Unusual Nernst Effect Suggesting Time-Reversal Violation in the Striped Cuprate Superconductor ${\mathrm{La}}_{2-x}{\mathrm{Ba}}_x{\mathrm{CuO}}_4$

The striped cuprate ${\mathrm{La}}_{2-x}{\mathrm{Ba}}_x{\mathrm{CuO}}_4$ ($x=\frac{1}{8}$) undergoes several transitions below the charge-ordering temperature $T_{\mathrm{co}}=54\mathrm{K}$. From Nernst experiments, we find that, below $T_{\mathrm{co}}$, there exists a large, anomalous Nernst signal $e_{N,\mathrm{even}}(H,T)$ that is symmetric in field $H$, and remains finite as $H\to 0$. The time-reversal violating signal suggests that, below $T_{\mathrm{co}}$, vortices of one sign are spontaneously created to relieve interlayer phase frustration.

Figure 1

Traces of the observed (raw) Nernst signal $e_y^{\mathrm{obs}}(H,T)$ vs applied field $H$ at selected $T$ from 160 to 45 K (Panel a) and below 35 K (b). The curves in Panel (a) are nominally linear in $H$, with an intercept at $H=0$ that comes from “pick up” of the longitudinal thermopower $S$ due to contact misalignment. The Nernst coefficient $\nu$ is obtained from the slope near $H=0$. Below 30 K [(panel (b)], the curves of $e_y^{\mathrm{obs}}(H,T)$ display prominent oscillatory features at low $H$ which we identify with an anomalous field-symmetric Nernst signal $e_{N,\mathrm{even}}(H,T)$.

Figure 2

Subtraction of the thermopower to extract the anomalous Nernst signal. Panel (a) compares the observed Nernst signal $E_y^{\mathrm{obs}}(0,T)$ with the thermopower $S(0,T)$ at $H=0$. The Nernst results include two sets of data taken with $|\nabla T|\sim 2\mathrm{K}/\mathrm{cm}$ (solid symbols) and $\sim 4\mathrm{K}/\mathrm{cm}$ (open). By fixing the scaling number $k=-9.8$, the two curves can be superposed in the interval 50–90 K. Below 32 K, the curves strongly deviate from each other. The difference is identified with the zero-$H$ anomalous Nernst signal $E_N(0,T)$, which is plotted in panel (b). For $30<T<50\mathrm{K}$, $|E_N(0,T)|$ is small ($0.2\mu \mathrm{V}/\mathrm{K}$) but well-resolved. Below 30 K, it rises abruptly to a prominent peak at 20 K before decreasing to zero near 5 K. The irreversibility field $H_{\mathrm{irr}}$ measured by torque magnetometry is plotted as solid triangles.

Figure 3

Panel (a): Comparison of the raw, field-symmetrized, Nernst signal $e_{y,\mathrm{even}}^{\mathrm{obs}}(H,T)$ (solid curves) with the thermopower $S(H,T)$ (scaled by $k=-9.8$, dashed curves) at selected $T\le 20\mathrm{K}$. Note that $S(H,T)$ is actually negative below 40 K (at all $H$ shown). The two sets of curves have very different field dependences. Panel (b) displays the curves of the intrinsic field-symmetrized Nernst signal $e_{N,\mathrm{even}}(H,T)$ obtained by subtracting the two sets of curves [see Eq. (1)]. The oscillatory features are absent in $S(H,T)$. At large $H$, $e_{N,\mathrm{even}}(H,T)$ is suppressed to zero.

Figure 4

Panel (a): Semilog plot of the fields $H_1(T)$, $H_2(T)$, $H_{\rho b}(T)$ and $H_{\rho c}(T)$. The data for $H_1$ (solid triangles) fit the form $H_0\exp (-T/T0)$ (straight line), with $H_0=8.28\mathrm{T}$ and $T_0=6.86\mathrm{K}$. $H_{\rho a}$ (open circles), inferred from $d{\rho }_{ab}/dT$ [7], falls on the same line as $H_1$. $H_{\rho c}$ (open diamonds) obtained from $d{\rho }_c/dT$ [7] is roughly of the same field scale as $H_2$. Panel (b) defines $H_1$ and $H_2$ for the curve $e_{N,\mathrm{even}}$ at 5 K. Panel (c) displays the $T$ dependence of the Nernst coefficient $\nu =e^{N,\mathrm{odd}}/H$ (solid circles) and the torque susceptibility $\Delta \chi ={\chi }_c-{\chi }_a$ (solid triangles) measured with $\mathbf{H}$ (7 T) at 15° to $\mathbf{c}$. The increase in $\nu$ below $T_{\mathrm{onset}}\sim 110\mathrm{K}$ correlates with a diamagnetic contribution to $\chi$ from orbital currents. Below $T_{\mathrm{co}}$, the increase in $\nu$ is abruptly interrupted, but it resumes its steep increase below 20 K. Below $T_{\mathrm{co}}$, the large spin susceptibility obscures supercurrent contributions to ${\chi }_c$.