Distinct vortex-glass phases in Yb$_{3}$Rh$_{4}$Sn$_{13}$ at high and low magnetic fields

The vortex lattice (VL) in the mixed state of the stannide superconductor Yb$_{3}$Rh$_{4}$Sn$_{13}$ has been studied using small-angle neutron scattering (SANS). The field dependencies of the normalized longitudinal and transverse correlation lengths of the VL, $xi_L/a_0$ and $xi_T /a_0$, reveal two distinct anomalies that are associated with vortex-glass phases below $mu_0H_l$~$approx$~700~G and above $mu_{0}H_h$~$sim$~1.7~T ($a_0$ is the intervortex distance). At high fields, around 1.7~T, the longitudinal correlation decreases abruptly with increasing fields indicating a weakening (but not a complete destruction) of the VL due to a phase transition into a glassy phase, below $mu_{0}H_{c_2}$(1.8 K)~$approx$~2.5~T. $xi_L/a_0$ and $xi_T /a_0$, gradually decrease for decreasing fields of strengths less than 1~T and tend towards zero. The shear elastic modulus $c_{66}$ and the tilting elastic modulus $c_{44}$ vanish at a critical field $mu_0H_l$~$approx$~700~G, providing evidence for a disorder-induced transition into a vortex-glass. A ring of scattered intensity is observed for fields lower than 700~G, $i.e.$, $mu_{0}H_{c_1}$~=~135~G~$<$~$mu_{0}H$~$<$~700~G. This low-field phenomenon is of different nature than the one observed at high fields, where $xi_L/a_0$ but not $xi_T/a_0$, decreases abruptly to an intermediate value.