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.

Evidence for time-reversal symmetry-breaking kagome superconductivity.

Superconductivity and magnetism are often antagonistic in quantum matter, although their intertwining has long been considered in frustrated-lattice systems. Here we utilize scanning tunnelling microscopy and muon spin resonance to demonstrate time-reversal symmetry-breaking superconductivity in kagome metal Cs(V, Ta)3Sb5, where the Cooper pairing exhibits magnetism and is modulated by it. In the magnetic channel, we observe spontaneous internal magnetism in a fully gapped superconducting state. Under the perturbation of inverse magnetic fields, we detect a time-reversal asymmetrical interference of Bogoliubov quasi-particles at a circular vector. At this vector, the pairing gap spontaneously modulates, which is distinct from pair density waves occurring at a point vector and consistent with the theoretical proposal of an unusual interference effect under time-reversal symmetry breaking. The correlation between internal magnetism, Bogoliubov quasi-particles and pairing modulation provides a chain of experimental indications for time-reversal symmetry-breaking kagome superconductivity.

Anomalous Hall effect in Weyl semimetal half-Heusler compounds RPtBi (R = Gd and Nd).

Topological materials ranging from topological insulators to Weyl and Dirac semimetals form one of the most exciting current fields in condensed-matter research. Many half-Heusler compounds, RPtBi (R = rare earth), have been theoretically predicted to be topological semimetals. Among various topological attributes envisaged in RPtBi, topological surface states, chiral anomaly, and planar Hall effect have been observed experimentally. Here, we report an unusual intrinsic anomalous Hall effect (AHE) in the antiferromagnetic Heusler Weyl semimetal compounds GdPtBi and NdPtBi that is observed over a wide temperature range. In particular, GdPtBi exhibits an anomalous Hall conductivity of up to 60 Ω-1⋅cm-1 and an anomalous Hall angle as large as 23%. Muon spin-resonance (µSR) studies of GdPtBi indicate a sharp antiferromagnetic transition (TN) at 9 K without any noticeable magnetic correlations above TN Our studies indicate that Weyl points in these half-Heuslers are induced by a magnetic field via exchange splitting of the electronic bands at or near the Fermi energy, which is the source of the chiral anomaly and the AHE.

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.

Extended Magnetic Dome Induced by Low Pressures in Superconducting FeSe_{1-x}S_{x}.

We report muon spin rotation and magnetization measurements under pressure on Fe_{1+δ}Se_{1-x}S_{x} with x≈0.11. Above p≈0.6 GPa we find a microscopic coexistence of superconductivity with an extended dome of long range magnetic order that spans a pressure range between previously reported separated magnetic phases. The magnetism initially competes on an atomic scale with the coexisting superconductivity leading to a local maximum and minimum of the superconducting T_{c}(p). The maximum of T_{c} corresponds to the onset of magnetism while the minimum coincides with the pressure of strongest competition. A shift of the maximum of T_{c}(p) for a series of single crystals with x up to 0.14 roughly extrapolates to a putative magnetic and superconducting state at ambient pressure for x≥0.2.

Observation of Anomalous Meissner Screening in Cu/Nb and Cu/Nb/Co Thin Films.

We have observed the spatial distribution of magnetic flux in Nb, Cu/Nb, and Cu/Nb/Co thin films using muon-spin rotation. In an isolated 50-nm-thick Nb film, we find a weak flux expulsion (Meissner effect) which becomes significantly enhanced when adding an adjacent 40 nm layer of Cu. The added Cu layer exhibits a Meissner effect (due to induced superconducting pairs) and is at least as effective as the Nb to expel flux. These results are confirmed by theoretical calculations using the quasiclassical Green's function formalism. An unexpected further significant enhancement of the flux expulsion is observed when adding a thin (2.4 nm) ferromagnetic Co layer to the bottom side of the Nb. This observed cooperation between superconductivity and ferromagnetism, by an unknown mechanism, forms a key ingredient for developing superconducting spintronics.

Microscopic probing of the superconducting and normal state properties of Ta2V3.1Si0.9 by muon spin rotation.

