\({\mu }^{+}\)SR Knight shift of the hole-doped organic metal \(\kappa \)-(ET)\(_4\)Hg\(_{3-\delta }\)Cl\(_{8}\), \(\delta =22\%\)

We measured the \({\varvec{\mu }}^{\varvec{+}}\) ${\mathit{\mu }}^{\mathbf{+}}$ SR Knight shift in the hole-doped organic metal \(\varvec{\kappa }\) $\mathit{\kappa }$ -(ET) \(_{\varvec{4}}\) $_{\mathbf{4}}^{}$ Hg \(_{\varvec{3-\delta }}\) $_{\mathbf{3}\mathbf{-}\mathit{\delta }}^{}$ Cl \(_{\varvec{8}}\) $_{\mathbf{8}}^{}$ , \(\varvec{\delta }\) $\mathit{\delta }$ =22%, and re-analyzed temperature dependence of \({\varvec{\mu }}^{\varvec{+}}\) ${\mathit{\mu }}^{\mathbf{+}}$ SR Knight shift of the isostructural compound \(\varvec{\kappa }\) $\mathit{\kappa }$ -(ET) \(_{\varvec{4}}\) $_{\mathbf{4}}^{}$ Hg \(_{\varvec{3-\delta }}\) $_{\mathbf{3}\mathbf{-}\mathit{\delta }}^{}$ Br \(_{\varvec{8}}\) $_{\mathbf{8}}^{}$ , \(\varvec{\delta }\) $\mathit{\delta }$ =11%. The former underwent insulating and the latter has superconducting ground state. By lowering temperature the Knight shift gradually increased and was almost unchanged for \(\varvec{\kappa }\) $\mathit{\kappa }$ -HgCl and \(\varvec{\kappa }\) $\mathit{\kappa }$ -HgBr metals, respectively. We found a prominent deviation from linearity in the \(\varvec{K(\chi )}\) $\mathit{K}\mathbf{(}\mathit{\chi }\mathbf{)}$ plot of \(\varvec{\kappa }\) $\mathit{\kappa }$ -HgCl below 100 K whereas the result of reanalysis of \(\varvec{\kappa }\) $\mathit{\kappa }$ -HgBr shows there is almost no linearity of the \(\varvec{K(\chi )}\) $\mathit{K}\mathbf{(}\mathit{\chi }\mathbf{)}$ plot, although the absolute value of the \(\varvec{{\mu }}^{\varvec{+}}\) ${\mathit{\mu }}^{\mathbf{+}}$ Knight shift \(\varvec{K}\) $\mathit{K}$ is comparable with that of \(\varvec{\kappa }\) $\mathit{\kappa }$ -HgCl at low-temperature. The hyperfine coupling constant of \(\varvec{\kappa }\) $\mathit{\kappa }$ -HgCl was estimated as \(\varvec{A}_{\varvec{hf}}(\varvec{\kappa }\) ${\mathit{A}}_{\mathit{hf}}(\mathit{\kappa }$ -HgCl) = 282 Oe/ \(\varvec{\mu }_{\varvec{B}}\) ${\mathit{\mu }}_{\mathit{B}}$ . This value is comparable with our calculation assuming a point dipole between muon site, determined by the electronic potential calculation using density functional theory, and the localized spin at the Cl site. In consideration of both samples being in the vicinity of same quantum criticality, the muon Knight shift is more sensitive to the insulating sample with enhanced antiferromagnetic fluctuations. We discuss the relation between enhanced antiferromagnetic spin fluctuations, Non-Fermi liquidity, and superconductivity in these systems.