Low-energy spin dynamics and critical hole concentrations in ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$ $\left(0.07\le x\le 0.2\right)$ revealed by ${}^{139}\mathrm{La}$ and ${}^{63}\mathrm{Cu}$ nuclear magnetic resonance

We report a comprehensive ${}^{139}\mathrm{La}$ and ${}^{63}\mathrm{Cu}$ nuclear magnetic resonance study on ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$ $\left(0.07\le x\le 0.2\right)$ single crystals. The ${}^{139}\mathrm{La}$ spin-lattice relaxation rate ${}^{139}\mathrm{T}_1^{-1}$ is drastically influenced by Sr doping $x$ at low temperatures. A detailed field dependence of ${}^{139}\mathrm{T}_1^{-1}$ at $x=1/8$ suggests that charge ordering induces the critical slowing down of spin fluctuations toward glassy spin order and competes with superconductivity. On the other hand, the ${}^{63}\mathrm{Cu}$ relaxation rate ${}^{63}\mathrm{T}_1^{-1}$ is well described by a Curie-Weiss law at high temperatures, yielding the Curie-Weiss temperature $\mathrm{\Theta }$ as a function of doping. $\mathrm{\Theta }$ changes sharply through a critical hole concentration $x_c\sim 0.09$. $x_c$ appears to correspond to the delocalization limit of doped holes, above which the bulk nature of superconductivity is established.

Figure 1

(a) $x\text{−}T$ phase diagram of ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$. $T_S$ and $T_c$ were all determined by our NMR measurements, except $T_c$ for $x=0.07$ which was determined by a weak drop in dc susceptibility measurement. As clearly shown in the inset, the SC transition for $x=0.07$ was not observed in the in situ ac susceptibility ${\chi }_{\text{ac}}$, in contrast to the sharp SC transition for $x=0.1$. (b) The Curie-Weiss temperature $\mathrm{\Theta }$ extracted from ${}^{63}\mathrm{T}_1^{-1}$ measurements as a function of doping $x$. Above $x_c=0.09,\mathrm{\Theta }$ abruptly changes and quickly approaches a constant value.

Figure 2

(a) Temperature dependence of ${}^{139}\left(T_{1}T\right)^{-1}$ as a function of doping $x$ measured at 10.7 T. The structural transition temperature $T_S$ is identified from the sharp peak of ${}^{139}\left(T_{1}T\right)^{-1}$ and denoted by the down arrows. The background ${}^{139}\left(T_{1}T\right)^{-1}$ (solid horizontal line) is nearly independent of $x$, which is slightly reduced below $T_S$ (dotted horizontal line). (b) At low temperatures, ${}^{139}\left(T_{1}T\right)^{-1}$ drastically changes depending on $x$. The prominent enhancement of ${}^{139}\left(T_{1}T\right)^{-1}$ for $x=1/8$ is clearly shown.

Figure 3

(a) ${}^{139}\mathrm{T}_1^{-1}$ versus $T$ as a function of $H$ in LSCO:1/8 shows a strong field dependence. In particular, the ${}^{139}\mathrm{T}_1^{-1}$ upturn is suppressed with decreasing $H$, i.e., with increasing $T_c$ which is denoted by the up arrows. Inset: $T_1^{-1}\left(H\right)$ divided by $T_1^{-1}$ at $H=16T$. The significant suppression of $T_1^{-1}$ below $T_c(H=0)$ is clearly shown. (b) Stretching exponent $\beta$ versus $T$ in LSCO:1/8. The deviation of $\beta$ from one occurs near 75 K. Clearly, $\beta \left(T\right)$ is almost independent of $H$ except for the superconducting region.

Figure 4

(a) ${}^{63}\mathrm{Cu}$ $T_1^{-1}$ versus $T$ for different $x$ measured at 8.2 T applied along the $c$ axis. $T_1^{-1}$ at $x=0.07$ is clearly distinct from other data for $x\ge 0.1$ which show almost $x$ independent behavior. (b) Linear fits of $T_{1}T$ at high temperatures yield the Curie-Weiss temperature $\mathrm{\Theta }$ which abruptly changes near the critical doping $x_c\sim 0.09$. (c) ${}^{63}\left(T_{1}T\right)^{-1}$ vs $T$. For $0.1\le x\le 0.15,{}^{63}\left(T_{1}T\right)^{-1}$ forms a clear peak at the same temperature $\sim 50$ K. At $x=0.2$, the peak is notably suppressed.