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There is considerable evidence that the superconducting state of Sr 2 RuO 4 breaks time reversal symmetry. In the experiments showing time reversal symmetry breaking, its onset temperature, T TRSB , is generally found to match the critical temperature, T c , within resolution. In combination with evidence for even parity, this result has led to consideration of a d x z  ±  i d y z order parameter. The degeneracy of the two components of this order parameter is protected by symmetry, yielding T TRSB  =  T c , but it has a hard-to-explain horizontal line node at k z  = 0. Therefore, s  ±  i d and d  ±  i g order parameters are also under consideration. These avoid the horizontal line node, but require tuning to obtain T TRSB  ≈  T c . To obtain evidence distinguishing these two possible scenarios (of symmetry-protected versus accidental degeneracy), we employ zero-field muon spin rotation/relaxation to study pure Sr 2 RuO 4 under hydrostatic pressure, and Sr 1.98 La 0.02 RuO 4 at zero pressure. Both hydrostatic pressure and La substitution alter T c without lifting the tetragonal lattice symmetry, so if the degeneracy is symmetry-protected, T TRSB should track changes in T c , while if it is accidental, these transition temperatures should generally separate. We observe T TRSB to track T c , supporting the hypothesis of d x z  ±  i d y z order. Two possible scenarios of the superconducting order parameter in Sr 2 RuO 4 remain difficult to distinguish. Here, the authors observe that the onset temperature of time reversal symmetry breaking tracks the superconducting transition temperature in Sr 2 RuO 4 , supporting a d x z  ± i d y z order parameter.

The recently discovered kagome superconductor CsV3Sb5 (Tc ≃ 2.5 K) has been found to host charge order as well as a non-trivial band topology, encompassing multiple Dirac points and probable surface states. Such a complex and phenomenologically rich system is, therefore, an ideal playground for observing unusual electronic phases. Here, we report anisotropic superconducting properties of CsV3Sb5 by means of transverse-field muon spin rotation (μSR) experiments. The fits of temperature dependences of in-plane and out-of-plane components of the magnetic penetration depth suggest that the superconducting order parameter may have a two-gap (s + s)-wave symmetry. The multiband nature of superconductivity could be further supported by the different temperature dependences of the anisotropic magnetic penetration depth γλ(T) and upper critical field γBc2(T). The relaxation rates obtained from zero field μSR experiments do not show noticeable change across the superconducting transition, indicating that superconductivity does not break time reversal symmetry.

Pseudogap versus superconductivity in cuprates A pairing gap and coherence are the two hallmarks of superconductivity. In a classical BCS (Bardeen–Cooper–Schreiffer) superconductor they are established simultaneously at the critical temperature, T c . In the cuprates however, an energy gap (pseudogap) extends above T c . The origin of this gap is one of the central issues in high-temperature superconductivity. Kondo et al . report evidence from angle-resolved photoemission spectroscopy (ARPES) that the pseudogap and high-temperature superconductivity represent two competing orders, with the pseudogap competing with the superconductivity by depleting the spectral weight available for pairing. In a classical Bardeen–Cooper–Schrieffer superconductor, pairing and coherence are established simultaneously below the critical transition temperature ( T c ). But in the copper oxide high- T c superconductors, a pseudogap extends above T c . Spectral gaps arising from pairing precursors are qualitatively similar to those caused by competing states, rendering a standard approach to their analysis inconclusive. This paper reports that the spectral weight of the superconducting coherent peak increases away from the node following the trend of the superconducting gap, but then starts to decrease in the antinodal region. In a classical Bardeen–Cooper–Schrieffer superconductor, pairing and coherence of electrons are established simultaneously below the critical transition temperature ( T c ), giving rise to a gap in the electronic energy spectrum. In the high- T c copper oxide superconductors, however, a pseudogap 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 extends above T c . The relationship between the pseudogap and superconductivity is one of the central issues in this field 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 . Spectral gaps arising from pairing precursors are qualitatively similar to those caused by competing electronic states, rendering a standard approach to their analysis inconclusive 10 , 11 , 12 , 13 , 14 , 15 , 16 . The issue can be settled, however, by studying the correlation between the weights associated with the pseudogap and superconductivity spectral features. Here we report a study of two spectral weights using angle-resolved photoemission spectroscopy. The weight of the superconducting coherent peak increases away from the node following the trend of the superconducting gap, but starts to decrease in the antinodal region. This striking non-monotonicity reveals the presence of a competing state. We demonstrate a direct correlation, for different values of momenta and doping, between the loss in the low-energy spectral weight arising from the opening of the pseudogap and a decrease in the spectral weight associated with superconductivity. We therefore conclude that the pseudogap competes with the superconductivity by depleting the spectral weight available for pairing.