The two-dimensional kagome lattice is an experimental playground for novel physical phenomena, from frustrated magnetism and topological matter to chiral charge order and unconventional superconductivity. A newly identified kagome superconductor, Ta2V3.1Si0.9 has recently gained attention for possessing a record high critical temperature, T C = 7.5 K for kagome metals at ambient pressure. In this study we conducted a series of muon spin rotation measurements to delve deeper into understanding the superconducting and normal state properties of Ta2V3.1Si0.9. We demonstrate that Ta2V3.1Si0.9 is a bulk superconductor with either a s+s-wave or anisotropic s-wave gap symmetry, and has an unusual paramagnetic shift in response to external magnetic fields in the superconducting state. Additionally, we observe an exceptionally low superfluid density - a distinctive characteristic of unconventional superconductivity - which remarkably is comparable to the superfluid density found in hole-doped cuprates. In its normal state, Ta2V3.1Si0.9 exhibits a significant increase in the zero-field muon spin depolarisation rate, starting at approximately 150 K, which has been observed in other kagome-lattice superconductors, and therefore hints at possible hidden magnetism. These findings characterise Ta2V3.1Si0.9 as an unconventional superconductor and a noteworthy new member of the vanadium-based kagome material family.

Depth-dependent study of time-reversal symmetry-breaking in the kagome superconductor AV3Sb5.

The breaking of time-reversal symmetry (TRS) in the normal state of kagome superconductors AV3Sb5 stands out as a significant feature, but its tunability is unexplored. Using low-energy muon spin rotation and local field numerical analysis, we study TRS breaking as a function of depth in single crystals of RbV3Sb5 (with charge order) and Cs(V0.86Ta0.14)3Sb5 (without charge order). In the bulk of RbV3Sb5 (>33 nm from the surface), we observed an increase in the internal magnetic field width in the charge-ordered state. Near the surface (<33 nm), the muon spin relaxation rate is significantly enhanced and this effect commences at temperatures significantly higher than the onset of charge order. In contrast, no similar field width enhancement was detected in Cs(V0.86Ta0.14)3Sb5, either in the bulk or near the surface. These observations indicate a strong connection between charge order and TRS breaking and suggest that TRS breaking can occur prior to long-range charge order.

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.

Strain-induced ferromagnetism in antiferromagnetic LuMnO3 thin films.

Single phase and strained LuMnO(3) thin films are discovered to display coexisting ferromagnetic and antiferromagnetic orders. A large moment ferromagnetism (≈1µ(B)), which is absent in bulk samples, is shown to display a magnetic moment distribution that is peaked at the highly strained substrate-film interface. We further show that the strain-induced ferromagnetism and the antiferromagnetic order are coupled via an exchange field, therefore demonstrating strained rare-earth manganite thin films as promising candidate systems for new multifunctional devices.

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.

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.

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.

Singlet ground state of the quantum antiferromagnet Ba(3)CuSb(2)O(9).

We present local probe results on the honeycomb lattice antiferromagnet Ba(3)CuSb(2)O(9). Muon spin relaxation measurements in a zero field down to 20 mK show unequivocally that there is a total absence of spin freezing in the ground state. Sb NMR measurements allow us to track the intrinsic susceptibility of the lattice, which shows a maximum at around 55 K and drops to zero in the low-temperature limit. The spin-lattice relaxation rate shows two characteristic energy scales, including a field-dependent crossover to exponential low-temperature behavior, implying gapped magnetic excitations.

Avoided ferromagnetic quantum critical point: unusual short-range ordered state in CeFePO.

Cerium 4f electronic spin dynamics in single crystals of the heavy-fermion system CeFePO is studied by means of ac susceptibility, specific heat, and muon-spin relaxation (µSR). Short-range static magnetism occurs below the freezing temperature T(g) ≈ 0.7 K, which prevents the system from accessing a putative ferromagnetic quantum critical point. In the µSR, the sample-averaged muon asymmetry function is dominated by strongly inhomogeneous spin fluctuations below 10 K and exhibits a characteristic time-field scaling relation expected from glassy spin dynamics, strongly evidencing cooperative and critical spin fluctuations. The overall behavior can be ascribed neither to canonical spin glasses nor other disorder-driven mechanisms.

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.

Two-dimensional magnetic and superconducting phases in metal-insulator La(2-x)Sr(x)CuO(4) superlattices measured by muon-spin rotation.

We show, by means of low-energy muon-spin rotation measurements, that few-unit-cells thick La(2)CuO(4) layers synthesized digitally by molecular beam epitaxy are antiferromagnetically ordered. Below a thickness of about 5 CuO(2) layers the long-range ordered state breaks down, and a magnetic state appears with enhanced quantum fluctuations and a reduced spin stiffness. This magnetic state can exist in close proximity (few Å) to high-temperature superconducting layers, without transmitting supercurrents.

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.