Time-reversal symmetry-breaking charge order in a kagome superconductor.

The kagome lattice1, which is the most prominent structural motif in quantum physics, benefits from inherent non-trivial geometry so that it can host diverse quantum phases, ranging from spin-liquid phases, to topological matter, to intertwined orders2-8 and, most rarely, to unconventional superconductivity6,9. Recently, charge sensitive probes have indicated that the kagome superconductors AV3Sb5 (A = K, Rb, Cs)9-11 exhibit unconventional chiral charge order12-19, which is analogous to the long-sought-after quantum order in the Haldane model20 or Varma model21. However, direct evidence for the time-reversal symmetry breaking of the charge order remains elusive. Here we use muon spin relaxation to probe the kagome charge order and superconductivity in KV3Sb5. We observe a noticeable enhancement of the internal field width sensed by the muon ensemble, which takes place just below the charge ordering temperature and persists into the superconducting state. Notably, the muon spin relaxation rate below the charge ordering temperature is substantially enhanced by applying an external magnetic field. We further show the multigap nature of superconductivity in KV3Sb5 and that the [Formula: see text] ratio (where Tc is the superconducting transition temperature and λab is the magnetic penetration depth in the kagome plane) is comparable to those of unconventional high-temperature superconductors. Our results point to time-reversal symmetry-breaking charge order intertwining with unconventional superconductivity in the correlated kagome lattice.

Designing the stripe-ordered cuprate phase diagram through uniaxial-stress.

The ability to efficiently control charge and spin in the cuprate high-temperature superconductors is crucial for fundamental research and underpins technological development. Here, we explore the tunability of magnetism, superconductivity, and crystal structure in the stripe phase of the cuprate La[Formula: see text]Ba[Formula: see text]CuO[Formula: see text], with [Formula: see text] = 0.115 and 0.135, by employing temperature-dependent (down to 400 mK) muon-spin rotation and AC susceptibility, as well as X-ray scattering experiments under compressive uniaxial stress in the CuO[Formula: see text] plane. A sixfold increase of the three-dimensional (3D) superconducting critical temperature [Formula: see text] and a full recovery of the 3D phase coherence is observed in both samples with the application of extremely low uniaxial stress of [Formula: see text]0.1 GPa. This finding demonstrates the removal of the well-known 1/8-anomaly of cuprates by uniaxial stress. On the other hand, the spin-stripe order temperature as well as the magnetic fraction at 400 mK show only a modest decrease under stress. Moreover, the onset temperatures of 3D superconductivity and spin-stripe order are very similar in the large stress regime. However, strain produces an inhomogeneous suppression of the spin-stripe order at elevated temperatures. Namely, a substantial decrease of the magnetic volume fraction and a full suppression of the low-temperature tetragonal structure is found under stress, which is a necessary condition for the development of the 3D superconducting phase with optimal [Formula: see text]. Our results evidence a remarkable cooperation between the long-range static spin-stripe order and the underlying crystalline order with the three-dimensional fully coherent superconductivity. Overall, these results suggest that the stripe- and the SC order may have a common physical mechanism.

Superconductivity in a unique type of copper oxide.

The mechanism of superconductivity in cuprates remains one of the big challenges of condensed matter physics. High-T c cuprates crystallize into a layered perovskite structure featuring copper oxygen octahedral coordination. Due to the Jahn Teller effect in combination with the strong static Coulomb interaction, the octahedra in high-T c cuprates are elongated along the c axis, leading to a 3dx 2-y 2 orbital at the top of the band structure wherein the doped holes reside. This scenario gives rise to 2D characteristics in high-T c cuprates that favor d-wave pairing symmetry. Here, we report superconductivity in a cuprate Ba2CuO4-y , wherein the local octahedron is in a very exceptional compressed version. The Ba2CuO4-y compound was synthesized at high pressure at high temperatures and shows bulk superconductivity with critical temperature (T c ) above 70 K at ambient conditions. This superconducting transition temperature is more than 30 K higher than the T c for the isostructural counterparts based on classical La2CuO4 X-ray absorption measurements indicate the heavily doped nature of the Ba2CuO4-y superconductor. In compressed octahedron, the 3d3z 2-r 2 orbital will be lifted above the 3dx 2-y 2 orbital, leading to significant 3D nature in addition to the conventional 3dx 2-y 2 orbital. This work sheds important light on advancing our comprehensive understanding of the superconducting mechanism of high T c in cuprate materials.

