${\mathrm{SrPt}}_3\mathrm{P}$: A two-band single-gap superconductor

The magnetic penetration depth $\left(\lambda \right)$ as a function of applied magnetic field and temperature in ${\mathrm{SrPt}}_3\mathrm{P}$ ($T_c\simeq 8.4$ K) was studied by means of muon-spin rotation $\left(\mu \mathrm{SR}\right)$. The dependence of ${\lambda }^{-2}$ on temperature suggests the existence of a single $s$-wave energy gap with the zero-temperature value ${\Delta }_0=1.55\left(2\right)$ meV. At the same time $\lambda$ was found to be strongly field dependent which is the characteristic feature of the nodal gap and/or multiband systems. The multiband nature of the superconducting state is further suggested by the upward curvature of the upper critical field. This apparent contradiction is resolved by ${\mathrm{SrPt}}_3\mathrm{P}$ being a particular two-band superconductor with equal gaps but different coherence lengths within the two Fermi surface sheets.

Figure 1

The temperature dependence of the upper critical field $B_{c2}$ of ${\mathrm{SrPt}}_3\mathrm{P}$ (closed circles). The dotted lines are linear fits of $B_{c2}\left(T\right)$ in the vicinity of $T_c$ and for $T\le 6$ K. Open circles are $B_{c2}\left(T\right)$ data points from Ref. [6]. The inset shows the temperature dependence of the zero-field-cooled (ZFC) and field-cooled (FC) magnetization measured at ${\mu }_{0}H=0.3$ mT.

Figure 2

The dependence of the depolarization rate ${\sigma }_{\mathrm{sc}}$ on the applied field $B$ at $T=1.7$ K. The dashed black line represents ${\sigma }_{\mathrm{sc}}\left(B\right)$ as expected within the model of Brandt [34] for $\lambda =162\left(4\right)$ nm and $B_{c2}=4.5$ T obtained in magnetization experiments. The red solid line is the fit by means of the two-component model from Ref. [35] with the parameters ${\xi }_1=8.6$ nm, ${\xi }_2=26$ nm, $\lambda =134\left(2\right)$ nm, and $w=0.72\left(2\right)$; see Sec. S2 in the Supplemental Material [8]. The inset shows the temperature dependence of the depolarization rate ${\sigma }_{\mathrm{sc}}$ caused by the formation of FLL in ${\mathrm{SrPt}}_3\mathrm{P}$ in fields of 0.05, 0.15, 0.3, and 0.45 T.

Figure 3

${\lambda }^{-2}\left(T\right)$ normalized to its value averaged over the temperature range $1.7$–3.5 K as a function of $T/T_c\left(B\right)$. The solid line is the fit obtained by using the weak-coupling BCS model [see Eq. (3)]. The inset shows the dependence of ${\lambda }^{-2}$ on the applied field at $T=1.7$, 4.1, and 6.1 K.

Figure 4

Schematic diagram representing relations between the various types of a single-band, two-band, and multiband superconductors.