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Low-dimensional quantum magnets are a versatile materials platform for studying the emergent many-body physics and collective excitations that can arise even in systems with only short-range interactions. Understanding their low-temperature structure and spin Hamiltonian is key to explaining their magnetic properties, including unconventional quantum phases, phase transitions, and excited states. We study the metal-organic coordination compound (C$_5$H$_9$NH$_3$)$_2$CuBr$_4$ and its deuterated counterpart, which upon its discovery was identified as a candidate two-leg quantum ($S = 1/2$) spin ladder in the strong-leg coupling regime. By growing large single crystals and probing them with both bulk and microscopic techniques, we deduce that two previously unknown structural phase transitions take place between 136 K and 113 K. The low-temperature structure has a monoclinic unit cell giving rise to two inequivalent spin ladders. We further confirm the absence of long-range magnetic order down to 30 mK and discuss the implications of this two-ladder structure for the magnetic properties of (C$_5$H$_9$NH$_3$)$_2$CuBr$_4$.

We present a combined growth and transport study of superconducting single-crystalline NdO$_{0.5}$F$_{0.5}$BiS$_2$. Evidence of two-dimensional superconductivity with significant phase fluctuations of preformed Cooper pairs preceding the superconducting transition is reported. This result is based on three key observations. (1) The resistive superconducting transition temperature $T_c$ (defined by resistivity $\rho \rightarrow 0$) increases with increasing disorder. (2) As $T\rightarrow T_c$, the conductivity diverges significantly faster than what is expected from Gaussian fluctuations in two and three dimensions. (3) Non-Ohmic resistance behavior is observed in the superconducting state. Altogether, our observations are consistent with a temperature regime of phase-fluctuating superconductivity. The crystal structure with magnetic ordering tendencies in the NdO$_{0.5}$F$_{0.5}$ layers and (super)conductivity in the BiS$_2$ layers is likely responsible for the two-dimensional phase fluctuations. As such, NdO$_{0.5}$F$_{0.5}$BiS$_2$ falls into the class of unconventional ``laminar" bulk superconductors that include cuprate materials and 4Hb-TaS$_2$.

Unconventional superconductivity often couples to other electronic orders in a cooperative or competing fashion. Identifying external stimuli that tune between these two limits is of fundamental interest. Here, we show that strain perpendicular to the copper-oxide planes couples directly to the competing interaction between charge stripe order and superconductivity in La$_{1.88}$Sr$_{0.12}$CuO$_4$ (LSCO). Compressive $c$-axis pressure amplifies stripe order within the superconducting state, while having no impact on the normal state. By contrast, strain dramatically diminishes the magnetic field enhancement of stripe order in the superconducting state. These results suggest that $c$-axis strain acts as tuning parameter of the competing interaction between charge stripe order and superconductivity. This interpretation implies a uniaxial pressure-induced ground state in which the competition between charge order and superconductivity is reduced.

We present the magnetic orders and excitations of the distorted kagome intermetallic magnet TmAgGe. Using neutron single crystal diffraction we identify the propagation vectors $\bf{k}$ = (1/2 0 0) and $\bf{k}$ = (0 0 0) and determine the magnetic structures of the zero-field and magnetic field-induced phases for $H$ along the $a$ and [-1 1 0] crystal directions. We determine the experimental magnetic field-temperature ($H$, $T$)-phase diagram and reproduce it by Monte-Carlo simulations of an effective spin exchange Hamiltonian for one distorted kagome layer. Our model includes a strong axial single-ion anisotropy and significantly smaller exchange couplings which span up to the third-nearest neighbours within the layer. Single crystal inelastic neutron scattering (INS) measurements reveal an almost flat, only weakly dispersive mode around 7 meV that we use alongside bulk magnetization data to deduce the crystal-electric field (CEF) scheme for the Tm$^{3+}$ ions. Random phase approximation (RPA) calculations based on the determined CEF wave functions of the two lowest quasi-doublets enable an estimation of the interlayer coupling that is compatible with the experimental INS spectra. No evidence for low-energy spin waves associated to the magnetic order was found, which is consistent with the strongly Ising nature of the ground state., Comment: 16 pages, 12 figures, accepted for publication in Phys. Rev. B

