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Register a new userA neutron scattering study of the mixed state of Yb$_{3}$Rh$_{4}$Sn$_{13}$
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Using the small angle neutron scattering (SANS) technique we investigated the vortex lattice (VL) in the mixed state of the stannide superconductor Yb$_{3}$Rh$_{4}$Sn$_{13}$. We find a single domain VL of slightly distorted hexagonal geometry for field strengths between 350 and 18500 G and temperatures between T = 0.05 and T = 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 Yb$_{3}$Rh$_{4}$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 isotropic gapped order parameter with an amplitude of $Delta(0)$ = 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 $AA$ and a Ginzburg coherence length of $xi$ = 100 $pm$ 1.3 $AA$, i.e., it is a strongly type-II superconductor, $kappa$ = $lambda_{L}/xi$ = 25.
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We perform optical spectroscopy measurement across the charge density wave (CDW) phase transitions on single-crystal samples of Sr$_{3}$Rh$_{4}$Sn$_{13}$ and (Sr$_{0.5}$Ca$_{0.5}$)$_{3}$Rh$_{4}$Sn$_{13}$. Formation of CDW energy gap was clearly observed for both single-crystal samples when they undergo the phase transitions. The existence of a Drude component in $sigma_1(omega)$ below TCDW indicates that the Fermi surface is only partially gapped in the CDW state. The obtained value of 2$Delta$/K$_{B}$T$_{CDW}$ is roughly 13 for both Sr$_{3}$Rh$_{4}$Sn$_{13}$ and (Sr$_{0.5}$Ca$_{0.5}$)$_{3}$Rh$_{4}$Sn$_{13}$ compounds. The value is considerably larger than the mean-field value based on the weak-coupling BCS theory. The observed spectral feature in (Sr$_{x}$Ca$_{1-x}$)$_{3}$Rh$_{4}$Sn$_{13}$ resembles those seen in many other CDW systems.
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.
The comprehensive research of the electronic structure, thermodynamic and electrical transport properties reveals the existence of inhomogeneous superconductivity due to structural disorder in Ca$_3$Rh$_4$Sn$_{13}$ doped with La (Ca$_{3-x}$La$_x$Rh$_4$Sn$_{13}$) or Ce (Ca$_{3-x}$Ce$_x$Rh$_4$Sn$_{13}$) with superconducting critical temperatures $T_c^{star}$ higher than those ($T_c$) observed in the parent compounds. The $T-x$ diagrams and the entropy $S(x)_T$ isotherms well document the relation between degree of an atomic disorder and separation of the {it high-temperature} $T_c^{star}$ and $T_c$-bulk phases. In these dirty superconductors with the mean free path much smaller than the coherence length, the Werthamer-Helfand-Hohenber theoretical model does not well fits the $H_{c2}(T)$ data. We suggest that this can result from two-band superconductivity or from the presence of strong inhomogeneity in these systems. The multiband model very well describes the $H-T$ dependencies, but the present results as well as our previous studies give arguments for the scenario based on the presence of nanoscopic inhomogeneity of the superconducting state. We also revisited the nature of structural phase transition at $T^{star}sim 130-170$ K and documented that there might be another precursor transition at higher temperatures. The impact of the magnetic Ce-Ce correlations on the increase of $T_c$ in respect to the critical temperatures of Ca$_{3-x}$La$_x$Rh$_4$Sn$_{13}$ is also discussed.
The quasi-skutterudite superconductor Sr$_3$Rh$_4$Sn$_{13}$ features a pronounced anomaly in electrical resistivity at $T^*sim$138 K. We show that the anomaly is caused by a second-order structural transition, which can be tuned to 0 K by applying physical pressure and chemical pressure via the substitution of Ca for Sr. A broad superconducting dome is centred around the structural quantum critical point. Detailed analysis of the tuning parameter dependence of $T^*$ as well as insights from lattice dynamics calculations strongly support the existence of a structural quantum critical point at ambient pressure when the fraction of Ca is 0.9 (i.e., $x_c=0.9$). This establishes (Ca$_x$Sr$_{1-x}$)$_3$Rh$_4$Sn$_{13}$ series as an important system for exploring the physics of structural quantum criticality without the need of applying high pressures.
We report a study of the magnetization density in the mixed state of the unconventional superconductor S2RuO4. On entering the superconducting state we find no change in the magnitude or distribution of the induced moment for a magnetic field of 1 Tesla applied within the RuO2 planes. Our results are consistent with a spin-triplet Cooper pairing with spins lying in the basal plane. This is in contrast with similar experiments performed on conventional and high-Tc superconductors.
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