Rm C2 Research Articles

Anisotropic enhancement of lower critical field in ultraclean crystals of spin-triplet superconductor candidate UTe2

The paramagnetic spin-triplet superconductor UTe$_2$ has attracted significant attention because of its exotic superconducting properties including an extremely high upper critical field and possible chiral superconducting states. Recently, ultraclean single crystals of UTe$_2$ have become available, and thus measurements on these crystals are crucial to elucidate the intrinsic superconducting properties. Here, we report the thermodynamic critical field $H_{\rm c}$, the lower critical field $H_{\rm c1}$, and the upper critical field $H_{\rm c2}$ at low fields of these high-quality single crystals. From the comparison of the anisotropies in $H_{\rm c1}$ and $H_{\rm c2}$, we find that the experimental $H_{\rm c1}$ values with the magnetic field along $b$- and $c$-axes are anomalously enhanced, showing unusual low-temperature upturns. We propose an effect of the strong Ising-like ferromagnetic fluctuations on the vortex line energy as the origin of the anisotropic enhancement of $H_{\rm c1}$.

Enhanced Superconducting Pairing Strength near a Pure Nematic Quantum Critical Point

The quest for high-temperature superconductivity at ambient pressure is a central issue in physics. In this regard, the relationship between unconventional superconductivity and the quantum critical point (QCP) associated with the suppression of some form of symmetry-breaking order to zero temperature has received particular attention. The key question is how the strength of the electron pairs changes near the QCP, and this can be verified by high-field experiments. However, such studies are limited mainly to superconductors with magnetic QCPs, and the possibility of unconventional mechanisms by which nonmagnetic QCP promotes strong pairing remains a nontrivial issue. Here, we report systematic measurements of the upper critical field $H_{{\rm c2}}$ in nonmagnetic FeSe$_{1-x}$Te$_{x}$ superconductors, which exhibit a QCP of electronic nematicity characterized by spontaneous rotational-symmetry breaking. As the magnetic field increases, the superconducting phase of FeSe$_{1-x}$Te$_{x}$ shrinks to a narrower dome surrounding the nematic QCP. The analysis of $H_{{\rm c2}}$ reveals that the Pauli-limiting field is enhanced toward the QCP, implying that the pairing interaction is significantly strengthened via nematic fluctuations emanated from the QCP. Remarkably, this nonmagnetic nematic QCP is not accompanied by a divergent effective mass, distinct from the magnetically mediated pairing. Our observation opens up a nonmagnetic route to high-temperature superconductivity.

High-entropy silicide superconductors with W5Si3 -type structure

We report the synthesis, crystal structure and physical properties of two new high-entropy silicides (HESs), namely (Nb$_{0.1}$Mo$_{0.3}$W$_{0.3}$Re$_{0.2}$Ru$_{0.1}$)$_{5}$Si$_{3}$ and (Nb$_{0.2}$Mo$_{0.3}$W$_{0.3}$Re$_{0.1}$Ru$_{0.1}$)$_{5}$Si$_{3}$. Structural analysis indicates that both HESs consist of a (nearly) single tetragonal W$_{5}$Si$_{3}$-type phase (space group $I$4/$mcm$) with a disordered cation distribution. Electrical resistivity, magnetic susceptibility and specific heat measurements show that (Nb$_{0.1}$Mo$_{0.3}$W$_{0.3}$Re$_{0.2}$Ru$_{0.1}$)$_{5}$Si$_{3}$ and (Nb$_{0.2}$Mo$_{0.3}$W$_{0.3}$Re$_{0.1}$Ru$_{0.1}$)$_{5}$Si$_{3}$ are weakly coupled bulk superconductors, which represent the first superconducting high-entropy nonoxide ceramics. In particular, these HESs have higher $T_{\rm c}$ values (3.2-3.3 K) compared with those of the binary counterparts, and their $B_{\rm c2}$(0)/$T_{\rm c}$ ratios are the largest among superconductors of the same structural type.

