Evolution of superconducting correlations within magnetic-field-decoupled La${}_{2-x}$Ba${}_x$CuO${}_4$ ($x=0.095$)

We explore the evolution of superconductivity in La${}_{2-x}$Ba${}_x$CuO${}_4$ with $x=0.095$ in magnetic fields of up to 35 T applied perpendicular to the CuO${}_2$ planes. Previous work on this material has shown that perpendicular fields enhance both charge- and spin-stripe order within the planes. We present measurements of the resistivity parallel and perpendicular to the planes, as well as the Hall effect. Measurements of magnetic susceptibility for fields of up to 15 T applied both parallel and perpendicular to the planes provide complementary measures of the superconductivity. We show that fields sufficient to destroy pair tunneling between the planes do not disrupt the superconducting correlations within the planes. In fact, we observe an onset of large-amplitude but phase-disordered superconductivity within the planes at approximately 30 K that is remarkably insensitive to field. With further cooling, we observe a phase-transition-like drop in the in-plane resistivity to an apparent state of superconductivity despite the lack of phase coherence between the layers. These observations raise interesting questions concerning the identification of the upper critical field, where pairing is destroyed, in underdoped cuprates.

Figure 1

Phase diagrams in $H_{\perp }$-$T$ space obtained from measurements of (a) ${\rho }_{\perp }$ and (b) ${\rho }_{\parallel }$. In (a), triangles indicate the onset of finite ${\rho }_{\perp }$ at $H_c^{\perp }$; squares denote $H_Q$, corresponding to the interlayer phase-decoupling crossover. In (b), circles indicate onset of finite ${\rho }_{\parallel }$ at $H_c^{\parallel }$; vertical solid line corresponds to $T_c^{2\mathrm{D}}$, the crossover from the layered vortex liquid (LVL) phase to the normal state. In both (a) and (b), the shaded contours correspond to the resistivity normalized to an extrapolation of the normal-state behavior obtained at the maximum field. (c) Doping dependence of $T_c$ in La${}_{2-x}$Ba${}_x$CuO${}_4$, from Ref. 30; vertical line denotes present sample. (d) Hall coefficient $R_{\mathrm{H}}$ in $H_{\perp }$-$T$ space. For panels (a)–(c), the zero-resistance state ($\rho /{\rho }_n<{10}^{-3}$) corresponds to the regions in cyan. Note that the region of negative Hall constant [dark blue in (d)] corresponds to the regime of layered phase-decoupled superconductivity (LPD-SC) with finite ${\rho }_{\perp }$ and negligible ${\rho }_{\parallel }$.

Figure 2

Measurements of (a) ${\rho }_{\perp }$ and (b) ${\rho }_{\parallel }$ as a function of $H_{\perp }$, obtained at various fixed temperatures as listed in each panel.

Figure 3

Plot of ${\rho }_{\parallel }$ (solid lines) as a function of $H_{\perp }^2$ for $T\gtrsim T_c$, with temperatures listed to the right. Dashed lines correspond to fits of Eq. (3) to data for ${\left({\mu }_0{H}_{\perp }\right)}^2>1000{\mathrm{T}}^2$, except for $T=40$ K, where the value of ${\rho }_n(H_{\perp }=0)$ was replaced with the linearly extrapolated value from Fig. 4b.

Figure 4

(a) Coefficient $a_{\rho }$ vs $T$ obtained from the fits shown in Fig. 3. The dashed line has a slope of $-0.5$. (b) Plot of the ${\rho }_{\parallel ,n}(H_{\perp }=0)$ vs $T$ from the fits in Fig. 3. The dashed line is a fit to the points for 50 K $\le T\le 100$ K.

Figure 5

Conductivity due to superconducting fluctuations determined with Eq. (4) for $T\gtrsim T_c$. The dashed line indicates the calculated conductivity from fluctuations in a 2D superconductor according to Eq. (5) from Ref. 17, assuming $T=30$ K as discussed in the text.

Figure 6

Plot of ${\rho }_{\perp }$ as a function of $H_{\perp }^2$ for $T\gtrsim T_c$, including sweeps of both increasing and decreasing fields.

Figure 7

Data for $R_{\mathrm{H}}$ vs $H_{\perp }$ for various temperatures. Above 35 K, $R_{\mathrm{H}}$ is essentially independent of field; below 25 K, there is notable field dependence, with $R_{\mathrm{H}}$ dipping negative.

Figure 8

Data for $R_{\mathrm{H}}$ vs $T$ for ${\mu }_0{H}_{\perp }=6$ and 34 T. The drop below 40 K correlates with the growth of strong superconducting correlations within the planes.

Figure 9

Magnetic susceptibility data measured for fields applied parallel and perpendicular to the $ab$ planes. Data for ${\mu }_{0}H=7$ and 15 T were obtained with a VSM; the 1-T data are from Ref. 46.

Figure 10

Diamagnetic magnetization obtained from $\chi \left(H\perp ab\right)$ data of Fig. 9 after subtracting a linear fit to the data between 80 and 100 K. The high-field crossover at $T\sim 30$ K is consistent with the appearance of the LVL state, as discussed in the text.

Figure 11

Measurements of (a) ${\rho }_{\perp }$ and (b) ${\rho }_{\parallel }$ as a function of temperature for ${\mu }_0{H}_{\perp }=0$, 20, and 35 T. The dashed lines in (a) are guides to the eye. The solid lines in (b) are calculations of 2D flux-flow resistivity, as discussed in the text. Inset of (b) shows $\Delta {\rho }_{\parallel }/\Delta T$ as a function of $H_{\perp }$ and $T$.

Figure 12

Plot of $R_{\perp }/R_Q$ vs ${[(H_{\perp }-H_c^{\perp })/(H_Q-H_c^{\perp })]}^{\alpha \left(T\right)}$, as described in the text, for data at temperatures from 1.6 to 27 K. The dashed straight line is for reference. The $T$ dependence of the exponent $\alpha$ is plotted in the inset. Dashed line represents ${\alpha }_{\mathrm{K}}$, as described in the text; solid line corresponds to $\alpha ={\alpha }_{\mathrm{K}}+0.35+4.5t^2$, with $t=(T_{c0}-T)/T_{c0}$ and $T_{c0}=31.5$ K.

Figure 13

Plot of ${\rho }_{\parallel }\left(H_{\perp }\right)$ normalized to approximate normal-state values (see text). Squares indicate fields at which data cross ${10}^{-3}$ (dashed line). Solid lines are calculations using Eq. (6), as discussed in the text.

Figure 14

Phase diagram for LBCO as a function of $T$, $H_{\perp }$, and $x$ comparing results for various samples. For the $T$-$x$ plane at $H_{\perp }=0$, spin order (SO) sets in below the thick line, and superconductivity (SC) occurs in the shaded region below the thin line (Ref. 30). The field-dependent results for $x=0.095$ are from Fig. 1, and the results for $x=\frac{1}{8}$ are from Ref. 40.