Time-reversal symmetry breaking and multigap superconductivity in the noncentrosymmetric superconductor ${\mathrm{La}}_7{\mathrm{Ni}}_3$

The ${\mathrm{Th}}_7{\mathrm{Fe}}_3$ family of superconductors provides a rich playground for unconventional superconductivity. ${\mathrm{La}}_7{\mathrm{Ni}}_3$ is the latest member of this family, which we here investigate by means of thermodynamic and muon spin rotation and relaxation measurements. Our specific heat data provides evidence for two distinct and approximately isotropic superconducting gaps. The larger gap has a value slightly higher than that of weak-coupling BCS theory, indicating the presence of significant correlations. These observations are confirmed by transverse-field muon spin rotation/relaxation measurements. Furthermore, zero-field measurements reveal small internal fields in the superconducting state, which occur close to the onset of superconductivity and indicate that the superconducting order parameter breaks time-reversal symmetry. We discuss two possible microscopic scenarios—an unconventional $E_2(1,i)$ state and an $s+is$ superconductor, which is reached by two consecutive transitions—and illustrate which interactions will favor these phases. Our results establish ${\mathrm{La}}_7{\mathrm{Ni}}_3$ as the first member of the ${\mathrm{Th}}_7{\mathrm{Fe}}_3$ family displaying both time-reversal-symmetry-breaking and multigap superconductivity.

Figure 1

(a) Powder XRD pattern of ${\mathrm{La}}_7{\mathrm{Ni}}_3$ is presented by red dots whereas the black line corresponds to the Rietveld refinement. (b) Magnetization as a function of temperature collected in the zero-field cooled warming (ZFCW) and field cooled cooling (FCC), confirming superconductivity with critical temperature $T_c=2.3$ K. (c) Temperature dependence of normalized electronic specific heat data, where the dashed and solid lines represent fits to the different models described in the main text.

Figure 2

The time-domain TF spectra taken above and below $T_c$ in an applied magnetic field of 10 mT. The solid lines show the fitting using Eq. (1).

Figure 3

(a) Temperature dependence of the muon spin depolarization rate at different applied magnetic fields from 10 mT to 40 mT in TF-$\mu \mathrm{SR}$ measurements. The approximately constant value in the normal state is indicated by the solid black line. (b) ${\sigma }_{\text{sc}}\left(H\right)$ at various temperatures ($T=0.125\text{K}$ to $T=2.80\text{K}$), including the one designated by the dashed line in (a). The data were fitted using Eq. (3) to extract the temperature dependence of the inverse square of the magnetic penetration depth. (c) The calculated ${\lambda }^{-2}$(T) where the solid line represents the best fit using Eq. (5).

Figure 4

(a) The asymmetry spectra collected at 0.2 K (orange) and 2.9 K (brown) in ZF-$\mu \mathrm{SR}$, together with the LF-$\mu \mathrm{SR}$ data taken at 0.1 K in an applied field of 5 mT (green). The solid lines are fits of Eq. (7). (b) $\mathrm{\Lambda }\left(T\right)$ exhibits a significant increase below $T_c=2.3\text{K}$ and suggests the appearance of a spontaneous magnetic field in the superconducting state. (c) Temperature dependence of $\mathrm{\Delta }$, the relaxation of muon spins due to the static distribution of magnetic fields produced by nuclear magnetic moments which shows no dependence on temperature.

Figure 5

Schematic illustration of the two possible pairing scenarios, $E_2(1,i)$ and $s+is$, consistent with experiment. (a) Phase of the order parameter (color) for the $E_2(1,i)$ state in a 2D cut (at fixed $k_z$) of the Brillouin zone for the lowest-order basis functions. As long as no Fermi surfaces (such as the examples shown in gray) go through the high-symmetry lines marked by black dots (thick black lines in the inset), the state is fully gapped. As indicated by the thickness of the gray lines, the gap in generals differs on symmetry-unrelated Fermi pockets, $|{\mathrm{\Delta }}_1|\ne |{\mathrm{\Delta }}_2|$, in agreement with experiment. For the $s+is$ state, shown in (b), the TRS breaking results from nontrivial relative phases (indicated by colors) of the order parameter between pockets that are not related by symmetry, i.e., ${\mathrm{\Delta }}_j/\left|{\mathrm{\Delta }}_j\right|$ depends on $j$.

Figure 6

(a) Lower critical field $H_{c1}$ as a function of temperature. Inset shows the low-field magnetization curves obtained at different fixed temperatures. (b) Upper critical field $H_{c2}$ of ${\mathrm{La}}_7{\mathrm{Ni}}_3$ versus temperature, where the blue line represents a fit with Eq. (A2). Inset shows the susceptibility as a function of temperature at different fields.

Figure 7

Resistivity as a function of temperature in zero applied field over the range 1.9 K $\le$ T $\le$ 300 K. The line shows a fitting with parallel resistor model. Inset: $\rho \left(T\right)$ at low temperature exhibiting a drop in resistivity at $T_{c,\text{onset}}=2.6\text{K}$.