The kagome metals of the family A V 3 Sb 5 , featuring a unique structural motif, harbor an array of intriguing phenomena such as chiral charge order and superconductivity. CsV 3 Sb 5 is of particular interest because it displays a double superconducting dome in the region of the temperature-pressure phase diagram where charge order is still present. However, the microscopic origin of such an unusual behavior remains an unsolved issue. Here, to address it, we combine high-pressure, low-temperature muon spin relaxation/rotation with first-principles calculations. We observe a pressure-induced threefold enhancement of the superfluid density, which also displays a double-peak feature, similar to the superconducting critical temperature. This leads to three distinct regions in the phase diagram, each of which features distinct slopes of the linear relation between superfluid density and the critical temperature. These results are attributed to a possible evolution of the charge order pattern from the superimposed tri-hexagonal Star-of-David phase at low pressures (within the first dome) to the staggered tri-hexagonal phase at intermediate pressures (between the first and second domes). Our findings suggest a change in the nature of the charge-ordered state across the phase diagram of CsV 3 Sb 5 , with varying degrees of competition with superconductivity. Kagome metals can house a complex interplay of competing phenomenon and there has been significant investigation into how to engineer the resultant properties, as well as understand the underlying physics. Here, the authors investigate the competition between charge density wave order and superconductivity for CsV 3 Sb 5 using a combination of high-pressure and muon spin rotation measurements.

The K 2 Cr 8 O 16 compound belongs to a series of quasi-1D compounds with intriguing magnetic properties that are stabilized through a high-pressure synthesis technique. In this study, a muon spin rotation, relaxation and resonance ( μ + SR) technique is used to investigate the pressure dependent magnetic properties up to 25 kbar. μ + SR allows for measurements in true zero applied field and hereby access the true intrinsic material properties. As a result, a refined temperature/pressure phase diagram is presented revealing a novel low temperature/high pressure ( p C1  = 21 kbar) transition from a ferromagnetic insulating to a high-pressure antiferromagnetic insulator. Finally, the current study also indicates the possible presence of a quantum critical point at p C2  ~ 33 kbar where the magnetic order in K 2 Cr 8 O 16 is expected to be fully suppressed even at T = 0 K.

Exchange interactions are mediated via orbital overlaps across chemical bonds. Thus, modifying the bond angles by physical pressure or strain can tune the relative strength of competing interactions. Here we present a remarkable case of such tuning between the Heisenberg ( J ) and Kitaev ( K ) exchange, which respectively establish magnetically ordered and spin liquid phases on a honeycomb lattice. We observe a rapid suppression of the Néel temperature ( T N ) with pressure in Ag 3 LiRh 2 O 6 , a spin-1/2 honeycomb lattice with both J and K couplings. Using a combined analysis of x-ray data and first-principles calculations, we find that pressure modifies the bond angles in a way that increases the ∣ K / J ∣ ratio and thereby suppresses T N . Consistent with this picture, we observe a spontaneous onset of muon spin relaxation ( μ SR) oscillations below T N at low pressure, whereas in the high pressure phase, oscillations appear only when T  <  T N /2. Unlike other candidate Kitaev materials, Ag 3 LiRh 2 O 6 is tuned toward a quantum critical point by pressure while avoiding a structural dimerization in the relevant pressure range. Kitaev interactions on a honeycomb lattice can potentially lead to a quantum spin liquid state. Unfortunately, materials hosting Kitaev interactions also host Heisenberg interactions favouring long range order. Here, Sakrikar, Shen, Poldi and coauthors find that the relative strength of the Heisenberg and Kitaev interactions can be tuned by pressure in Ag 3 LiRh 2 O 6 .

The recent discovery of pressure ( p ) induced superconductivity in the binary helimagnet CrAs has raised questions on how superconductivity emerges from the magnetic state and on the mechanism of the superconducting pairing. In the present work the suppression of magnetism and the occurrence of superconductivity in CrAs were studied by means of muon spin rotation. The magnetism remains bulk up to p    3.5 kbar while its volume fraction gradually decreases with increasing pressure until it vanishes at p    7 kbar. At 3.5 kbar superconductivity abruptly appears with its maximum T c    1.2 K which decreases upon increasing the pressure. In the intermediate pressure region (3.5    p    7 kbar) the superconducting and the magnetic volume fractions are spatially phase separated and compete for phase volume. Our results indicate that the less conductive magnetic phase provides additional carriers (doping) to the superconducting parts of the CrAs sample thus leading to an increase of the transition temperature ( T c ) and of the superfluid density (ρ s ). A scaling of ρ s with as well as the phase separation between magnetism and superconductivity point to a conventional mechanism of the Cooper-pairing in CrAs.