Using Uniaxial Stress to Probe the Relationship between Competing Superconducting States in a Cuprate with Spin-stripe Order.

We report muon spin rotation and magnetic susceptibility experiments on in-plane stress effects on the static spin-stripe order and superconductivity in the cuprate system La_{2-x}Ba_{x}CuO_{4} with x=0.115. An extremely low uniaxial stress of ∼0.1 GPa induces a substantial decrease in the magnetic volume fraction and a dramatic rise in the onset of 3D superconductivity, from ∼10 to 32 K; however, the onset of at-least-2D superconductivity is much less sensitive to stress. These results show not only that large-volume-fraction spin-stripe order is anticorrelated with 3D superconducting coherence but also that these states are energetically very finely balanced. Moreover, the onset temperatures of 3D superconductivity and spin-stripe order are very similar in the large stress regime. These results strongly suggest a similar pairing mechanism for spin-stripe order and the spatially modulated 2D and uniform 3D superconducting orders, imposing an important constraint on theoretical models.

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.

Mutual Independence of Critical Temperature and Superfluid Density under Pressure in Optimally Electron-Doped Superconducting LaFeAsO(1-x)F(x).

The superconducting properties of LaFeAsO(1-x)F(x) under conditions of optimal electron doping are investigated upon the application of external pressure up to ∼23 kbar. Measurements of muon-spin spectroscopy and dc magnetometry evidence a clear mutual independence between the critical temperature T(c) and the low-temperature saturation value for the ratio n(s)/m(*) (superfluid density over effective band mass of Cooper pairs). Remarkably, a dramatic increase of ∼30% is reported for n(s)/m(*) at the maximum pressure value while T(c) is substantially unaffected in the whole accessed experimental window. We argue and demonstrate that the explanation for the observed results must take the effect of nonmagnetic impurities on multiband superconductivity into account. In particular, the unique possibility to modify the ratio between intraband and interband scattering rates by acting on structural parameters while keeping the amount of chemical disorder constant is a striking result of our proposed model.

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.

Kondo screening in a Majorana metal.

Kondo impurities provide a nontrivial probe to unravel the character of the excitations of a quantum spin liquid. In the S = 1/2 Kitaev model on the honeycomb lattice, Kondo impurities embedded in the spin-liquid host can be screened by itinerant Majorana fermions via gauge-flux binding. Here, we report experimental signatures of metallic-like Kondo screening at intermediate temperatures in the Kitaev honeycomb material α-RuCl3 with dilute Cr3+ (S = 3/2) impurities. The static magnetic susceptibility, the muon Knight shift, and the muon spin-relaxation rate all feature logarithmic divergences, a hallmark of a metallic Kondo effect. Concurrently, the linear coefficient of the magnetic specific heat is large in the same temperature regime, indicating the presence of a host Majorana metal. This observation opens new avenues for exploring uncharted Kondo physics in insulating quantum magnets.

In situ uniaxial pressure cell for x-ray and neutron scattering experiments.

We present an in situ uniaxial pressure device optimized for small angle x-ray and neutron scattering experiments at low-temperatures and high magnetic fields. A stepper motor generates force, which is transmitted to the sample via a rod with an integrated transducer that continuously monitors the force. The device has been designed to generate forces up to 200 N in both compressive and tensile configurations, and a feedback control allows operating the system in a continuous-pressure mode as the temperature is changed. The uniaxial pressure device can be used for various instruments and multiple cryostats through simple and exchangeable adapters. It is compatible with multiple sample holders, which can be easily changed depending on the sample properties and the desired experiment and allow rapid sample changes.

Tunable unconventional kagome superconductivity in charge ordered RbV3Sb5 and KV3Sb5.

Unconventional superconductors often feature competing orders, small superfluid density, and nodal electronic pairing. While unusual superconductivity has been proposed in the kagome metals AV3Sb5, key spectroscopic evidence has remained elusive. Here we utilize pressure-tuned and ultra-low temperature muon spin spectroscopy to uncover the unconventional nature of superconductivity in RbV3Sb5 and KV3Sb5. At ambient pressure, we observed time-reversal symmetry breaking charge order below [Formula: see text] 110 K in RbV3Sb5 with an additional transition at [Formula: see text] 50 K. Remarkably, the superconducting state displays a nodal energy gap and a reduced superfluid density, which can be attributed to the competition with the charge order. Upon applying pressure, the charge-order transitions are suppressed, the superfluid density increases, and the superconducting state progressively evolves from nodal to nodeless. Once optimal superconductivity is achieved, we find a superconducting pairing state that is not only fully gapped, but also spontaneously breaks time-reversal symmetry. Our results point to unprecedented tunable nodal kagome superconductivity competing with time-reversal symmetry-breaking charge order and offer unique insights into the nature of the pairing state.

