A quantum magnetic analogue to the critical point of water.

At the liquid-gas phase transition in water, the density has a discontinuity at atmospheric pressure; however, the line of these first-order transitions defined by increasing the applied pressure terminates at the critical point1, a concept ubiquitous in statistical thermodynamics2. In correlated quantum materials, it was predicted3 and then confirmed experimentally4,5 that a critical point terminates the line of Mott metal-insulator transitions, which are also first-order with a discontinuous charge carrier density. In quantum spin systems, continuous quantum phase transitions6 have been controlled by pressure7,8, applied magnetic field9,10 and disorder11, but discontinuous quantum phase transitions have received less attention. The geometrically frustrated quantum antiferromagnet SrCu2(BO3)2 constitutes a near-exact realization of the paradigmatic Shastry-Sutherland model12-14 and displays exotic phenomena including magnetization plateaus15, low-lying bound-state excitations16, anomalous thermodynamics17 and discontinuous quantum phase transitions18,19. Here we control both the pressure and the magnetic field applied to SrCu2(BO3)2 to provide evidence of critical-point physics in a pure spin system. We use high-precision specific-heat measurements to demonstrate that, as in water, the pressure-temperature phase diagram has a first-order transition line that separates phases with different local magnetic energy densities, and that terminates at an Ising critical point. We provide a quantitative explanation of our data using recently developed finite-temperature tensor-network methods17,20-22. These results further our understanding of first-order quantum phase transitions in quantum magnetism, with potential applications in materials where anisotropic spin interactions produce the topological properties23,24 that are useful for spintronic applications.

Evidence of a Coulomb-Interaction-Induced Lifshitz Transition and Robust Hybrid Weyl Semimetal in T_{d}-MoTe_{2}.

Using soft x-ray angle-resolved photoemission spectroscopy we probed the bulk electronic structure of T_{d}-MoTe_{2}. We found that on-site Coulomb interaction leads to a Lifshitz transition, which is essential for a precise description of the electronic structure. A hybrid Weyl semimetal state with a pair of energy bands touching at both type-I and type-II Weyl nodes is indicated by comparing the experimental data with theoretical calculations. Unveiling the importance of Coulomb interaction opens up a new route to comprehend the unique properties of MoTe_{2}, and is significant for understanding the interplay between correlation effects, strong spin-orbit coupling and superconductivity in this van der Waals material.

Time-Reversal Symmetry Breaking in Re-Based Superconductors.

To trace the origin of time-reversal symmetry breaking (TRSB) in Re-based superconductors, we performed comparative muon-spin rotation and relaxation (µSR) studies of superconducting noncentrosymmetric Re_{0.82}Nb_{0.18} (T_{c}=8.8 K) and centrosymmetric Re (T_{c}=2.7 K). In Re_{0.82}Nb_{0.18}, the low-temperature superfluid density and the electronic specific heat evidence a fully gapped superconducting state, whose enhanced gap magnitude and specific-heat discontinuity suggest a moderately strong electron-phonon coupling. In both Re_{0.82}Nb_{0.18} and pure Re, the spontaneous magnetic fields revealed by zero-field µSR below T_{c} indicate time-reversal symmetry breaking and thus unconventional superconductivity. The concomitant occurrence of TRSB in centrosymmetric Re and noncentrosymmetric ReT (T=transition metal), yet its preservation in the isostructural noncentrosymmetric superconductors Mg_{10}Ir_{19}B_{16} and Nb_{0.5}Os_{0.5}, strongly suggests that the local electronic structure of Re is crucial for understanding the TRSB superconducting state in Re and ReT. We discuss the superconducting order parameter symmetries that are compatible with the experimental observations.

Pauling Entropy, Metastability, and Equilibrium in Dy_{2}Ti_{2}O_{7} Spin Ice.

Determining the fate of the Pauling entropy in the classical spin ice material Dy_{2}Ti_{2}O_{7} with respect to the third law of thermodynamics has become an important test case for understanding the existence and stability of ice-rule states in general. The standard model of spin ice-the dipolar spin ice model-predicts an ordering transition at T≈0.15 K, but recent experiments by Pomaranski et al. suggest an entropy recovery over long timescales at temperatures as high as 0.5 K, much too high to be compatible with the theory. Using neutron scattering and specific heat measurements at low temperatures and with long timescales (0.35 K/10^{6} s and 0.5 K/10^{5} s, respectively) on several isotopically enriched samples, we find no evidence of a reduction of ice-rule correlations or spin entropy. High-resolution simulations of the neutron structure factor show that the spin correlations remain well described by the dipolar spin ice model at all temperatures. Furthermore, by careful consideration of hyperfine contributions, we conclude that the original entropy measurements of Ramirez et al. are, after all, essentially correct: The short-time relaxation method used in that study gives a reasonably accurate estimate of the equilibrium spin ice entropy due to a cancellation of contributions.