Fifty years after Anderson's resonating valence-bond proposal, the spin-1/2 triangular-lattice Heisenberg antiferromagnet (TLHAF) remains the ultimate platform to explore highly entangled quantum spin states in proximity to magnetic order. Yb-based delafossites are ideal candidate TLHAF materials, which allow experimental access to the full range of applied in-plane magnetic fields. We perform a systematic neutron scattering study of CsYbSe$_2$, first proving the Heisenberg character of the interactions and quantifying the second-neighbour coupling. We then measure the complex evolution of the excitation spectrum, finding extensive continuum features near the 120$^{\circ}$-ordered state, throughout the 1/3-magnetization plateau and beyond this up to saturation. We perform cylinder matrix-product-state (MPS) calculations to obtain an unbiased numerical benchmark for the TLHAF and spectacular agreement with the experimental spectra. The measured and calculated longitudinal spectral functions reflect the role of multi-magnon bound and scattering states. These results provide valuable insight into unconventional field-induced spin excitations in frustrated quantum materials., Comment: 10 + 14 pages, 4 + 16 figures

Electrons at the border of localization generate exotic states of matter across all classes of strongly correlated electron materials and many other quantum materials with emergent functionality. Heavy electron metals are a model example, in which magnetic interactions arise from the opposing limits of localized and itinerant electrons. This remarkable duality is intimately related to the emergence of a plethora of novel quantum matter states such as unconventional superconductivity, electronic-nematic states, hidden order and most recently topological states of matter such as topological Kondo insulators and Kondo semimetals and putative chiral superconductors. The outstanding challenge is that the archetypal Kondo lattice model that captures the underlying electronic dichotomy is notoriously difficult to solve for real materials. Here we show, using the prototypical strongly-correlated antiferromagnet CeIn$_3$, that a multi-orbital periodic Anderson model embedded with input from ab initio bandstructure calculations can be reduced to a simple Kondo-Heisenberg model, which captures the magnetic interactions quantitatively. We validate this tractable Hamiltonian via high-resolution neutron spectroscopy that reproduces accurately the magnetic soft modes in CeIn$_3$, which are believed to mediate unconventional superconductivity. Our study paves the way for a quantitative understanding of metallic quantum states such as unconventional superconductivity.

In high-temperature cuprate superconductors, stripe order refers broadly to a coupled spin and charge modulation with a commensuration of eight and four lattice units, respectively. How this stripe order evolves across optimal doping remains a controversial question. Here we present a systematic resonant inelastic x-ray scattering (RIXS) study of weak charge correlations in La2-xSrxCuO4 (LSCO) and La1.8-xEu0.2SrxCuO4 (LESCO). Ultra high energy resolution experiments demonstrate the importance of the separation of inelastic and elastic scattering processes. Upon increasing doping x, the long-range temperature dependent stripe order is found to be replaced by short-range temperature independent correlations at a critical point xc = 0.15 distinct from the pseudogap critical doping. We argue that the doping and temperature independent short-range correlations originate from unresolved electron-phonon coupling that broadly peaks at the stripe ordering vector. In LSCO, long-range static stripe order vanishes in a quantum critical point around optimal doping.

We report an excellent realization of the highly non-classical incommensurate spin-density wave (SDW) state in the quantum frustrated antiferromagnetic insulator Cs$_2$CoBr$_4$. In contrast to the well-known Ising spin chain case, here the SDW is stabilized by virtue of competing planar in-chain anisotropies and frustrated interchain exchange. Adjacent to the SDW phase is a broad $m = 1/3$ magnetization plateau that can be seen as a commensurate locking of the SDW state into the up-up-down (UUD) spin structure. This represents the first example of long-sought SDW-UUD transition in triangular-type quantum magnets., Comment: 13 pages, 13 figures

The coupling of spin, charge and lattice degrees of freedom results in the emergence of novel states of matter across many classes of strongly correlated electron materials. A model example is unconventional superconductivity, which is widely believed to arise from the coupling of electrons via spin excitations. In cuprate high-temperature superconductors, the interplay of charge and spin degrees of freedom is also reflected in a zoo of charge and spin-density wave orders that are intertwined with superconductivity. A key question is whether the different types of density waves merely coexist or are indeed directly coupled. Here we use a novel neutron diffraction technique with superior beam-focusing that allows us to probe the subtle spin-density wave order in the prototypical high-temperature superconductor La1.88Sr0.12CuO4 under applied uniaxial pressure to demonstrate that it is immediately coupled with charge-density wave order. Our result shows that suitable models for high-temperature superconductivity must equally account for charge and spin degrees of freedom via uniaxial charge-spin stripe fluctuations.

