Polar Kerr Effect from Time-Reversal Symmetry Breaking in the Heavy-Fermion Superconductor ${\mathrm{PrOs}}_4{\mathrm{Sb}}_{12}$

We present polar Kerr effect measurements of the filled skutterudite superconductor ${\mathrm{PrOs}}_4{\mathrm{Sb}}_{12}$. Simultaneous ac susceptibility measurements allow us to observe the superconducting transition under the influence of heating from the optical beam. A nonzero Kerr angle ${\theta }_K$ develops below the superconducting transition, saturating at $\sim 300\mathrm{nrad}$ at low temperatures. This result is repeated across several measurements of multiple samples. By extrapolating the measured ${\theta }_K(T)$ to zero optical power, we are able to show that the Kerr angle onset temperature in one set of measurements is consistent with the transition to the $B$ phase at $T_{C2}$. We discuss the possible explanations for this result and its impact on the understanding of multiphase and inhomogeneous superconductivity in ${\mathrm{PrOs}}_4{\mathrm{Sb}}_{12}$.

Figure 1

Ac susceptibility as a function of temperature, with the optical beam off (blue circles), and at $20\mu \mathrm{W}$ incident power (red diamonds), measured on sample A. Two transitions are apparent in each curve. The solid lines are phenomenological fits emphasizing the multiple transitions. Increasing optical power heats the sample, causing the transitions to occur at lower measured fridge temperature. Inset: A schematic of our mutual inductance apparatus (not to scale). An astatically-wound pickup coil sits inside a drive coil, with the end butted up against a thin sapphire wafer that supports the sample (labeled SC). The optical beam (dashed red arrow) is incident from above.

Figure 2

(a) Kerr angle as a function of temperature at $20\mu \mathrm{W}$ incident power after cooling in zero field (data from sample E). Error bars represent statistical error of hundreds of data points averaged together [34]. Two different runs are shown; one shows a positive Kerr signal, saturating at $\sim 250\mathrm{nrad}$, while the other shows a small negative signal. This sample showed Kerr signals with random amplitude and sign after cooling in zero field. (b) Kerr angle at $10\mu \mathrm{W}$ power after cooling in various fields (data from sample C). A nonzero ${\theta }_K$ develops symmetrically below $\sim 1.5\mathrm{K}$, saturating at $\sim 300\mathrm{nrad}$. The saturating amplitude is independent of field strength.

Figure 3

Averaged Kerr data taken on sample E at $20\mu \mathrm{W}$ incident power. Error bars are statistical errors (one-$\sigma$). Fits with two critical temperatures (solid blue line) or one (dashed green line) are overlaid.

Figure 4

Measured values of $T_{C1}$ (orange circles), $T_{C2}$ (light green circles), and $T_K$ (blue squares) as a function of optical power on sample C. Error bars indicate 95% confidence intervals on the values of $T_K$ extracted from Kerr data fits. The dashed line is a linear fit to $T_K(P)$ from $5–20\mu \mathrm{W}$, extrapolating back to $T_K(0)=1.694\pm 0.072\mathrm{K}$ (white square), which is consistent with $T_{C2}$.