Quasi-two-dimensional fluctuations in the magnetization of $\mathrm{L}{\mathrm{a}}_{1.9}\mathrm{C}{\mathrm{a}}_{1.1}\mathrm{C}{\mathrm{u}}_2{\mathrm{O}}_{6+\delta }$ superconductors

We report the results of magnetization measurements with the magnetic field applied along the $c$ axis on superconducting $\mathrm{L}{\mathrm{a}}_{1.9}\mathrm{C}{\mathrm{a}}_{1.1}\mathrm{C}{\mathrm{u}}_2{\mathrm{O}}_{6+\delta }$ single crystals processed under ultrahigh oxygen pressure. Strong fluctuation effects were found in both low- and high-field regimes. Scaling analysis of the high-field magnetization data near the critical temperature $(T_c=53.5\mathrm{K})$ region reveals the characteristics of critical fluctuation behavior of quasi-two-dimensional (2D) superconductivity, described by Ginzburg-Landau theory using the lowest Landau level approximation. Low-field magnetic susceptibility data can be successfully explained by the Lawrence-Doniach model for a quasi-2D superconductor, from which we obtained the $ab$ plane Ginzburg-Landau coherence length of this system, ${\xi }_{ab}\left(0\right)=11.8\pm 0.9\AA$. The coherence length along the $c$ axis, ${\xi }_c\left(0\right)$, is estimated to be about 1.65 Å, which is in between those of 2D cuprate systems, such as $\mathrm{B}{\mathrm{i}}_2\mathrm{S}{\mathrm{r}}_2\mathrm{C}{\mathrm{a}}_2\mathrm{C}{\mathrm{u}}_3{\mathrm{O}}_{10}$ and $\mathrm{B}{\mathrm{i}}_2\mathrm{S}{\mathrm{r}}_2\mathrm{CaC}{\mathrm{u}}_2{\mathrm{O}}_8$, and quasi-three-dimensional (3D) cuprate systems, such as overdoped $\mathrm{L}{\mathrm{a}}_{2-x}\mathrm{S}{\mathrm{r}}_x\mathrm{Cu}{\mathrm{O}}_4$ and $\mathrm{YB}{\mathrm{a}}_2\mathrm{C}{\mathrm{u}}_3{\mathrm{O}}_{7-\delta }$. Our studies suggest a strong interplay among the fluctuation effects, dimensionalities, and the ratios of the interlayer Cu-O plane spacing, $s$, to the c-axis coherence lengths. A high $s/{\xi }_c\left(0\right)$ was observed in the high-pressure oxygenated $\mathrm{L}{\mathrm{a}}_{1.9}\mathrm{C}{\mathrm{a}}_{1.1}\mathrm{C}{\mathrm{u}}_2{\mathrm{O}}_{6+\delta }$, and that apparently drives this system to behave more like a quasi-2D superconductor.

Figure 1

Crystal structure of (a) $\mathrm{L}{\mathrm{a}}_2\mathrm{CaC}{\mathrm{u}}_2{\mathrm{O}}_6$ and (b) $\mathrm{L}{\mathrm{a}}_2\mathrm{CaC}{\mathrm{u}}_2{\mathrm{O}}_{6+\delta }$.

Figure 2

(a) Temperature dependence of the magnetic susceptibility of $\mathrm{L}{\mathrm{a}}_{1.9}\mathrm{C}{\mathrm{a}}_{1.1}\mathrm{C}{\mathrm{u}}_2{\mathrm{O}}_{6+\delta }$. (b) Low-field parts of $M\left(H\right)$ at various temperature for $H\parallel c$ with demagnetization correct, respectively. The solid line is the “Meissner line.” Here, the field $H$ is equal to $H_a-NM$, which has already taken into account the demagnetization factor $N$ at applied field $H_a=2\mathrm{Oe}$.

Figure 3

Temperature dependence of the magnetization ($H\parallel c$ axis) of $\mathrm{L}{\mathrm{a}}_{1.9}\mathrm{C}{\mathrm{a}}_{1.1}\mathrm{C}{\mathrm{u}}_2{\mathrm{O}}_{6+\delta }$ in various magnetic fields parallel to the $c$ axis.

Figure 4

(a) 2D scaling of the magnetization data for $\mathrm{L}{\mathrm{a}}_{1.9}\mathrm{C}{\mathrm{a}}_{1.1}\mathrm{C}{\mathrm{u}}_2{\mathrm{O}}_{6+\delta }$ measured at 10 000, 30 000, and 50 000 Oe with magnetic fields parallel to the $c$ axis. (b) 3D scaling of the same magnetization data as shown in (a).

Figure 5

Temperature dependence of $T/\chi$ (a) and $\chi$ (b), measured at 300 and 500 Oe. The solid line in (a) represents the linear fit of the data and the solid curve in (b) is a theoretical fit to the data of 300 Oe using Eq. (3).

Figure 6

3D plot of Cooper pair-coupling behavior based on the data listed in Table 1. We choose $\mathrm{B}{\mathrm{i}}_2\mathrm{S}{\mathrm{r}}_2\mathrm{C}{\mathrm{a}}_2\mathrm{C}{\mathrm{u}}_3{\mathrm{O}}_{10}$, $\mathrm{L}{\mathrm{a}}_{1.9}\mathrm{C}{\mathrm{a}}_{1.1}\mathrm{C}{\mathrm{u}}_2{\mathrm{O}}_{6+\delta }$ in this paper and $\mathrm{YB}{\mathrm{a}}_2\mathrm{C}{\mathrm{u}}_3{\mathrm{O}}_{7-\delta }$ for 2D, 2D to 3D crossover, and 3D behavior, respectively. Here, we fix the interspacing distance between layers $s$ for all the samples and ${\xi }_c$ (0) changes according to the ratio of ${\xi }_c\left(0\right)/s$ listed in Table 1. The anisotropy value $\gamma$ is applied to decide ${\xi }_{ab}\left(0\right)$. The different colors represent the electron concentration levels, where the red part means the highest concentration (set to 1 in the color bar) and the dark blue (set to be 0 in the color bar) shows the lowest concentration. The pictorial representation where the overlap is the greatest corresponds to the 3D system where the coherence length is longer than the interlayer spacing, while the one where the two lobes are completely separated corresponds to the bona fide 2D case with the crossover scenario being in the middle.