Static stripe order is detrimental to superconductivity. Yet, it has been proposed that transverse stripe fluctuations may enhance the inter-stripe Josephson coupling and thus promote superconductivity. Direct experimental studies of stripe dynamics, however, remain difficult. From a strong-coupling perspective, transverse stripe fluctuations are realized in the form of dynamic "kinks" -- sideways shifting stripe sections. Here, we show how modest uniaxial pressure tuning reorganizes directional kink alignment. Our starting point is La$_{1.88}$Sr$_{0.12}$CuO$_4$, where transverse kink ordering results in a rotation of stripe order away from the crystal axis. Application of mild uniaxial pressure changes the ordering pattern and pins the stripe order to the crystal axis. This reordering occurs at a much weaker pressure than that to detwin the stripe domains and suggests a rather weak transverse stripe stiffness. Weak spatial stiffness and transverse quantum fluctuations are likely key prerequisites for stripes to coexist with superconductivity., Comment: Accepted in Nature Communications

Excitonic insulators are usually considered to form via the condensation of a soft charge mode of bound electron-hole pairs. This, however, presumes that the soft exciton is of spin-singlet character. Early theoretical considerations have also predicted a very distinct scenario, in which the condensation of magnetic excitons results in an antiferromagnetic excitonic insulator state. Here we report resonant inelastic x-ray scattering (RIXS) measurements of Sr3Ir2O7. By isolating the longitudinal component of the spectra, we identify a magnetic mode that is well-defined at the magnetic and structural Brillouin zone centers, but which merges with the electronic continuum in between these high-symmetry points and which decays upon heating concurrent with a decrease in the material's resistivity. We show that a bilayer Hubbard model, in which electron-hole pairs are bound by exchange interactions, consistently explains all the electronic and magnetic properties of Sr3Ir2O7 indicating that this material is a realization of the long-predicted antiferromagnetic excitonic insulators phase., Comment: accepted in Nature Communications; 6 pages main materials

Spinons are well-known as the elementary excitations of one-dimensional antiferromagnetic chains, but means to realize spinons in higher dimensions is the subject of intense research. Here, we use resonant x-ray scattering to study the layered trimer iridate Ba4Ir3O10, which shows no magnetic order down to 0.2 K. An emergent one-dimensional spinon continuum is observed that can be well-described by XXZ spin-1/2 chains with magnetic exchange of ~55 meV and a small Ising-like anisotropy. With 2% isovalent Sr doping, magnetic order appears below TN=130 K along with sharper excitations, indicating that the spinons become more confined in (Ba1-xSrx)4Ir3O10. We propose that the frustrated intra-trimer interactions effectively reduce the system into decoupled spin chains, the subtle balance of which can be easily tipped by perturbations such as chemical doping. Our results put Ba4Ir3O10 between the one-dimensional chain and two-dimensional quantum spin liquid scenarios, illustrating a new way to suppress magnetic order and realize fractional spinons., Comment: Accepted in Physical Review Letters; 5 pages not including references or supplementary

The rare earth nickelates RNiO3 are metallic at high temperatures and insulating and magnetically ordered at low temperatures. The low temperature phase has been predicted to be type II multiferroic, i.e. ferroelectric and magnetic order are coupled and occur simultaneously. Confirmation of those ideas has been inhibited by the absence of experimental data on single crystals. Here we report on Raman spectroscopic data of RNiO3 single crystals (R = Y, Er, Ho, Dy, Sm, Nd) for temperatures between 10 K and 1000 K. Entering the magnetically ordered phase we observe the appearance of a large number of additional vibrational modes, implying a breaking of inversion symmetry expected for multiferroic order., Comment: 10 pages, 8 figures