RENiO 3 (RE=rare-earth element) and V 2 O 3 are archetypal Mott insulator systems. When tuned by chemical substitution (RENiO 3 ) or pressure (V 2 O 3 ), they exhibit a quantum phase transition (QPT) between an antiferromagnetic Mott insulating state and a paramagnetic metallic state. Because novel physics often appears near a Mott QPT, the details of this transition, such as whether it is first or second order, are important. Here, we demonstrate through muon spin relaxation/rotation (μSR) experiments that the QPT in RENiO 3 and V 2 O 3 is first order: the magnetically ordered volume fraction decreases to zero at the QPT, resulting in a broad region of intrinsic phase separation, while the ordered magnetic moment retains its full value until it is suddenly destroyed at the QPT. These findings bring to light a surprising universality of the pressure-driven Mott transition, revealing the importance of phase separation and calling for further investigation into the nature of quantum fluctuations underlying the transition. Knowing whether a quantum phase transition is first- or second-order is crucial for understanding any associated exotic phenomena, but direct experimental evidence has been scarce. Here, Frandsen et al . report first-order magnetic quantum phase transitions in archetypal Mott systems, providing insight into the underlying quantum fluctuations.

In second-order quantum phase transitions from magnetically ordered to paramagnetic states at T  = 0, tuned by pressure or chemical substitution, a quantum critical point is expected to appear with critical behavior manifesting in the slowing down of spin fluctuations in the paramagnetic state and a continuous development of the order parameter in the ordered state. Quantum criticality is discussed widely as a possible driving force for unconventional superconductivity and other exotic phenomena in correlated electron systems. In the real world, however, quantum critical points and quantum criticality are often masked by a preceding first-order transition and/or the development of competing states. Pressure tuning of the itinerant-electron helical magnet MnSi is a well-known example of the suppression of a quantum critical point due to a first-order phase transition and resulting destruction of the ordered state. Utilizing muon spin relaxation experiments, here we report that 15% Fe-substituted (Mn,Fe)Si exhibits completely different behavior with pressure tuning, including the restoration of second-order quantum critical behavior and a quantum critical point at p QPC  ~ 21–23 kbar, which coincides with the T  = 0 crossing point of the extrapolated phase boundary line of pure MnSi. This result is quantitatively consistent with the recent theory of itinerant-electron ferromagnets by Sang, Belitz, and Kirkpatrick, who argued that disorder would restore a quantum critical point which is otherwise hidden by a first-order transition. Quantum criticality: Iron aids restoration An exotic quantum state of matter is identified in a new material by researchers in the USA, Switzerland and Germany. Yasutomo Uemura from Columbia University and co-workers observe quantum criticality in a material in which it was previously unseen just by adding iron. As pressure is increasingly applied to pure manganese silicon at absolute zero temperature, it can suddenly change from an ordered magnetic state to an unordered one. Uemura et al. now show that a slower continuous, or second-order, transition is observed instead when fifteen percent of the manganese atoms are replaced with iron atoms. This is indicative that a quantum critical point exists at a pressure of between 21 and 23 kilobar. They believe that criticality is restored because the iron atoms introduce disorder into the system.

The temperature dependencies of the in-plane (λab) and out-of-plane (λc) components of the magnetic field penetration depth were investigated near the surface and in the bulk of the electron-doped superconductor Sr0.9La0.1CuO2 by means of magnetization measurements. The measured λab(T) and λc(T) were analyzed in terms of a two-gap model with mixed s+d-wave symmetry of the order parameter. λab(T) is well described by an almost pure anisotropic d-wave symmetry component (≃96%), mainly reflecting the surface properties of the sample. In contrast, λc(T) exhibits a mixed s+d-wave order parameter with a substantial s-wave component of more than 50%. The comparison of λab−2(T) measured near the surface with that determined in the bulk by means of the muon-spin rotation/relaxation technique demonstrates that the suppression of the s-wave component of the order parameter near the surface is associated with a reduction of the superfluid density by more than a factor of two.