Small-angle neutron scattering study of the mixed state of ${\mathrm{Yb}}_3{\mathrm{Rh}}_4{\mathrm{Sn}}_{13}$

Using the small angle neutron scattering (SANS) technique we investigated the vortex lattice (VL) in the mixed state of the stannide superconductor ${\mathrm{Yb}}_3{\mathrm{Rh}}_4{\mathrm{Sn}}_{13}$. We find a single domain VL of slightly distorted hexagonal geometry for field strengths between 350 and 18 500 G and temperatures between $T=0.05$ and 6.5 K. We observe a clear in-plane rotation of the VL for different magnetic field directions relative to the crystallographic axes. We also find that the hexagonal symmetry of the VL is energetically favorable in ${\mathrm{Yb}}_3{\mathrm{Rh}}_4{\mathrm{Sn}}_{13}$ for external fields oriented along axes of different symmetries: twofold [110], threefold [111], and fourfold [100]. The observed behavior is different from other conventional and unconventional superconductors. The superconducting state is characterized by an isotropically gapped order parameter with an amplitude of $\Delta \left(0\right)=1.57\pm 0.05$ meV. At the lowest temperatures, the field dependence of the magnetic form factor in our material reveals a London penetration depth of ${\lambda }_L=2508\pm 17$ Å and a Ginzburg coherence length of $\xi =100\pm 1.3$ Å, i.e., it is a strongly type-II superconductor, $\kappa ={\lambda }_L/\xi =25$.

Figure 1

Phase diagram of the mixed state of Yb${}_3$Rh${}_4$Sn${}_{13}$. Electrical resistivity measurements revealed ${\mu }_0{H}_{c_2}\left(T\right)$ (black dots). The blue area indicates the region where a SANS signal was observed. In the striped area, no SANS signal was observed. (Insert) Electrical resistivity data at ${\mu }_{0}H=0$ T.

Figure 2

Vortex lattice diffraction pattern at $T=1.8$ K and ${\mu }_{0}H=3500$ G for (a) $\vec{H}\left|\right|$[100], (b) $\vec{H}\left|\right|$[111], and (c) $\vec{H}\left|\right|$[110].

Figure 3

(a) Field dependence of the magnetic form factor for three crystal directions at $T$ = 50 mK and 1.8 K. (b) Temperature dependence of the superfluid density. The data reveal a $s$-wave superconducting order parameter.

Figure 4

Field dependence of the $q$ vector of the VL. $q\left(H\right)$ follows a square-root behavior.