_c\left(H\right)$ of other groups(Refs. 7, 19, 20, 21, 22) are also shown for comparison.