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.

Local spectroscopic evidence for a nodeless magnetic kagome superconductor CeRu2.

We report muon spin rotation (µSR) experiments on the microscopic properties of superconductivity and magnetism in the kagome superconductor CeRu2withTc≃5 K. From the measurements of the temperature-dependent magnetic penetration depthλ, the superconducting order parameter exhibits nodeless pairing, which fits best to an anisotropics-wave gap symmetry. We further show that theTc/λ-2ratio is comparable to that of unconventional superconductors. Furthermore, the powerful combination of zero-field (ZF)-µSR and high-fieldµSR has been used to uncover magnetic responses across three characteristic temperatures, identified asT1∗≃110 K,T2∗≃65 K, andT3∗≃40 K. Our experiments classify CeRu2as an exceedingly rare nodeless magnetic kagome superconductor.

Tunable anomalous Hall conductivity through volume-wise magnetic competition in a topological kagome magnet.

Magnetic topological phases of quantum matter are an emerging frontier in physics and material science. Along these lines, several kagome magnets have appeared as the most promising platforms. Here, we explore magnetic correlations in the kagome magnet Co3Sn2S2. Using muon spin-rotation, we present evidence for competing magnetic orders in the kagome lattice of this compound. Our results show that while the sample exhibits an out-of-plane ferromagnetic ground state, an in-plane antiferromagnetic state appears at temperatures above 90 K, eventually attaining a volume fraction of 80% around 170 K, before reaching a non-magnetic state. Strikingly, the reduction of the anomalous Hall conductivity (AHC) above 90 K linearly follows the disappearance of the volume fraction of the ferromagnetic state. We further show that the competition of these magnetic phases is tunable through applying either an external magnetic field or hydrostatic pressure. Our results taken together suggest the thermal and quantum tuning of Berry curvature induced AHC via external tuning of magnetic order.

Unconventional scaling of the superfluid density with the critical temperature in transition metal dichalcogenides.

We report on muon spin rotation experiments probing the magnetic penetration depth λ(T) in the layered superconductors in 2H-NbSe2 and 4H-NbSe2. The current results, along with our earlier findings on 1T'-MoTe2 (Guguchia et al.), demonstrate that the superfluid density scales linearly with T c in the three transition metal dichalcogenide superconductors. Upon increasing pressure, we observe a substantial increase of the superfluid density in 2H-NbSe2, which we find to correlate with T c. The correlation deviates from the abovementioned linear trend. A similar deviation from the Uemura line was also observed in previous pressure studies of optimally doped cuprates. This correlation between the superfluid density and T c is considered a hallmark feature of unconventional superconductivity. Here, we show that this correlation is an intrinsic property of the superconductivity in transition metal dichalcogenides, whereas the ratio T c/T F is approximately a factor of 20 lower than the ratio observed in hole-doped cuprates. We, furthermore, find that the values of the superconducting gaps are insensitive to the suppression of the charge density wave state.

Magnetism in semiconducting molybdenum dichalcogenides.

Transition metal dichalcogenides (TMDs) are interesting for understanding the fundamental physics of two-dimensional (2D) materials as well as for applications to many emerging technologies, including spin electronics. Here, we report the discovery of long-range magnetic order below T M = 40 and 100 K in bulk semiconducting TMDs 2H-MoTe2 and 2H-MoSe2, respectively, by means of muon spin rotation (µSR), scanning tunneling microscopy (STM), and density functional theory (DFT) calculations. The µSR measurements show the presence of large and homogeneous internal magnetic fields at low temperatures in both compounds indicative of long-range magnetic order. DFT calculations show that this magnetism is promoted by the presence of defects in the crystal. The STM measurements show that the vast majority of defects in these materials are metal vacancies and chalcogen-metal antisites, which are randomly distributed in the lattice at the subpercent level. DFT indicates that the antisite defects are magnetic with a magnetic moment in the range of 0.9 to 2.8 µB. Further, we find that the magnetic order stabilized in 2H-MoTe2 and 2H-MoSe2 is highly sensitive to hydrostatic pressure. These observations establish 2H-MoTe2 and 2H-MoSe2 as a new class of magnetic semiconductors and open a path to studying the interplay of 2D physics and magnetism in these interesting semiconductors.

