Evidence for the coexistence of time-reversal symmetry breaking and Bardeen-Cooper-Schrieffer-like superconductivity in ${\mathrm{La}}_7{\mathrm{Pd}}_3$

Time-reversal symmetry breaking (TRSB) with a Bardeen-Cooper-Schrieffer (BCS) -like superconductivity occurs in a small, but growing number of noncentrosymmetric (NCS) materials, although the mechanism is poorly understood. We present heat capacity, magnetization, resistivity, and muon spin resonance/relaxation ($\mu \mathrm{SR}$) measurements on polycrystalline samples of NCS ${\mathrm{La}}_7{\mathrm{Pd}}_3$. Transverse-field $\mu \mathrm{SR}$ and heat capacity data show ${\mathrm{La}}_7{\mathrm{Pd}}_3$ is a type-II superconductor with a BCS-like gap structure, while zero-field $\mu \mathrm{SR}$ results provide evidence of TRSB. We discuss the implications of these results for both the ${\mathrm{La}}_7{X}_3$ (where $X=$ Ni, Pd, Rh, Ir) group of superconductors and other CS and NCS superconductors for which TRSB has been observed.

Figure 1

(a) Temperature dependence of the dc volume magnetic susceptibility ${\chi }_{\mathrm{dc}}$ for ${\mathrm{La}}_7{\mathrm{Pd}}_3$, in zero-field-cooled warming (ZFCW) mode, measured in an applied magnetic field 1.2 mT showing a superconducting onset temperature $T_{\mathrm{c}}^{\mathrm{onset}}=1.46\left(5\right)$ K. (b) Lower critical field $H_{\mathrm{c}1}$ versus temperature for ${\mathrm{La}}_7{\mathrm{Pd}}_3$. The dashed line shows a fit to the data using $H_{\mathrm{c}1}\left(T\right)=H_{\mathrm{c}1}\left(0\right)\left[1-t_{\mathrm{r}}^2\right]$, which gives ${\mu }_0{H}_{\mathrm{c}1}\left(0\right)=6.9\left(2\right)$ mT.

Figure 2

Normal state properties of ${\mathrm{La}}_7{\mathrm{Pd}}_3$. Temperature dependence of electronic resistivity from 1 to 300 K with zero applied magnetic field. The residual resistivity ratio (RRR) for ${\mathrm{La}}_7{\mathrm{Pd}}_3$ is approximately 4.2 and the residual resistivity just above the transition, ${\rho }_0\left(2\mathrm{K}\right)=48.4\left(3\right)\mu \mathrm{\Omega }$ cm. Inset: Temperature dependence of the magnetic susceptibility in an applied field of 0.5 T (in the normal state). An upturn at low temperature is consistent with the small quantity of paramagnetic impurities present in the La used to prepare the sample.

Figure 3

(a) Temperature dependence of the zero-field heat capacity for ${\mathrm{La}}_7{\mathrm{Pd}}_3$ between 0.45 and 2.75 K showing a superconducting transition at $T_{\mathrm{c}}=1.45\left(5\right)$ K. The shape of the $C$ vs $T$ is indicative of a typical type-II superconductor. Fitting the data above $T_{\mathrm{c}}$ in the normal-state using Eq. (1) gives ${\gamma }_{\mathrm{n}}=50.2\left(2\right)$ mJ ${\mathrm{mol}}^{-1}$ ${\mathrm{K}}^{-2}$. (b) Normalized electronic heat capacity $C_{\mathrm{el}}/{\gamma }_{\mathrm{n}}T$ vs the reduced temperature $T/T_{\mathrm{c}}$ in zero applied field. The dotted line shows a fit to the data for an isotropic $s$-wave gap made using Eqs. (2) and (3).

Figure 4

(a) Temperature dependence of the resistivity of ${\mathrm{La}}_7{\mathrm{Pd}}_3$ showing the suppression and broadening of the resistive superconducting transition in applied fields from 0 to 450 mT. (b) $C/T$ versus $T^2$ for ${\mathrm{La}}_7{\mathrm{Pd}}_3$ showing the suppression and broadening of the superconducting transition as the applied field is increased from 0 to 500 mT. (c) Temperature dependence of the upper critical field for ${\mathrm{La}}_7{\mathrm{Pd}}_3$. The $H_{\mathrm{c}2}\left(T\right)$ values were extracted from the midpoints of the anomalies in $C\left(T\right)/T$ and the midpoints of the resistive transitions. The dotted and dash-dotted lines show fits to the ${\mu }_0{H}_{\mathrm{c}2}\left(T\right)$ data using the GL and WHH models [39, 46], respectively.

Figure 5

Transverse-field $\mu \mathrm{SR}$ spectra for ${\mathrm{La}}_7{\mathrm{Pd}}_3$ collected at 100 mK (top) and 2.25 K (bottom) in an applied magnetic field of 20 mT. The solid lines are fits to the data using Eq. (4). Below the superconducting transition temperature the field distribution of the FLL causes the spectra to be significantly depolarized. Above the superconducting transition temperature the randomly oriented array of nuclear magnetic moments continue to depolarize the muons but at a reduced rate.

Figure 6

(a) Temperature dependence of the total spin depolarization $\sigma$ for ${\mathrm{La}}_7{\mathrm{Pd}}_3$ collected in fields between 10 and 40 mT. Isothermal cuts (the dashed line shows the cut made at 0.8 K) were used to calculate the field dependence of ${\sigma }_{\mathrm{FLL}}$ in ${\mathrm{La}}_7{\mathrm{Pd}}_3$. (b) Field dependence of the muon spin relaxation due to the flux line lattice ${\sigma }_{\mathrm{FLL}}$ at different temperatures. The solid lines are fits to the data using Eq. (6). (c) Temperature dependence of the inverse square of the penetration depth, ${\lambda }^{-2}$. The dashed line is a fit to the data using Eq. (7).

Figure 7

(a) ZF and LF-$\mu \mathrm{SR}$ spectra collected at 0.1 (green) and 2.75 K (red), the data are fit using the Gaussian Kubo-Toyabe model (dashed lines). (b) Temperature dependence of the electronic relaxation rate $\mathrm{\Lambda }$ can be seen to increase below 1.2 K just below $T_{\mathrm{c}}$. (c) Temperature dependence of the nuclear relaxation rate $\sigma$ shows no change at $T_{\mathrm{c}}$.