Uniaxial linear resistivity of superconducting La${}_{1.905}$Ba${}_{0.095}$CuO${}_4$ induced by an external magnetic field

We present an experimental study of the anisotropic resistivity of superconducting La${}_{2-x}$Ba${}_x$CuO${}_4$ with $x=0.095$ and transition temperature $T_c=32$ K. In a magnetic field perpendicular to the CuO${}_2$ layers $H_{\perp }$, we observe that the resistivity perpendicular to the layers ${\rho }_{\perp }$ becomes finite at a temperature consistent with previous studies on very similar materials; however, the onset of finite parallel resistivity ${\rho }_{\parallel }$ occurs at a much higher temperature. This behavior contradicts conventional theory, which predicts that ${\rho }_{\perp }$ and ${\rho }_{\parallel }$ should become finite at the same temperature. Voltage versus current measurements near the threshold of voltage detectability indicate linear behavior perpendicular to the layers, becoming nonlinear at higher currents, while the behavior is nonlinear from the onset parallel to the layers. These results, in the presence of moderate $H_{\perp }$, appear consistent with superconducting order parallel to the layers with voltage fluctuations between the layers due to thermal noise. In search of uncommon effects that might help to explain this behavior, we have performed diffraction measurements that provide evidence for $H_{\perp }$-induced charge- and spin-stripe order. The field-induced decoupling of superconducting layers is similar to the decoupled phase observed previously in La${}_{2-x}$Ba${}_x$CuO${}_4$ with $x=1/8$ in zero field.

Figure 1

Resistivities vs temperature for a range of magnetic fields, corresponding to the configurations (a) ${\rho }_{\perp }$ in $H_{\perp }$; (b) ${\rho }_{\perp }$ in $H_{\parallel }$; (c) ${\rho }_{\parallel }$ in $H_{\perp }$; (d) ${\rho }_{\parallel }$ in $H_{\parallel }$. The values of ${\mu }_{0}H$, ranging from 9 T (red) to 0 T (violet), are indicated by values and arrow in (c). The orientations of the measuring current $I$ and the magnetic field are indicated in the insets. (e) Phase diagram for $H_{\perp }$ indicating anisotropic boundaries for the onset of finite resistivity. (f) Similar phase diagram for $H_{\parallel }$.

Figure 2

Diagrams indicating contact configurations for the measurements of (a) ${\rho }_{\parallel }$ and (b) ${\rho }_{\perp }$. In (a), the voltage contacts extend across one side of the crystal to ensure adequate sensing of transport in the CuO${}_2$ planes.

Figure 3

Further data sets for ${\rho }_{\perp }$ with (a) $H_{\perp }$, (b) $H_{\parallel }$. Magnetic field values are listed in the legends.

Figure 4

Measurements of ${\rho }_{\parallel }$ in LSCO with $x=0.092$ from Sasagawa et al. (Ref. 19) (dashed lines) and in LBCO with $x=0.10$ from Adachi et al. (Ref. 21) (solid lines), with values of ${\mu }_0{H}_{\perp }$ labeling the curves.

Figure 5

Results for ${\rho }_{\parallel }$ measured in $H_{\perp }$ with voltage contacts on a crystal face perpendicular to the crystallographic $c$ axis (open diamonds) and parallel to $c$ (filled symbols), as indicated by the insets. In both cases, violet symbols correspond to zero field, red to ${\mu }_0{H}_{\perp }=9$ T.

Figure 6

Rocking curve scans at the (200)/(020) Bragg reflection for La${}_{2-x}$Ba${}_x$CuO${}_4$ crystals with a range of Ba concentrations, as indicated. Solid lines correspond to scans at $60\pm 10$ K, above the structural transition; dashed lines were measured at approximately 10 K, below the transition. The peaks split symmetrically about zero at 60 K correspond to twinned reflections. For $x=0.095$ at 60 K, the extra peak at ${0.1}^{\circ }$ corresponds to a small-volume domain with a more complicated twin relationship.

Figure 7

Resistivities vs temperature for a range of magnetic fields, corresponding to the configurations (a) ${\rho }_{\perp }$ in $H_{\perp }$, (b) ${\rho }_{\perp }$ in $H_{\parallel }$, (c) ${\rho }_{\parallel }$ in $H_{\perp }$, (d) ${\rho }_{\parallel }$ in $H_{\parallel }$. The values of ${\mu }_{0}H$, ranging from 9 T (red) to 0 T (violet), are indicated in (c). The orientations of the measuring current $I$ and the magnetic field are indicated in the insets.

Figure 8

Measurements of the in-plane thermopower $S_{\parallel }$ with ${\mu }_0{H}_{\perp }=0$, 1, 3, 5, and 9 T.

Figure 9

(a) Data for ${\rho }_{\perp }$ in ${\mu }_{0}H=7$ T applied both parallel (diamonds) and perpendicular (circles) to the planes. (b) Field-cooled spin susceptibility in the form ${(g_{\mathrm{ave}}/g_i)}^2{\chi }_i^s$ for $i=\parallel$ (diamonds) and $\perp$ (circles) obtained with ${\mu }_{0}H=7$ T, as discussed in the text.

Figure 10

Points indicate measured ${\rho }_{\parallel }$ vs $T$ for various values of ${\mu }_0{H}_{\perp }$, as indicated in the legend. Lines are fitted curves corresponding to a model of flux-flow resistivity (Ref. 46) as discussed in the text.

Figure 11

(a) $E_{\parallel }$ vs $J_{\parallel }$ in zero field for $T\sim T_c$. (b) Exponent from power-law dependence of $E_{\parallel }$ vs $J_{\parallel }$ for several values of $H_{\parallel }$. Error bars, corresponding to one standard deviation, were determined from least-squares fits to the data.

Figure 12

$E_{\perp }$ vs $J_{\perp }$ in (a) zero field for temperatures from 36 down to 31.7 K, as indicated in the legend, and (b) ${\mu }_0{H}_{\perp }=9$ T for temperatures from 8 down to 5 K. Lines indicate $E_{\perp }\sim J_{\perp }$.

Figure 13

Data for ${\rho }_{\perp }\left(T\right)$ with ${\mu }_0{H}_{\perp }=2$ to 9 T plotted vs $1/\left[T{\mu }_0(H_{\perp }+H_0)\right]$, with ${\mu }_0{H}_0=2.2$ T.

Figure 14

(a) Integrated intensity of the magnetic superlattice peak at wave vector $(0.6,0.5,0)$ in ${\mu }_0{H}_{\perp }=0$ T (violet circles) and 7 T (red squares), obtained by neutron diffraction. (b) Integrated intensity of the charge-order superlattice peak $(0.2,0,8.5)$ in ${\mu }_0{H}_{\perp }=0$ T (violet circles) and 10 T (red diamonds), obtained by x-ray diffraction. (c) Integrated intensity of the (300) superlattice peak, characterizing the structural transition to the low-temperature phase, in 0 and 10 T as in (b). For (a) and (b), intensities are normalized (approximately) to results for LBCO $x=0.125$ in zero field (Ref. 49); for (c), intensities are normalized at low temperature. Error bars correspond to one standard deviation of counting statistics. Lines through the data points are guides to the eye. Gray regions emphasize the change induced by the magnetic field.