Superconductivity in (TMTSF)$_2$ClO$_4$ probed by $^{77}$Se NMR

Superconductivity in the Bechgaard salts (TMTSF)$_2$X, with X=PF$_6$, ClO$_4$, survives well beyond the paramagnetic limit set by the transition temperature $T_c\approx$1K. As a result, it has been hypothesized that the spin pairing is triplet. We report on measurements of the $^{77}$Se Knight shift and spin-lattice relaxation rate $T_1^{-1}$, conducted {\it in situ} with interlayer resistivity, deep within the superconducting state of (TMTSF)$_2$ClO$_4$. At fields $H_0\approx$10kOe aligned along the $\mathbf{a}-$ and $\mathbf{b'}-$axes, the Knight shift reveals a decrease in spin susceptibility $\chi_s$ that is likely consistent with singlet pairing. The field dependence of $T_1^{-1}$ at temperatures $T\ll T_c$ exhibits a very sharply-defined increase at a field $H_s\approx$15kOe. For $H_0>H_s$, $T_1^{-1}$ is close to the normal state value, even though $H_{c2}\gg H_s$ and $R_{zz}=0$ to within experimental uncertainty. We discuss the implications for interpreting the results as evidence for a crossover, or a phase transition within the superconducting state.