Evidence for Charge Glasslike Behavior in Lightly Doped ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$ at Low Temperatures

A $c$-axis magnetotransport and resistance noise study in ${\mathrm{La}}_{1.97}{\mathrm{Sr}}_{0.03}{\mathrm{CuO}}_4$ reveals clear signatures of glassiness, such as hysteresis, memory, and slow, correlated dynamics, but only at temperatures ($T$) well below the spin glass transition temperature $T_{\mathrm{sg}}$. The results strongly suggest the emergence of charge glassiness, or dynamic charge ordering, as a result of Coulomb interactions.

Figure 1

(a) Schematic phase diagram of hole-doped cuprates. (b) ZFC $R(T)$. (c) Sample 2. The differences between field-cooled (FC) (squares: in 5 T, dots: in 9 T) and ZFC $R$ vs $T$ vanish at $T_B=T_{5\mathrm{T}}$ and $T_{9\mathrm{T}}$, respectively. Dashed lines guide the eye. The same results were obtained with 0.24, 0.014, and $0.007\mathrm{K}/\min$ cooling rates.

Figure 2

Sample 1. $R$ vs time $t$ upon the subsequent application and removal of (a) $B=1$, 2, 5, 6, 8 T, and (b) $B=6$, 1, 2, 8, 1 T. (c) Sample 2. $R$ vs $B$. The arrows and numbers denote the direction and the order of $B$-sweeps. The sweep rate ($0.001\mathrm{T}/\min$ for $B<1\mathrm{T}$, $0.005\mathrm{T}/\min$ for $B>1\mathrm{T}$) was low enough to avoid the sample heating. Inset: Subloops shifted vertically to 0 for comparison. The hysteretic and memory effects are similar for positive and negative $B$, and for both $B\parallel c$ and $B\perp c$. They become smaller with increasing $T$, and vanish for $T\gtrsim 1\mathrm{K}$.

Figure 3

Sample 1. (a) $\Delta R/⟨R⟩=(R-⟨R⟩)/⟨R⟩$ ($⟨R⟩$—the time-averaged $R$) vs $t$ for $B=0$ at several $T$. (b) An expanded section of (a). All traces are shifted for clarity. (c) PDF vs $\Delta R/⟨R⟩$ for the 12-hour time interval. (d) The octave-averaged power spectra $S_R(f)$ have been corrected for the white background noise. Solid lines are fits to $S_R\propto 1/f^{\alpha }$.

Figure 4

Sample 1. (a) ZFC $\Delta R/⟨R⟩$ vs $t$ at $T=0.150\mathrm{K}$ for several $B\parallel c$. All traces are shifted for clarity. Inset: A section of the noise at 5 T. (b) $S_R(f=1\mathrm{mHz})$ and (c) $\alpha$ vs $T$ (●) and $B$ (□). The error bars in (b) are standard deviations of the data. Dashed lines in (c) guide the eye.

Figure 5

(a) The normalized second spectra $S_2$($f_2$), with the Gaussian background subtracted, for two $T$. Solid lines are fits to $S_2\propto 1/f_2^{1-\beta }$. (b) ($1-\beta$) vs $T$ (▴; sample 1) and $B$ (●: sample 1, ▪: sample 2). The dashed line guides the eye. The results shown in (a) and (b) were obtained by averaging over the 0.5–1, 1–2, and $2–4\mathrm{mHz}$ octaves. The error bar in (b) shows the maximum standard deviation of the data. (c) $S_2$ measured in octaves $f=(f_L,2f_L)$. Dashed lines are linear fits to guide the eye.