Complementary Response of Static Spin-Stripe Order and Superconductivity to Nonmagnetic Impurities in Cuprates.

We report muon-spin rotation and neutron-scattering experiments on nonmagnetic Zn impurity effects on the static spin-stripe order and superconductivity of the La214 cuprates. Remarkably, it was found that, for samples with hole doping x≈1/8, the spin-stripe ordering temperature T_{so} decreases linearly with Zn doping y and disappears at y≈4%, demonstrating a high sensitivity of static spin-stripe order to impurities within a CuO_{2} plane. Moreover, T_{so} is suppressed by Zn in the same manner as the superconducting transition temperature T_{c} for samples near optimal hole doping. This surprisingly similar sensitivity suggests that the spin-stripe order is dependent on intertwining with superconducting correlations.

Distinct Evolutions of Weyl Fermion Quasiparticles and Fermi Arcs with Bulk Band Topology in Weyl Semimetals.

The Weyl semimetal phase is a recently discovered topological quantum state of matter characterized by the presence of topologically protected degeneracies near the Fermi level. These degeneracies are the source of exotic phenomena, including the realization of chiral Weyl fermions as quasiparticles in the bulk and the formation of Fermi arc states on the surfaces. Here, we demonstrate that these two key signatures show distinct evolutions with the bulk band topology by performing angle-resolved photoemission spectroscopy, supported by first-principles calculations, on transition-metal monophosphides. While Weyl fermion quasiparticles exist only when the chemical potential is located between two saddle points of the Weyl cone features, the Fermi arc states extend in a larger energy scale and are robust across the bulk Lifshitz transitions associated with the recombination of two nontrivial Fermi surfaces enclosing one Weyl point into a single trivial Fermi surface enclosing two Weyl points of opposite chirality. Therefore, in some systems (e.g., NbP), topological Fermi arc states are preserved even if Weyl fermion quasiparticles are absent in the bulk. Our findings not only provide insight into the relationship between the exotic physical phenomena and the intrinsic bulk band topology in Weyl semimetals, but also resolve the apparent puzzle of the different magnetotransport properties observed in TaAs, TaP, and NbP, where the Fermi arc states are similar.

Negative oxygen isotope effect on the static spin stripe order in superconducting La(2-x)Ba(x)CuO(4) (x=1/8) observed by muon-spin rotation.

Large negative oxygen-isotope (^{16}O and ^{18}O) effects (OIEs) on the static spin-stripe-ordering temperature T_{so} and the magnetic volume fraction V_{m} were observed in La_{2-x}Ba_{x}CuO_{4}(x=1/8) by means of muon-spin-rotation experiments. The corresponding OIE exponents were found to be α_{T_{so}}=-0.57(6) and α_{V_{m}}=-0.71(9), which are sign reversed to α_{T_{c}}=0.46(6) measured for the superconducting transition temperature T_{c}. This indicates that the electron-lattice interaction is involved in the stripe formation and plays an important role in the competition between bulk superconductivity and static stripe order in the cuprates.

Correlated decay of triplet excitations in the Shastry-Sutherland compound SrCu2(BO3)2.

The temperature dependence of the gapped triplet excitations (triplons) in the 2D Shastry-Sutherland quantum magnet SrCu(2)(BO(3))(2) is studied by means of inelastic neutron scattering. The excitation amplitude rapidly decreases as a function of temperature, while the integrated spectral weight can be explained by an isolated dimer model up to 10 K. Analyzing this anomalous spectral line shape in terms of damped harmonic oscillators shows that the observed damping is due to a two-component process: one component remains sharp and resolution limited while the second broadens. We explain the underlying mechanism through a simple yet quantitatively accurate model of correlated decay of triplons: an excited triplon is long lived if no thermally populated triplons are nearby but decays quickly if there are. The phenomenon is a direct consequence of frustration induced triplon localization in the Shastry-Sutherland lattice.

Two-dimensional superfluid density in an alkali metal-organic solvent intercalated iron selenide superconductor Li(C5H5N)0.2Fe2Se2.

We report the low-temperature electronic and magnetic properties of the alkali metal-organic solvent intercalated iron selenide superconductor Li(C5H5N)0.2Fe2Se2 using muon-spin-spectroscopy measurements. The zero-field muon spin relaxation (µSR) results indicate that nearly half of the sample is magnetically ordered and spatially phase separated from the superconducting region. The transverse-field µSR results reveal that the superfluid density of Li(C5H5N)0.2Fe2Se2 is two dimensional in nature. The temperature dependence of the penetration depth λ(T) can be explained using a two-gap s-wave model. This implies that, despite the 2D nature of the superfluid density, the symmetry of the superconducting gap remains unaltered to the parent compound FeSe.