Violation of Pauli-Clogston limit in the heavy-fermion superconductor CeRh2As2 : Duality of itinerant and localized 4f electrons

We theoretically propose a mechanism to understand the violation of the Pauli-Clogston limit for the upper critical field H$_{\rm c2}$ observed in the Ce bearing heavy Fermion material CeRh$_2$As$_2$ from the view point of spin singlet pairing. It is based on a duality concept, the dual simultaneous aspects of an electron: the itinerant part and localized part of quasi-particles (QPs) originated from the 4f electrons of the Ce atoms. While the itinerant QPs directly participate in forming the Cooper pairs, the localized QPs exert the internal field so as to oppose the applied field through the antiferromagnetic exchange interaction between them. This is inherent in the dense Kondo lattice system in general. We argue that this mechanism can be applied not only to the locally noncentrosymmetric material CeRh$_2$As$_2$, but also to globally inversion symmetry broken Ce-based materials such as CePt$_3$Si. Moreover, we point out that it also works for strongly Pauli limit violated spin triplet pairing systems, such as UTe$_2$.

Nonunitary triplet superconductivity tuned by field-controlled magnetization: URhGe, UCoGe, and UTe2

We report on theoretical studies on ferromagnetic superconductors, URhGe, and UCoGe and identifies the pairing state as a non-unitary spin-triplet one, analogous to superfluid $^3$He-A phase. A recently found superconductor UTe$_2$ with almost ferromagnet is analyzed by the same manner. Through investigating their peculiar upper critical field $H_{\rm c2}$ shapes, it is shown that the pairing symmetry realized in all three compounds can be tuned by their magnetization curves under applied fields. This leads to the reentrant $H_{\rm c2}$ in URhGe, an S-shaped in UCoGe and an L-shaped $H_{\rm c2}$ in UTe$_2$ observed under the field direction parallel to the magnetic hard axis in orthorhombic crystals in common. The identification with double chiral form: ${\bf d}(k)=(\hat{b}+i\hat{c})(k_b+ik_c)$ in UTe$_2$ naturally enables us to understand (1) multiple phases with A$_1$, A$_2$, and A$_0$ phases observed under pressure, (2) the enhanced reentrant $H_{\rm c2}$ for the off-axis direction fields associated with first order meta-magnetic transition, and (3) Weyl point nodes oriented along the $a$-axis. All three compounds are found to be topologically rich solid-state materials worth further investigation.

Thermodynamic evidence for the formation of a Fulde-Ferrell-Larkin-Ovchinnikov phase in the organic superconductor λ−(BETS)2GaCl4

In this work, the thermodynamic properties of the organic superconductor $\lambda$-(BETS)$_2$GaCl$_4$ are investigated to study a high-field superconducting state known as the putative Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase. We observed a small thermodynamic anomaly in the field $H_{\rm FFLO}$ $\sim$ 10~T, which corresponds to the Pauli limiting field $H_{\rm P}$. This anomaly probably originates from a transition from a uniform superconducting state to the FFLO state. $H_{\rm FFLO}$ does not show a strong field-angular dependence due to a quasi-isotropic paramagnetic effect in $\lambda$-(BETS)$_2$GaCl$_4$. The thermodynamic anomaly at $H_{\rm FFLO}$ is smeared out and low-temperature upper critical field $H_{\rm c2}$ changes significantly if fields are not parallel to the conducting plane even for a deviation of $\sim$0.5$^{\circ}$. This behavior indicates that the high-field state is very unstable, as it is influenced by the strongly anisotropic orbital effect. Our results are consistent with the theoretical predictions on the FFLO state, and show that the high-field superconductivity is probably an FFLO state in $\lambda$-(BETS)$_2$GaCl$_4$ from a thermodynamic point of view.