Revealing the predominant driving force behind symmetry breaking in correlated materials is sometimes a formidable task due to the intertwined nature of different degrees of freedom. This is the case for La2-xSrxNiO4+{\delta} in which coupled incommensurate charge and spin stripes form at low temperatures. Here, we use resonant X-ray photon correlation spectroscopy to study the temporal stability and domain memory of the charge and spin stripes in La2-xSrxNiO4+{\delta}. Although spin stripes are more spatially correlated, charge stripes maintain a better temporal stability against temperature change. More intriguingly, charge order shows robust domain memory with thermal cycling up to 250 K, far above the ordering temperature. These results demonstrate the pinning of charge stripes to the lattice and that charge condensation is the predominant factor in the formation of stripe orders in nickelates., Comment: 7 pages; accepted in Physical Review Letters

The Kitaev quantum spin liquid epitomizes an entangled topological state, for which two flavors of fractionalized low-energy excitations are predicted: the itinerant Majorana fermion and the Z2 gauge flux. Detection of these excitations remains challenging, because of their fractional quantum numbers and non-locality. It was proposed recently that fingerprints of fractional excitations are encoded in the phonon spectra of Kitaev quantum spin liquids through a novel fractional-excitation-phonon coupling. Here, we uncover this effect in $\alpha$-RuCl3 using inelastic X-ray scattering with meV resolution. At high temperature, we discover interlaced optical phonons intercepting a transverse acoustic phonon between 3 and 7 meV. Upon decreasing temperature, the optical phonons display a large intensity enhancement near the Kitaev energy, JK~8 meV, that coincides with a giant acoustic phonon softening near the Z2 gauge flux energy scale. This fractional excitation induced phonon anomalies uncover the key ingredient of the quantum thermal Hall effect in $\alpha$-RuCl3 and demonstrates a proof-of-principle method to detect fractional excitations in topological quantum materials.

Topological states in quantum materials are defined by non-trivial topological invariants, such as the Chern number, which are properties of their bulk wave functions. A remarkable consequence of topological wave functions is the emergence of edge modes, a phenomenon known as bulk-edge correspondence, that gives rise to quantized or chiral physical properties. While edge modes are widely presented as signatures of non-trivial topology, how bulk wave functions can manifest explicitly topological properties remains unresolved. Here, using high-resolution inelastic x-ray spectroscopy (IXS) combined with first principles calculations, we report experimental signatures of chiral wave functions in the bulk phonon spectrum of BaPtGe, which we show to host a previously undiscovered twofold degenerate quadruple Weyl node. The chirality of the degenerate phononic wave function yields a non-trivial phonon dynamical structure factor, S(Q,$\omega$), along high-symmetry directions, that is in excellent agreement with numerical and model calculations. Our results establish IXS as a powerful tool to uncover topological wave functions, providing a key missing ingredient in the study of topological quantum matter., Comment: Data and movies that support the findings of this study are available from the corresponding author on reasonable request

The discovery of superconductivity in a $d^{9-{\delta}}$ nickelate has inspired disparate theoretical perspectives regarding the essential physics of this class of materials. A key issue is the magnitude of the magnetic superexchange, which relates to whether cuprate-like high-temperature nickelate superconductivity could be realized. We address this question using Ni L-edge and O K-edge spectroscopy of the reduced trilayer nickelate $d^{9-1/3}$ La4Ni3O8 and associated theoretical modeling. A magnon energy scale of ~80 meV resulting from a nearest-neighbor magnetic exchange of $J = 69(4)4$ meV is observed, proving that $d^{9-{\delta}}$ nickelates can host a large superexchange. This value, along with that of the Ni-O hybridization estimated from our O K-edge data, implies that trilayer nickelates represent an intermediate case between the infinite-layer nickelates and the cuprates, and suggests that they represent a promising route towards higher-temperature nickelate superconductivity., Comment: 7 pages not including supplmentary material; To appear in Physical Review Letters