1D to 2D Na+ ion diffusion inherently linked to structural transitions in Na0.7CoO2.

We report the observation of a stepwise "melting" of the low-temperature Na-vacancy order in the layered transition-metal oxide Na0.7CoO2. High-resolution neutron powder diffraction analysis indicates the existence of two first-order structural transitions, one at T1≈290 K followed by a second at T2≈400 K. Detailed analysis strongly suggests that both transitions are linked to changes in the Na mobility. Our data are consistent with a two-step disappearance of Na-vacancy order through the successive opening of first quasi-1D (T1>T>T2) and then 2D (T>T2) Na diffusion paths. These results shed new light on previous, seemingly incompatible, experimental interpretations regarding the relationship between Na-vacancy order and Na dynamics in this material. They also represent an important step towards the tuning of physical properties and the design of tailored functional materials through an improved control and understanding of ionic diffusion.

Fate of charge order in overdoped La-based cuprates.

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 study of weak charge correlations in La2-xSrxCuO4 and La1.8-xEu0.2SrxCuO4. Ultra high energy resolution experiments demonstrate the importance of the separation of inelastic and elastic scattering processes. Long-range temperature-dependent stripe order is only found below optimal doping. At higher doping, short-range temperature-independent correlations are present up to the highest doping measured. This transformation is distinct from and preempts 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 La2-xSrxCuO4, long-range static stripe order vanishes around optimal doping and we discuss both quantum critical and crossover scenarios.

Hidden magnetism uncovered in a charge ordered bilayer kagome material ScV6Sn6.

Charge ordered kagome lattices have been demonstrated to be intriguing platforms for studying the intertwining of topology, correlation, and magnetism. The recently discovered charge ordered kagome material ScV6Sn6 does not feature a magnetic groundstate or excitations, thus it is often regarded as a conventional paramagnet. Here, using advanced muon-spin rotation spectroscopy, we uncover an unexpected hidden magnetism of the charge order. We observe an enhancement of the internal field width sensed by the muon ensemble, which takes place within the charge ordered state. More importantly, the muon spin relaxation rate below the charge ordering temperature is substantially enhanced by applying an external magnetic field. Taken together with the hidden magnetism found in AV3Sb5 (A = K, Rb, Cs) and FeGe kagome systems, our results suggest ubiqitous time-reversal symmetry-breaking in charge ordered kagome lattices.

Coexistence of magnetism and superconductivity in the iron-based compound Cs0.8(FeSe0.98)2.

We report on muon-spin rotation and relaxation (µSR), electrical resistivity, magnetization and differential scanning calorimetry measurements performed on a high-quality single crystal of Cs(0.8)(FeSe(0.98))(2). Whereas our transport and magnetization data confirm the bulk character of the superconducting state below T(c)=29.6(2) K, the µSR data indicate that the system is magnetic below T(N)=478.5(3) K, where a first-order transition occurs. The first-order character of the magnetic transition is confirmed by differential scanning calorimetry data. Taken all together, these data indicate in Cs(0.8)(FeSe(0.98))(2) a microscopic coexistence between the superconducting phase and a strong magnetic phase. The observed T(N) is the highest reported to date for a magnetic superconductor.

Temperature and pressure evolution of the crystal structure of A(x)(Fe(1-y)Se)2 (A = Cs, Rb, K) studied by synchrotron powder diffraction.

Temperature-dependent synchrotron powder diffraction on Cs(0.83)(Fe(0.86)Se)(2) revealed first-order I4/m to I4/mmm structural transformation around 216 °C associated with a disorder of the Fe vacancies. Irreversibility observed during the transition is likely associated with a mobility of the intercalated alkali atoms. Pressure-dependent synchrotron powder diffraction on Cs(0.83)(Fe(1-y)Se)(2), Rb(0.85)(Fe(1-y)Se)(2), and K(0.8)(Fe(1-y)Se)(2) (y ~ 0.14) indicated that the I4/m superstructure reflections are present up to pressures of 120 kbar. This may indicate that the ordering of the Fe vacancies is present in both superconducting and nonsuperconductive states.

Synthesis and crystal growth of Cs(0.8)(FeSe(0.98))(2): a new iron-based superconductor with T(c) = 27 K.