Nonmagnetic-magnetic transition and magnetically ordered structure in SmS

SmS, a prototypical intermediate valence compound, has been studied by performing high-pressure nuclear magnetic resonance measurements on a $^{33}$S-enriched sample. The observation of an additional signal below 15-20 K above a nonmagnetic-magnetic transition pressure $P_{\rm c2} \approx 2$ GPa gives evidence of a magnetic transition. The absence of a Curie-term in the Knight shift near $P_{\rm c2}$ indicates that the localized character of $4f$ electrons is entirely screened and the mechanism of the magnetic ordering is not described within a simple localized model. Simultaneously, the line shape in the magnetically ordered state is incompatible with a spin density wave order. These suggest that the magnetic order in SmS may require an understanding beyond the conventional framework for heavy fermions. The fact that hyperfine fields from the ordered moments cancel out at the S site leads us to a conclusion that the ordered phase has a type II antiferromagnetic structure.

Two Qualitatively Different Superconducting Phases under High Pressure in Single-Crystalline CeNiGe3

We have measured the temperature dependence of resistivity in single-crystalline CeNiGe$_{3}$ under hydrostatic pressure in order to establish the characteristic pressure-temperature phase diagram. The transition temperature to AFM-I phase $T_{\rm N1}$ = 5.5 K at ambient pressure initially increases with increasing pressure and has a maximum at $\sim$ 3.0 GPa. Above 2.3 GPa, a clear zero-resistivity is observed (SC-I phase) and this superconducting (SC) state coexists with AFM-I phase. The SC-I phase suddenly disappears at 3.7 GPa simultaneously with the appearance of an additional kink anomaly corresponding to the phase transition to AFM-II phase. The AFM-II phase is continuously suppressed with further increasing pressure and disappears at $\sim$ 6.5 GPa. In the narrow range near the critical pressure, an SC phase reappears (SC-II phase). A large initial slope of upper critical field $\mu_0H_{\rm c2}$ and non-Fermi liquid behavior indicate that the SC-II phase is mediated by antiferromagnetic fluctuations. On the other hand, the robust coexistence of the SC-I phase and AFM-I phase is unusual on the contrary to superconductivity near a quantum critical point on most of heavy-fermion compounds.

Anisotropy of the Upper Critical Field in the Heavy-Fermion Superconductor UTe2 under Pressure

We studied the anisotropy of the superconducting upper critical field $H_{\rm c2}$ in the heavy-fermion superconductor UTe$_2$ under hydrostatic pressure by magnetoresistivity measurements. In agreement with previous experiments we confirm that superconductivity disappears near a critical pressure $p_{\rm c} \approx 1.5$~GPa, and a magnetically ordered state appears. The unusual $H_{\rm c2}(T)$ at low temperatures for $H \parallel a$ suggests that the multiple superconducting phases which appear under pressure have quite different $H_{\rm c2}$. For a field applied along the hard magnetization $b$ axis $H_{\rm c2} (0)$ is glued to the metamagnetic transition $H_{\rm m}$ which is suppressed near $p_{\rm c}$. The suppression of $H_{\rm m}$ with pressure follows the decrease of temperature $T_{\chi}^{\rm max}$, at the maximum in the susceptibility along $b$. The strong reinforcement of $H_{\rm c2}$ at ambient pressure for $H \parallel b$ above 16~T is rapidly suppressed under pressure due to the increase of $T_{\rm sc}$ and the decrease of $H_{\rm m}$. The change in the hierarchy of the anisotropy of $H_{\rm c2}(0)$ on approaching $p_{\rm c}$ points out that the $c$ axis becomes the hard magnetization axis.

