Pseudogap behavior in single-crystal ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$ probed by Cu NMR

We report that the nuclear spin-lattice relaxation rate divided by temperature, ${1/T}_{1}T,$ has a broad maximum around $T^{*}\sim 210\mathrm{K}$ and ∼100 K in underdoped and overdoped single crystals of ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$ (Bi2212) with $T_c=79\mathrm{}$ and 77.3 K, respectively, showing the normal-state spin-gap behavior. One result is that the steep decrease in the ${}^{63}$Cu Knight shift, $K\left(T\right),$ has been observed below $T_K^{*}\sim 200\mathrm{K}$ and ∼100 K, suggesting the normal-state pseudogap behavior in quasiparticle density of states (DOS), which is consistent with the pseudogap behavior below $T_{\mathrm{ARPES}}^{*}\sim 170\mathrm{K}$ revealed on underdoped Bi2212 from studies of angle-resolved photoemission spectroscopy. We propose that the spin-gap behavior in ${1/T}_{1}T$ has the same origin as the pseudogap in the quasiparticle DOS.