Broken time-reversal symmetry in superconducting ${\mathrm{Pr}}_{1-x}{\mathrm{Ce}}_x{\mathrm{Pt}}_4{\mathrm{Ge}}_{12}$

We report results of zero-field muon spin relaxation experiments on the filled-skutterudite superconductors ${\mathrm{Pr}}_{1-x}{\mathrm{Ce}}_x{\mathrm{Pt}}_4{\mathrm{Ge}}_{12},x=0$, 0.07, 0.1, and 0.2, to investigate the effect of Ce doping on broken time-reversal symmetry (TRS) in the superconducting state. In these alloys broken TRS is signaled by the onset of a spontaneous static local magnetic field $B_s$ below the superconducting transition temperature. We find that $B_s$ decreases linearly with $x$ and $\to 0$ at $x\approx 0.4$, close to the concentration above which superconductivity is no longer observed. The ${\text{(Pr,Ce)Pt}}_4{\mathrm{Ge}}_{12}$ and isostructural ${\text{(Pr,La)Os}}_4{\mathrm{Sb}}_{12}$ alloy series both exhibit superconductivity with broken TRS, and in both the decrease of $B_s$ is proportional to the decrease of Pr concentration. This suggests that Pr-Pr intersite interactions are responsible for the broken TRS. The two alloy series differ in that the La-doped alloys are superconducting for all La concentrations, suggesting that in ${\text{(Pr,Ce)Pt}}_4{\mathrm{Ge}}_{12}$ pair-breaking by Ce doping suppresses superconductivity. For all $x$ the dynamic muon spin relaxation rate decreases somewhat in the superconducting state. This may be due to Korringa relaxation by conduction electrons, which is reduced by the opening of the superconducting energy gap.

Figure 1

Time evolution of ${\mu }^{+}$ decay positron asymmetry, proportional to the ${\mu }^{+}$ spin polarization $P_{\mu }\left(t\right)$, above and below the superconducting transition in (a) ${\mathrm{PrPt}}_4{\mathrm{Ge}}_{12}$ and (b) ${\mathrm{Pr}}_{0.9}{\mathrm{Ce}}_{0.1}{\mathrm{Pt}}_4{\mathrm{Ge}}_{12}$. A constant signal from muons that miss the sample and stop in the silver sample holder has been subtracted from the data.

Figure 2

Temperature dependence of the ZF Kubo-Toyabe static relaxation rate $\Delta$ in (a) ${\mathrm{PrPt}}_4{\mathrm{Ge}}_{12}$, (b) ${\mathrm{Pr}}_{0.93}{\mathrm{Ce}}_{0.07}{\mathrm{Pt}}_4{\mathrm{Ge}}_{12}$, (c) ${\mathrm{Pr}}_{0.9}{\mathrm{Ce}}_{0.1}{\mathrm{Pt}}_4{\mathrm{Ge}}_{12}$, and (d) ${\mathrm{Pr}}_{0.8}{\mathrm{Ce}}_{0.2}{\mathrm{Pt}}_4{\mathrm{Ge}}_{12}$. Curves: Fits of Eq. (5) assuming the temperature dependence of the BCS order parameter for ${\Delta }_e\left(T\right)$. Arrows: Superconducting transition temperature $T_c^{C_p}$ from specific-heat measurements [21].

Figure 3

Points: Temperature dependence of the relaxation rate ${\Delta }_e$ in ${\text{(Pr,Ce)Pt}}_4{\mathrm{Ge}}_{12}$ (circles: $x=0$, squares: $x=0.07$, triangles: $x=0.1$, and diamonds: $x=0.2)$. Curves: Fits of Eq. (6) to the data. Inset: Dependence of the rms width ${\Delta }_e\left(0\right)/{\gamma }_{\mu }$ of the $T=0$ spontaneous field distribution on Ce concentration $x$ in ${\mathrm{Pr}}_{1-x}{\mathrm{Ce}}_x{\mathrm{Pt}}_4{\mathrm{Ge}}_{12}$. Solid line: Linear fit.

Figure 4

Temperature dependence of the ZF exponential damping rate $\Lambda$ in ${\mathrm{Pr}}_{1-x}{\mathrm{Ce}}_x{\mathrm{Pt}}_4{\mathrm{Ge}}_{12}$. (a) $x=0$. (b) $x=0.07$. (c) $x=0.1$. (d) $x=0.2$. Arrows: $T_c^{C_p}$ from specific-heat measurements [21].