Magneto-Optical Measurements of a Cascade of Transitions in Superconducting ${\mathrm{La}}_{1.875}{\mathrm{Ba}}_{0.125}{\mathrm{CuO}}_4$ Single Crystals

Recent experiments on the original cuprate high-temperature superconductor, ${\mathrm{La}}_{2-x}{\mathrm{Ba}}_x{\mathrm{CuO}}_4$, revealed a remarkable sequence of phase transitions. Here we investigate such crystals with the polar Kerr effect, which is sensitive to time-reversal-symmetry breaking. Concurrent birefringence measurements accurately locate the structural phase transitions from high-temperature tetragonal to low-temperature orthorhombic, and then to lower-temperature tetragonal, at which temperature strong Kerr signal onsets. Hysteretic behavior of the Kerr signal suggests that time-reversal symmetry is already broken well above room temperature, an effect that was previously observed in high quality ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6+x}$ crystals.

Figure 1

Zero-field cool Kerr effect of a cleaved sample. Here we mark (i) the LTO to LTT transition, $T_{\mathrm{LT}}$, which is also evident in the second-harmonic data; (ii) the onset of CO, $T_{\mathrm{CO}}$; the onset of spin ordering, $T_{\mathrm{SO}}$; and the temperature below which superconductivity is established in the $a\mathrm{\text{−}}b$ plane, $T_{\mathrm{SC}}$. The location of $T_{\mathrm{CO}}$, $T_{\mathrm{SO}}$, and $T_{\mathrm{SC}}$ are taken from Li et al. [1]. Susceptibility (dotted line) was measured on the same crystal at a magnetic field of 1 T applied in the $c$ direction, and is identical to the data in Ref. 14.

Figure 2

Second-harmonic signal of our apparatus detecting evolution of the birefringence in the $a\mathrm{\text{−}}b$ plane of the sample. Arrows mark the second-order transition from HTT to LTO at $T_{\mathrm{HT}}=230.8\mathrm{K}$, and the first-order transition from LTO to LTT at $T_{\mathrm{LT}}=53.7\mathrm{K}$ (see text). Inset shows a blowup of the middle of the first-order transition, taken at lower power, and at three different cycle rates. Clearly, the higher the rate, the larger is the hysteresis in the birefringence of the sample.

Figure 3

Training effect for a ${\mathrm{La}}_{1.875}{\mathrm{Ba}}_{0.125}{\mathrm{CuO}}_4$ crystal. Inset shows the schedule of training: the field was turned on to $H_{\mathrm{t}}$ at $T_0$, the sample was then cooled in a field to 4 K, the field was turned off at 5 K, and the sample was measured at zero field while warmed up. (a) Zero-field cool: $T_0=$ room temperature (RT) and $H_{\mathrm{t}}=0$; (b) succeeded (a) where $T_0=140\mathrm{K}$ and $H_{\mathrm{t}}=+4$ T; (c) succeeded (b) where $T_0=140\mathrm{K}$ and $H_{\mathrm{t}}=-4\mathrm{T}$. The vertical dashed line is the low field irreversibility temperature, indicating that when turning the field to zero at low temperatures flux is trapped as is evident from the response below $\sim 25\mathrm{K}$ in (b) and (c).

Figure 4

Training effect for a ${\mathrm{La}}_{1.875}{\mathrm{Ba}}_{0.125}{\mathrm{CuO}}_4$ crystal at high temperatures. Sample was first cooled in zero field to 5 K, and was measured warming up to RT (a). Sample was then warmed up to 400 K, then cooled down to RT in a field of $+4\mathrm{T}$, followed by cooling in zero field to 5 K, and then measured warming up to RT (b). The same procedure was repeated but with a field of $-4\mathrm{T}$ (c). We also show the second harmonic that is proportional to the birefringence of the sample.