Analysis of ${}^{13}\mathrm{C}-\mathrm{N}\mathrm{M}\mathrm{R}$ spectra in ${\mathrm{C}}_{60}$ superconductors: Hyperfine coupling constants, electronic correlation effect, and magnetic penetration depth

A ${}^{13}\mathrm{C}-\mathrm{N}\mathrm{M}\mathrm{R}$ anisotropic hyperfine coupling tensor was determined as $2\pi (-1.68,-1.68,3.37)\times {10}^6\mathrm{r}\mathrm{a}\mathrm{d}/\mathrm{s}\mathrm{e}\mathrm{c}$ for ${\mathrm{C}}_{60}^{3\mathrm{-}}$ in $A_3{\mathrm{C}}_{60}$ superconductors, where A is an alkali metal, by analyzing ${}^{13}\mathrm{C}-\mathrm{N}\mathrm{M}\mathrm{R}$ spectra below 85 K. Combined with an isotropic coupling constant of $(2\mathrm{}\pi \times 0.69)\times {10}^6\mathrm{r}\mathrm{a}\mathrm{d}/\mathrm{s}\mathrm{e}\mathrm{c},$ the $2s$ and $2p$ characters of the electronic wave functions at the Fermi level were deduced. The results were compatible with local-density-approximation band calculations. From a simulation of ${}^{13}\mathrm{C}-\mathrm{N}\mathrm{M}\mathrm{R}$ spectra at superconducting state, the traceless chemical (orbital) shift tensor and isotropic chemical shift were determined as (67, 34, -101) ppm and ∼150 ppm, respectively. An estimated magnetic penetration depth is larger than 570 nm in ${\mathrm{K}}_3{\mathrm{C}}_{60}.$ Furthermore, the modified Korringa relation, $T_1{\mathrm{TK}}^2\sim \beta S$ (with Knight shift K, spin-lattice relaxation time $T_1,$ and Korringa constant S), clearly showed the existence of weak but substantial antiferromagnetic spin fluctuation in $A_3{\mathrm{C}}_{60};$ $\beta =0.40\mathrm{}–0.58$ with an error of ±20%. The Stoner enhancement factor was also determined as 1–1.5 from a comparison between spin susceptibility obtained from NMR and band-calculation results.