Theory of Spin-polarized Superconductors —An Analogue of Superfluid 3He A-phase—

It is shown theoretically that ferromagnetic superconductors, UGe$_2$, URhGe, and UCoGe can be described in terms of the A-phase like triplet pairing similar to superfluid $^3$He in a unified way, including peculiar reentrant, S-shape, or L-shape $H_{\rm c2}$ curves. The associated double transition inevitable between the A$_1$ and A$_2$-phases in the $H$-$T$ plane is predicted, both of which are characterized by non-unitary state with broken time reversal symmetry and the half-gap. UTe$_2$, which has been discovered quite recently to be a spin-polarized superconductor, is analyzed successively in the same view point, pointing out that the expected A$_1$-A$_2$ transition is indeed emerging experimentally. Thus the four heavy Fermion compounds all together are entitled to be topologically rich solid state materials worth further investigating together with superfluid $^3$He A-phase.

Polymorphism and superconductivity in the V-Nb-Mo-Al-Ga high-entropy alloys

High-entropy alloys (HEAs) are at the focus of current research for their diverse properties, including superconductivity and structural polymorphism. However, the polymorphic transition has been observed only in nonsuperconducting HEAs and mostly under high pressure. Here we report the discovery of superconductivity and temperature-driven polymorphism in the (V$_{0.5}$Nb$_{0.5}$)$_{3-x}$Mo$_{x}$Al$_{0.5}$Ga$_{0.5}$ (0.2 $\leq$ $x$ $\leq$ 1.4) HEAs. It is found that the as-cast HEA is of a single body-centered cubic (bcc) structure for $x$ = 0.2 and a mixture of the bcc and A15 structures for higher $x$ values. Upon annealing, the bcc structure undergoes a polymorphic transformation to the A15 one and all HEAs exhibits bulk superconductivity. For $x$ = 0.2, whereas the bcc polymorph is not superconducting down to 1.8 K, the A15 polymorph has a superconducting transition temperature $T_{\rm c}$ of 10.2 K and an estimated zero-temperature upper critical field $B_{\rm c2}$(0) of 20.1 T, both of which are the highest among HEA superconductors. With increasing Mo content $x$, both $T_{\rm c}$ and $B_{\rm c2}$(0) of the A15-type HEAs decrease, yet the large ratio of $B_{\rm c2}$(0)/$T_{\rm c}$ signifies a disorder-induced enhancement of the upper critical field over a wide $x$ range. The decrease in $T_{\rm c}$ is attributed to the decrease in both the electronic specific-heat coefficient and electron-phonon coupling strength. Furthermore, the valence electron count dependence of $T_{\rm c}$, which is different from both the binary A15 and other structurally different HEA superconductors, suggests that $T_{\rm c}$ may be increased further by reducing the number of valence electrons. Our results not only uncover HEA superconductors of a new structural type, but also provide the first example of polymorphism dependent superconductivity in HEAs.

Anisotropy induced vortex lattice rearrangement in CaKFe4As4

The magnetic penetration depth anisotropy $\gamma_\lambda=\lambda_{c}/\lambda_{ab}$ ($\lambda_{ab}$ and $\lambda_{c}$ are the in-plane and the out-of-plane components of the magnetic penetration depth) in a CaKFe$_4$As$_4$ single crystal sample (the critical temperature $T_{\rm c}\simeq 35$ K) was studied by means of muon-spin rotation ($\mu$SR). $\gamma_\lambda$ is almost temperature independent for $T\lesssim 20$ K ($\gamma_\lambda\simeq 1.9$) and it reaches $\simeq 3.0$ by approaching $T_{\rm c}$. The change of $\gamma_\lambda$ induces the corresponding rearrangement of the flux line lattice (FLL), which is clearly detected via enhanced distortions of the FLL $\mu$SR response. Comparison of $\gamma_\lambda$ with the anisotropy of the upper critical field ($\gamma_{H_{\rm c2}}$) studied in Phys. Rev B {\bf 94}, 064501 (2016), reveals that $\gamma_\lambda$ is systematically higher than $\gamma_{H_{\rm c2}}$ at low-temperatures and approaches $\gamma_{H_{\rm c2}}$ for $T \rightarrow T_{\rm c}$. The anisotropic properties of $\lambda$ are explained by the multi-gap nature of superconductivity in CaKFe$_4$As$_4$ and are caused by anisotropic contributions of various bands to the in-plane and the out-of-plane components of the superfluid density.