We report on the synthesis of large single crystals of a new FeSe layer superconductor Cs(0.8)(FeSe(0.98))(2). X-ray powder diffraction, neutron powder diffraction and magnetization measurements have been used to compare the crystal structure and the magnetic properties of Cs(0.8)(FeSe(0.98))(2) with those of the recently discovered potassium intercalated system K(x)Fe(2)Se(2). The new compound, Cs(0.8)(FeSe(0.98))(2), shows a slightly lower superconducting transition temperature (T(c) = 27.4 K) in comparison to 29.5 in (K(0.8)(FeSe(0.98))(2)). The volume of the crystal unit cell increases by replacing K by Cs-the c parameter grows from 14.1353(13) to 15.2846(11) Å. For the alkali metal intercalated layered compounds known so far, (K(0.8)Fe(2)Se(2) and Cs(0.8)(FeSe(0.98))(2)), the T(c) dependence on the anion height (distance between Fe layers and Se layers) was found to be analogous to those reported for As-containing Fe superconductors and Fe(Se(1 - x)Ch(x)), where Ch = Te, S.

Giant magnetoresistance and topological Hall effect in the EuGa4antiferromagnet.

We report on systematic temperature- and magnetic field-dependent studies of the EuGa4binary compound, which crystallizes in a centrosymmetric tetragonal BaAl4-type structure with space groupI4/mmm. The electronic properties of EuGa4single crystals, with an antiferromagnetic (AFM) transition atTN∼ 16.4 K, were characterized via electrical resistivity and magnetization measurements. A giant nonsaturating magnetoresistance was observed at low temperatures, reaching∼7×104% at 2 K in a magnetic field of 9 T. In the AFM state, EuGa4undergoes a series of metamagnetic transitions in an applied magnetic field, clearly manifested in its field-dependent electrical resistivity. BelowTN, in the ∼4-7 T field range, we observe also a clear hump-like anomaly in the Hall resistivity which is part of the anomalous Hall resistivity. We attribute such a hump-like feature to the topological Hall effect, usually occurring in noncentrosymmetric materials known to host topological spin textures (as e.g., magnetic skyrmions). Therefore, the family of materials with a tetragonal BaAl4-type structure, to which EuGa4and EuAl4belong, seems to comprise suitable candidates on which one can study the interplay among correlated-electron phenomena (such as charge-density wave or exotic magnetism) with topological spin textures and topologically nontrivial bands.

Two-dimensional orbital-like magnetic order in the high-temperature La(2-x)Sr(x)CuO4 superconductor.

In high-temperature copper oxide superconductors, a novel magnetic order associated with the pseudogap phase has been identified in two different cuprate families over a wide region of temperature and doping. We report here the observation below 120 K of a similar magnetic ordering in the archetypal cuprate La(2-x)Sr(x)CuO4 (LSCO) system for x=0.085. In contrast with the previous reports, the magnetic ordering in LSCO is only short range with an in-plane correlation length of ∼10 A and is bidimensional (2D). Such a less pronounced order suggests an interaction with other electronic instabilities. In particular, LSCO also exhibits a strong tendency towards stripes ordering at the expense of the superconducting state.

Direct observation of impurity-induced magnetism in a spin-(1/2) antiferromagnetic Heisenberg two-leg spin ladder.

Nuclear magnetic resonance and magnetization measurements were used to probe the magnetic features of single-crystalline Bi(Cu(1-x)Zn(x))(2)PO(6) with 00 and we present clear evidence for a temperature-dependent variation of the local magnetization close to the Zn sites. The generic nature of this observation is indicated by results of model calculations on appropriate spin systems of limited size employing quantum Monte Carlo methods.

Pressure induced static magnetic order in superconducting FeSe1-x.

We report on a detailed investigation of the electronic phase diagram of FeSe1-x under pressures up to 1.4 GPa by means of ac magnetization and muon-spin rotation. At a pressure approximately 0.8 GPa the nonmagnetic and superconducting FeSe1-x enters a region where static magnetic order is realized above T{c} and bulk superconductivity coexists and competes on short length scales with the magnetic order below T{c}. For even higher pressures an enhancement of both the magnetic and the superconducting transition temperatures as well as of the corresponding order parameters is observed. These exceptional properties make FeSe1-x to be one of the most interesting superconducting systems investigated extensively at present.

Evolution of two-gap behavior of the superconductor FeSe1-x.

The superfluid density, rho{s}, of the iron chalcogenide superconductor, FeSe1-x, was studied as a function of pressure by means of muon-spin rotation. The analysis of rho{s}(T) within the two-gap scheme reveals that the effect on both, the transition temperature T{c} and rho{s}(0), is entirely determined by the band(s) where the large superconducting gap develops, while the band(s) with the small gap become practically unaffected.