Although ultrafast manipulation of magnetism holds great promise for new physical phenomena and applications, targeting specific states is held back by our limited understanding of how magnetic correlations evolve on ultrafast timescales. Using ultrafast resonant inelastic x-ray scattering we demonstrate that femtosecond laser pulses can excite transient magnons at large wavevectors in gapped antiferromagnets, and that they persist for several picoseconds which is opposite to what is observed in nearly gapless magnets. Our work suggests that materials with isotropic magnetic interactions are preferred to achieve rapid manipulation of magnetism., Comment: 6 pages, 4 figures, not including supplemental material; accepted in PNAS

The discovery of charge-density wave (CDW)-related effects in the resonant inelastic x-ray scattering (RIXS) spectra of cuprates holds the tantalizing promise of clarifying the interactions that stabilize the electronic order. Here, we report a comprehensive RIXS study of La2-xSrxCuO4 (LSCO) finding that CDW effects persist up to a remarkably high doping level of x = 0.21 before disappearing at x = 0.25. The inelastic excitation spectra remain essentially unchanged with doping despite crossing a topological transition in the Fermi surface. This indicates that the spectra contain little or no direct coupling to electronic excitations near the Fermi surface, rather they are dominated by the resonant cross-section for phonons and CDW-induced phonon-softening. We interpret our results in terms of a CDW that is generated by strong correlations and a phonon response that is driven by the CDW-induced modification of the lattice., Comment: 7 pages including references in long format

The unconventional normal-state properties of the cuprates are often discussed in terms of emergent electronic order that onsets below a putative critical doping of xc = 0.19. Charge-density wave (CDW) correlations represent one such order; however, experimental evidence for such order generally spans a limited range of doping that falls short of the critical value xc, leading to questions regarding its essential relevance. Here, we use x-ray diffraction to demonstrate that CDW correlations in La2-xSrxCuO4 persist up to a doping of at least x = 0.21. The correlations show strong changes through the superconducting transition, but no obvious discontinuity through xc = 0.19, despite changes in Fermi surface topology and electronic transport at this doping. These results demonstrate the interaction between CDWs and superconductivity even in overdoped cuprates and prompt a reconsideration of the role of CDW correlations in the high-temperature cuprate phase diagram., Comment: 8 pages + 5 pages of supplemental material; accepted in npj Quantum Materials

Quantum materials that feature magnetic long-range order often reveal complex phase diagrams when localized electrons become mobile. In many materials magnetism is rapidly suppressed as electronic charges dissolve into the conduction band. In materials where magnetism persists, it is unclear how the magnetic properties are affected. Here we study the evolution of the magnetic structure in Nd(1-x)Ce(x)CoIn(5) from the localized to the highly itinerant limit. We observe two magnetic ground states inside a heavy-fermion phase that are detached from unconventional superconductivity. The presence of two different magnetic phases provides evidence that increasing charge delocalization affects the magnetic interactions via anisotropic band hybridization.

Negative thermal expansion is an unusual phenomenon appearing in only a handful of materials, but pursuit and mastery of the phenomenon holds great promise for applications across disciplines and industries. Here we report use of X-ray spectroscopy and diffraction to investigate the 4f-electronic properties in Y-doped SmS and employ the Kondo volume collapse model to interpret the results. Our measurements reveal an unparalleled decrease of the bulk Sm valence by over 20% at low temperatures in the mixed-valent golden phase, which we show is caused by a strong coupling between an emergent Kondo lattice state and a large isotropic volume change. The amplitude and temperature range of the negative thermal expansion appear strongly dependent on the Y concentration and the associated chemical disorder, providing control over the observed effect. This finding opens new avenues for the design of Kondo lattice materials with tunable, giant and isotropic negative thermal expansion.