Competition between orthorhombic and re-entrant tetragonal phases in underdoped Ba1−xKxFe2As2 probed by the response to controlled disorder

Low-temperature (22~K) irradiation with 2.5~MeV electrons was used to study the competition between stripe ${\rm C_2}$ and tetragonal ${\rm C_4}$ antiferromagnetic phases which exist in a narrow doping range around $x=$0.25 in hole-doped Ba$_{1-x}$K$_x$Fe$_2$As$_2$. In nearby compositions outside of this range, at $x=$0.22 and $x=$0.19, the temperatures of both the concomitant orthorhombic/stripe antiferromagnetic transition $T_{\rm C2}$ and the superconducting transition $T_{\rm c}$ are monotonically suppressed by added disorder at similar rates of about 0.1~K/$\mu \Omega$cm, as revealed through using resistivity variation as an intrinsic measure of scattering rate. In a stark contrast, a rapid suppression of the ${\rm C_4}$ phase at the rate of 0.24 K/$\mu \Omega \cdot$cm is found at $x=$0.25. Moreover, this suppression of the ${\rm C_4}$ phase is accompanied by unusual disorder-induced stabilization of the ${\rm C_2}$ phase, determined by resistivity and specific heat measurements. The rate of the ${\rm C_4}$ phase suppression is notably higher than the suppression rate of the spin-vortex phase in the Ni-doped CaKFe$_4$As$_4$ (0.16 K/$\mu \Omega$cm).

Searching for Gap Zeros in Sr2RuO4 via Field-Angle-Dependent Specific-Heat Measurement

The gap structure of Sr$_2$RuO$_4$, which is a longstanding candidate for a chiral p-wave superconductor, has been investigated from the perspective of the dependence of its specific heat on magnetic field angles at temperatures as low as 0.06 K ($\sim 0.04T_{\rm c}$). Except near $H_{\rm c2}$, its fourfold specific-heat oscillation under an in-plane rotating magnetic field is unlikely to change its sign down to the lowest temperature of 0.06 K. This feature is qualitatively different from nodal quasiparticle excitations of a quasi-two-dimensional superconductor possessing vertical lines of gap minima. The overall specific-heat behavior of Sr$_2$RuO$_4$ can be explained by Doppler-shifted quasiparticles around horizontal line nodes on the Fermi surface, whose in-plane Fermi velocity is highly anisotropic, along with the occurrence of the Pauli-paramagnetic effect. These findings, in particular, the presence of horizontal line nodes in the gap, call for a reconsideration of the order parameter of Sr$_2$RuO$_4$.

Pseudogap temperature T* of cuprate superconductors from the Nernst effect

We use the Nernst effect to delineate the boundary of the pseudogap phase in the temperature-doping phase diagram of cuprate superconductors. New data for the Nernst coefficient $\nu(T)$ of YBa$_{2}$Cu$_{3}$O$_{y}$ (YBCO), La$_{1.8-x}$Eu$_{0.2}$Sr$_x$CuO$_4$ (Eu-LSCO) and La$_{1.6-x}$Nd$_{0.4}$Sr$_x$CuO$_4$ (Nd-LSCO) are presented and compared with previous data including La$_{2-x}$Sr$_x$CuO$_4$ (LSCO). The temperature $T_\nu$ at which $\nu/T$ deviates from its high-temperature behaviour is found to coincide with the temperature at which the resistivity deviates from its linear-$T$ dependence, which we take as the definition of the pseudogap temperature $T^\star$- in agreement with gap opening detected in ARPES data. We track $T^\star$ as a function of doping and find that it decreases linearly vs $p$ in all four materials, having the same value in the three LSCO-based cuprates, irrespective of their different crystal structures. At low $p$, $T^\star$ is higher than the onset temperature of the various orders observed in underdoped cuprates, suggesting that these orders are secondary instabilities of the pseudogap phase. A linear extrapolation of $T^\star(p)$ to $p=0$ yields $T^\star(p\to 0)\simeq T_N(0)$, the N\'eel temperature for the onset of antiferromagnetic order at $p=0$, suggesting that there is a link between pseudogap and antiferromagnetism. With increasing $p$, $T^\star(p)$ extrapolates linearly to zero at $p\simeq p_{\rm c2}$, the critical doping below which superconductivity emerges at high doping, suggesting that the conditions which favour pseudogap formation also favour pairing. We also use the Nernst effect to investigate how far superconducting fluctuations extend above $T_{\rm c}$, as a function of doping, and find that a narrow fluctuation regime tracks $T_{\rm c}$, and not $T^\star$. This confirms that the pseudogap phase is not a form of precursor superconductivity.

