Null Orbital Frustration at the Pseudogap Boundary in a Layered Cuprate Superconductor

We assess the relative importance of orbital frustration at the pseudogap closing field $H_{\mathrm{p}\mathrm{g}}$. Using interlayer tunneling transport in pulsed magnetic fields nearly up to 60 T, we track the field-temperature ($H$-$T$) phase diagram for fields parallel ($\parallel ab$) and normal ($\parallel c$) to the layered structure of ${\mathrm{B}\mathrm{i}}_2{\mathrm{S}\mathrm{r}}_2{\mathrm{C}\mathrm{a}\mathrm{C}\mathrm{u}}_2{\mathrm{O}}_{8+y}$. In contrast to large orientational anisotropy of the superconducting state related to the orbital motion of Cooper pairs, we find anisotropy of $H_{\mathrm{p}\mathrm{g}}$ temperature independent and small, due solely to the $g$ factor. The obtained Zeeman relation with the pseudogap temperature $T^{\star }$, $g^{\parallel c}{\mu }_B{H}_{\mathrm{p}\mathrm{g}}^{\parallel c}=g^{\parallel ab}{\mu }_B{H}_{\mathrm{p}\mathrm{g}}^{\parallel ab}\approx k_B{T}^{\star }$, is fully consistent with the correlations only in the spin channel.

Figure 1

${\rho }_c$ vs temperature in Bi-2212 for $H$$\parallel$$c$ and $H$$\parallel$$ab$ measured at 100 kHz in a 60 ms pulse 60 T magnet at National High Magnetic Field Laboratory (NHMFL) in Los Alamos using a lock-in technique. The upturn in ${\rho }_c(T)$ below $T^{\star }\sim 100\mathrm{K}$ is a consistent signature of the pseudogap present also below $T_c$. At high fields ($\sim 55$ T) the upturn is reduced, eventually restoring ${\rho }_c$ to its ungapped value ${\rho }_c^n(T)$ (dashed line). Inset: For $H$$\parallel$$c$ the pseudogap closing field $H_{\mathrm{p}\mathrm{g}}$ and $T^{\star }$ follow a simple Zeeman scale $g{\mu }_B{H}_{\mathrm{p}\mathrm{g}}^{\parallel c}\approx k_B{T}^{\star }$ with $g=2.0$ up to the hole doping level $p=0.225$.

Figure 2

Excess $c$-axis resistivity $\Delta {\rho }_c={\rho }_c-{\rho }_c^n$ vs field [after subtracting the ungapped normal state resistivity ${\rho }_c^n(T,H)$] for (a) $H$$\parallel$$c$ and (b) $H$$\parallel$$ab$. All curves are labeled by temperatures. $\Delta {\rho }_c$ above the resistivity maximum at $H_{\mathrm{s}\mathrm{c}}$ follows a power law. At each temperature the pseudogap is extinguished at a closing field $H_{\mathrm{p}\mathrm{g}}(T)$ when $\Delta {\rho }_c(H)\to 0$. Top inset: The high-field collapse on the same scaling curve of $\Delta {\rho }_c(H)$ plotted vs $H/H_{\mathrm{p}\mathrm{g}}$ for many temperatures enables us to independently track $H_{\mathrm{p}\mathrm{g}}(T)$ for $H$$\parallel$$c$ and $\parallel$$ab$. Above $0.5H_{\mathrm{p}\mathrm{g}}$ the Josephson current contribution is negligible. The bottom inset illustrates a power-law fit at $T=50$ K. Black bars indicate the errors associated with the fits.

Figure 3

Anisotropy in the superconducting state. (a) The peak field $H_{\mathrm{s}\mathrm{c}}(T)$ and (c) the irreversibility field $H_{\mathrm{i}\mathrm{r}\mathrm{r}}(T)$ for $H$$\parallel$$c$ and $H$$\parallel$$ab$. $H_{\mathrm{i}\mathrm{r}\mathrm{r}}$ was determined using a ${\rho }_c=0.01{\rho }_c^n$ criterion, consistent with our experimental resolution. Large anisotropy ratios for the two field configurations are shown in (b) for $H_{\mathrm{s}\mathrm{c}}$ and in (d) for $H_{\mathrm{i}\mathrm{r}\mathrm{r}}$. Solid line in (b) corresponds to $\gamma \approx 2.6(1-T/T_c{)}^{-1/2}$, the temperature-dependent anisotropy derived for a stack of weakly Josephson-coupled superconducting layers. $\gamma$ becomes very large near $T_c$.

Figure 4

$H$-$T$ diagram showing the pseudogap closing field $H_{\mathrm{p}\mathrm{g}}(T)$ for $H\parallel c$ (left hand side) and $H\parallel ab$ (right hand side). The error bars are obtained from the deviations in the power-law fit parameters. In contrast to the characteristic fields in the superconducting state, the small ratio ${\gamma }_{\mathrm{p}\mathrm{g}}=H_{\mathrm{p}\mathrm{g}}^{\parallel ab}(T)/H_{\mathrm{p}\mathrm{g}}^{\parallel c}(T)\approx 1.35$ is temperature independent (inset) and corresponds to the anisotropy of the $g$ factor.