Many remarkable properties of quantum materials emerge from states with intricate coupling between the charge, spin and orbital degrees of freedom. Ultrafast photo-excitations of these materials hold great promise for understanding and controlling the properties of these states. Here we introduce time-resolved resonant inelastic X-ray scattering (trRIXS) as a means of measuring charge, spin and orbital excitations out of equilibrium. These excitations encode the correlations and interactions that determine the detailed properties of the states generated. After outlining the basic principles and instrumentation of tr-RIXS, we review our first observations of transient antiferromagnetic correlations in quasi-two dimensions in a photo-excited Mott insulator and present possible future routes of this fast-developing technique. The increasing number of X-ray free electron laser facilities not only enables tackling long-standing fundamental scientific problems, but also promises to unleash novel inelastic X-ray scattering spectroscopies, Comment: 14 pages, 5 figures, supplementary information; Accepted in Philosophical Transactions A

Nd0.05Ce0.95CoIn5 features a magnetic field-driven quantum phase transition that separates two antiferromagnetic phases with an identical magnetic structure inside the superconducting condensate. Using neutron diffraction we demonstrate that the population of the two magnetic domains in the two phases is affected differently by the rotation of the magnetic field in the tetragonal basal plane. In the low-field SDW-phase the domain population is only weakly affected while in the high-field Q-phase they undergo a sharp switch for fields around the a-axis. Our results provide evidence that the anisotropic spin susceptibility in both phases arises ultimately from spin-orbit interactions but are qualitatively different in the two phases. This provides evidence that the electronic structure is changed at the quantum phase transition, which yields a modified coupling between magnetism and superconductivity in the Q-phase.

Unconventional superconductivity in many materials is believed to be mediated by magnetic fluctuations. It is an open question how magnetic order can emerge from a superconducting condensate and how it competes with the magnetic spin resonance in unconventional superconductors. Here we study a model d-wave superconductor that develops spin-density wave order, and find that the spin resonance is unaffected by the onset of static magnetic order. This result suggests a scenario, in which the resonance in Nd0.05Ce0.95CoIn5 is a longitudinal mode with fluctuating moments along the ordered magnetic moments.

The recent discovery of the topologically protected surface states in the beta-phase of PdBi2 has reignited the research interest in this class of superconductors. Here, we show results of our muon spin relaxation and rotation (muSR) measurements carried out to investigate the superconducting and magnetic properties and the topological effect in the superconducting ground state of beta-PdBi2. Zero-field muSR data reveal that no sizeable spontaneous magnetization arises with the onset of superconductivity implying that the time reversal symmetry is preserved in the superconducting state of beta-PdBi2. Further, a strong diamagnetic shift of the applied field has been observed in the transverse-field (TF) muSR experiments, indicating that any triplet-pairing channel, if present, does not dominate the superconducting condensate. Using TF-muSR, we estimate that the magnetic penetration depth is 263(10) nm at zero temperature. Temperature dependence of the magnetic penetration depth provides evidence for the existence of a nodeless single s-wave type isotropic energy gap of 0.78(1) meV at zero temperature. Our results further suggest that the topologically protected surface states have no effect on the bulk of the superconductor., Comment: accepted for publication as a Rapid Communication in Physical Review B

Superconductivity and magnetic order strongly compete in many conventional superconductors, at least partly because both tend to gap the Fermi surface. In magnetically-ordered conventional superconductors, the competition between these cooperative phenomena leads to anomalies at magnetic and superconducting phase boundaries. Here we reveal that in Pr2Pt3Ge5 superconducting and multiple magnetic order are intertwined within the same HT-phase space, but remain completely decoupled. Our thermal conductivity measurements provide evidence for normal electrons in the superconducting phase from which magnetic order emerges with negligible coupling to electron bands that contribute to superconductivity.

We investigated the crystal structure and lattice excitations of the ternary intermetallic stannide Ca3Ir4Sn13 using neutron and x-ray scattering techniques. For T > T* ~ 38 K the x-ray diffraction data can be satisfactorily refined using the space group Pm-3n. Below T* the crystal structure is modulated with a propagation vector of q = (1/2, 1/2, 0). This may arise from a merohedral twinning in which three tetragonal domains overlap to mimic a higher symmetry, or from a doubling of the cubic unit cell. Neutron diffraction and neutron spectroscopy results show that the structural transition at T* is of a second-order, and that it is well described by mean-field theory. Inelastic neutron scattering data point towards a displacive structural transition at T* arising from the softening of a low-energy phonon mode with an energy gap of Delta(120 K) = 1.05 meV. Using density functional theory the soft phonon mode is identified as a 'breathing' mode of the Sn12 icosahedra and is consistent with the thermal ellipsoids of the Sn2 atoms found by single crystal diffraction data.

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.

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.