Spatially Inhomogeneous Superconducting State near Hc2 in UPd2Al3

We have performed $^{27}$Al-NMR measurements on single-crystalline UPd$_2$Al$_3$ with the field parallel to the $c$ axis to investigate the superconducting (SC) properties near the upper critical field of superconductivity $H_{\rm c2}$. The broadening of the NMR linewidth below 14~K indicates the appearance of the internal field at the Al site, which originates from the antiferromagnetically ordered moments of U 5$f$ electrons. In the SC state well below $\mu_0H_{\rm c2}$ = 3.4~T, the broadening of the NMR linewidth due to the SC diamagnetism and a decrease in the Knight shift are observed, which are well-understood by the framework of spin-singlet superconductivity. In contrast, the Knight shift does not change below $T_{\rm c}(H)$, and the NMR spectrum is broadened symmetrically in the SC state in the field range of 3~T $< \mu_0 H < \mu_0 H_{\rm c2}$. The unusual NMR spectrum near $H_{\rm c2}$ suggests that a spatially inhomogeneous SC state such as the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state would be realized.

Anisotropy-governed competition of magnetic phases in the honeycomb quantum magnet Na3Ni2SbO6 studied by dilatometry and high-frequency ESR

Thermodynamic properties as well as low-energy magnon excitations of $S=1$ honeycomb-layered Na$_3$Ni$_2$SbO$_6$ have been investigated by high-resolution dilatometry, static magnetisation, and high-frequency electron spin resonance studies in magnetic fields up to 16 T. At $T_{\rm N}$ = 16.5 K, there is a tricritical point separating two distinct antiferromagnetic phases AF1 and AF2 from the paramagnetic regime. In addition, our data imply short-range antiferromagnetic correlations at least up to $\sim 5\cdot T_{\rm N}$. Well below $T_{\rm N}$, the magnetic field $B_{\rm C1}\approx$ 9.5 T is needed to stabilize AF2 against AF1. The thermal expansion and magnetostriction anomalies at $T_{\rm N}$ and $B_{\rm C1}$ imply significant magnetoelastic coupling, both of which associated with a sign change of $\partial L/\partial B$. The transition at $B_{\rm C1}$ is associated with softening of the antiferromagnetic resonance modes observed in the electron spin resonance spectra. The anisotropy gap $\Delta = 360$ GHz implies considerable uniaxial anisotropy. We conclude the crucial role of axial anisotropy favoring the AF1 spin structure over the AF2 one. While the magnetostriction data disprove a simple spin-flop scenario at $B_{\rm C1}$, the nature of a second transition at $B_{\rm C2}\approx$ 13 T remains unclear. Both the sign of the magnetostriction and Gr\"uneisen analysis suggest the short-range correlations at high temperatures to be of AF2-type.