Author Correction: Signatures of the topological s+- superconducting order parameter in the type-II Weyl semimetal T d -MoTe2.

The original version of this article omitted the following from the Acknowledgements: "CAM and AL were supported by the NSF MRSEC program through Columbia in the Center for Precision Assembly of Superstratic and Superatomic Solids (DMR-1420634). Additionally, this research used resources of the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility supported by the Office of Science of the U.S. Department of Energy under 'Contract No. DE-AC02-05CH11231'." This has now been corrected in both the PDF and HTML versions of the article.

Magnetic states of MnP: muon-spin rotation studies.

Muon-spin rotation data collected at ambient pressure (p) and at p = 2.42 GPa in MnP were analyzed to check their consistency with various low- and high-pressure magnetic structures reported in the literature. Our analysis confirms that in MnP the low-temperature and low-pressure helimagnetic phase is characterised by an increased value of the average magnetic moment compared to the high-temperature ferromagnetic phase. An elliptical double-helical structure with a propagation vector [Formula: see text], an a-axis moment elongated by approximately 18% and an additional tilt of the rotation plane towards c-direction by [Formula: see text]-8° leads to a good agreement between the theory and the experiment. The analysis of the high-pressure µSR data reveals that the new magnetic order appearing for pressures exceeding 1.5 GPa can not be described by keeping the propagation vector [Formula: see text]. Even the extreme case-decoupling the double-helical structure into four individual helices-remains inconsistent with the experiment. It is shown that the high-pressure magnetic phase which is a precursor of superconductivity is an incommensurate helical state with [Formula: see text].

Ground state selection under pressure in the quantum pyrochlore magnet Yb2Ti2O7.

A quantum spin liquid is a state of matter characterized by quantum entanglement and the absence of any broken symmetry. In condensed matter, the frustrated rare-earth pyrochlore magnets Ho2Ti2O7 and Dy2Ti2O7, so-called spin ices, exhibit a classical spin liquid state with fractionalized thermal excitations (magnetic monopoles). Evidence for a quantum spin ice, in which the magnetic monopoles become long range entangled and an emergent quantum electrodynamics arises, seems within reach. The magnetic properties of the quantum spin ice candidate Yb2Ti2O7 have eluded a global understanding and even the presence or absence of static magnetic order at low temperatures is controversial. Here we show that sensitivity to pressure is the missing key to the low temperature behaviour of Yb2Ti2O7. By combining neutron diffraction and muon spin relaxation on a stoichiometric sample under pressure, we evidence a magnetic transition from a disordered, non-magnetic, ground state to a splayed ferromagnetic ground state.

Hydrostatic pressure effects on the static magnetism in Eu(Fe0.925Co0.075)2As2.

EuFe2As2-based iron pnictides are quite interesting compounds, due to the two magnetic sublattices in them and the tunability to superconductors by chemical doping or application of external pressure. The effects of hydrostatic pressure on the static magnetism in Eu(Fe0.925Co0.075)2As2 are investigated by complementary electrical resistivity, ac magnetic susceptibility and single-crystal neutron diffraction measurements. A specific pressure-temperature (P-T) phase diagram of Eu(Fe0.925Co0.075)2As2 is established. The structural phase transition, as well as the spin-density-wave order of Fe sublattice, is suppressed gradually with increasing pressure and disappears completely above 2.0 GPa. In contrast, the magnetic order of Eu sublattice persists over the whole investigated pressure range up to 14 GPa, yet displaying a non-monotonic variation with pressure. With the increase of the hydrostatic pressure, the magnetic state of Eu evolves from the canted antiferromagnetic structure in the ground state, via a pure ferromagnetic structure under the intermediate pressure, finally to an "unconfirmed" antiferromagnetic structure under the high pressure. The strong ferromagnetism of Eu coexists with the pressure-induced superconductivity around 2 GPa. Comparisons between the P-T phase diagrams of Eu(Fe0.925Co0.075)2As2 and the parent compound EuFe2As2 were also made.