$^{13}$C NMR Study of Graphite Intercalated Superconductor CaC$_6$ Crystals in the Normal State

$^{13}$C NMR(Nuclear Magnetic Resonance) measurements have been performed to investigate the local electronic structure of a superconducting graphite intercalation compound CaC$_6$ ($T_c$ = 11.4 K). A large number of single crystals were packed and sealed in a quartz tube for naturally abundant $^{13}$C NMR. Spectrum, Knight shift, linewidth, spin-lattice relaxation time $T_1$, and the spin-spin relaxation time $T_2$ were measured in the normal state as function of temperature down to 70 K at 4.8 T and 8.0 T. $^{13}$C NMR spectrum shows a narrow peak with a very small Knight shift. Knight shift and linewidth of the $^ {13}$C NMR are almost temperature-independent around, respectively, 0.012\% and 1.2 kHz. The spin-lattice relaxation rate $1/T_1$ is proportional to temperature confirming a Korringa behavior as for nonmagnetic metals. The Korringa product is measured to be $T_1T$= 210 s.K. From this value, the Korringa ratio is deduced to be $\xi$ = 0.73, close to unity, which suggests that the independent-electron description works well for CaC$_6$, without complexity arising from correlation and many-body effects.