Thermodynamic study of gap structure and pair-breaking effect by magnetic field in the heavy-fermion superconductorCeCu2Si2

This paper presents the results of specific-heat and magnetization measurements, in particular their field-orientation dependence, on the first discovered heavy-fermion superconductor CeCu$_2$Si$_2$ ($T_{\rm c} \sim 0.6$ K). We discuss the superconducting gap structure and the origin of the anomalous pair-breaking phenomena, leading e.g., to the suppression of the upper critical field $H_{\rm c2}$, found in the high-field region. The data show that the anomalous pair breaking becomes prominent below about 0.15 K in any field direction, but occurs closer to $H_{\rm c2}$ for $H \parallel c$. The presence of this anomaly is confirmed by the fact that the specific-heat and magnetization data satisfy standard thermodynamic relations. Concerning the gap structure, field-angle dependences of the low-temperature specific heat within the $ab$ and $ac$ planes do not show any evidence for gap nodes. From microscopic calculations in the framework of a two-band full-gap model, the power-law-like temperature dependences of $C$ and $1/T_1$, reminiscent of nodal superconductivity, have been reproduced reasonably. These facts further support multiband full-gap superconductivity in CeCu$_2$Si$_2$.

Interplay between effective mass anisotropy and Pauli paramagnetic effects in a multiband superconductor: Application toSr2RuO4

We investigate the mixed state properties in a type II multiband superconductor with uniaxial anisotropy under the Pauli paramagnetic effects. Eilenberger theory extended to a multiband superconductor is utilized to describe the detailed vortex lattice properties, such as the flux line form factors, the vortex lattice anisotropy and magnetic torques. We apply this theory to Sr$_2$RuO$_4$ to analyze those physical quantities obtained experimentally, focusing on the interplay between the strong two-dimensional anisotropy and the Pauli paramagnetic effects. This study allows us to understand the origin of the disparity between the vortex lattice anisotropy ($\sim$60) and the $H_{\rm c2}$ anisotropy ($\sim$20). Among the three bands; $\gamma$ with the effective mass anisotropy $\sim$180, $\alpha$ with $\sim$120, and $\beta$ with $\sim$60, the last one is found to be the major band, responsible for various magnetic responses while the minor $\gamma$ band plays an important role in the vortex formation. Namely, in a field orientation slightly tilted away from the two dimensional basal plane those two bands cooperatively form the optimal vortex anisotropy which exceeds that given by the effective mass formula with infinite anisotropy. This is observed by small angle neutron scattering experiments on Sr$_2$RuO$_4$. The pairing symmetry of Sr$_2$RuO$_4$ realized is either spin singlet or spin triplet with the d-vector strongly locked in the basal plane. The gap structure is that the major $\beta$ band has a full gap and the minor $\gamma$ band has a $d_{x^2-y^2}$ like gap.

Structural anomalies and short-range magnetic correlations in the orbitally degenerate systemSr2VO4

We report on the electronic ground state of a layered perovskite vanadium oxide Sr$_2$VO$_4$ studied by the combined use of synchrotron radiation x-ray diffraction (SR-XRD) and muon spin rotation/relaxation ($\mu$SR) techniques, where $\mu$SR measurements were extended down to 30 mK. We found an intermediate orthorhombic phase between $T_{\rm c2} \sim$~130 K and $T_{\rm c1} \sim$~100 K, whereas a tetragonal phase appears for $T > T_{\rm c2}$ and $T < T_{\rm c1}$. The absence of long-range magnetic order was confirmed by $\mu$SR at the reentrant tetragonal phase below $T_{\rm c1}$, where the relative enhancement in the $c$-axis length versus that of the $a$-axis length was observed. However, no clear indication of the lowering of the tetragonal lattice symmetry with superlattice modulation, which is expected in the orbital order state with superstructure of $d_{yz}$ and $d_{zx}$ orbitals, was observed by SR-XRD below $T_{\rm c1}$. Instead, it was inferred from $\mu$SR that a magnetic state developed below $T_{\rm c0} \sim$~10 K, which was characterized by the highly inhomogeneous and fluctuating local magnetic fields down to 30 mK. We argue that the anomalous magnetic ground state below $T_{\rm c0}$ originates from the coexistence of ferromagnetic and antiferromagnetic correlations.