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Unambiguous identification of the superconducting order parameter symmetry of Sr$_2$RuO$_4$ has remained elusive for more than a quarter century. While a chiral $p$-wave ground state analogue to superfluid $^3$He-$A$ was ruled out only very recently, other proposed $p$-wave scenarios are still viable. Here, field-dependent $^{17}$O Knight shift measurements are compared to corresponding specific heat measurements, previously reported. We conclude that the shift results can be accounted for by the expected field-induced quasiparticle response only. An upper bound for the condensate magnetic response of $, Main Article: 4 pages 3 figures Supplement: 6 pages 4 figures

There is considerable evidence that the superconducting state of Sr2RuO4 breaks time reversal symmetry. In the experiments showing time reversal symmetry breaking, its onset temperature, TTRSB, is generally found to match the critical temperature, Tc, within resolution. In combination with evidence for even parity, this result has led to consideration of a dxz ± idyz order parameter. The degeneracy of the two components of this order parameter is protected by symmetry, yielding TTRSB = Tc, but it has a hard-to-explain horizontal line node at kz = 0. Therefore, s ± id and d ± ig order parameters are also under consideration. These avoid the horizontal line node, but require tuning to obtain TTRSB ≈ Tc. 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 Sr2RuO4 under hydrostatic pressure, and Sr1.98La0.02RuO4 at zero pressure. Both hydrostatic pressure and La substitution alter Tc without lifting the tetragonal lattice symmetry, so if the degeneracy is symmetry-protected, TTRSB should track changes in Tc, while if it is accidental, these transition temperatures should generally separate. We observe TTRSB to track Tc, supporting the hypothesis of dxz ± idyz order., Nature Communications, 12 (1), ISSN:2041-1723

A key question regarding the unconventional superconductivity of Sr$_2$RuO$_4$ remains whether the order parameter is single- or two-component. Under a hypothesis of two-component superconductivity, uniaxial pressure is expected to lift their degeneracy, resulting in a split transition. The most direct and fundamental probe of a split transition is heat capacity. Here, we report measurement of heat capacity of samples subject to large and highly homogeneous uniaxial pressure. We place an upper limit on the heat-capacity signature of any second transition of a few per cent of that of the primary superconducting transition. The normalized jump in heat capacity, $\Delta C/C$, grows smoothly as a function of uniaxial pressure, favouring order parameters which are allowed to maximize in the same part of the Brillouin zone as the well-studied van Hove singularity. Thanks to the high precision of our measurements, these findings place stringent constraints on theories of the superconductivity of Sr$_2$RuO$_4$., Comment: This manuscript is an extended version of the scientific part of arXiv:1906.07597, which is being split into two separate papers. An extended discussion on the experimental methods can be found at arXiv:2009.03125. It includes supplemental material

This work has been financially supported by the Deutsche Forschungsgemeinschaft (GR 4667/1, GRK 1621 and SFB 1143 projects C02 and C09) and the Max Planck Society. Y.M., T.M. and J.S.B. acknowledge the financial support of JSPS Kakenhi (JP15H5852, JP15K21717 and JP17H06136) and the JSPS Core-to-Core Program. N.K. acknowledges the financial support from JSPS Kakenhi (no. JP18K04715) and JST-Mirai Program (no. JPMJMI18A3). A.N. acknowledges funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement no. 701647. Strontium ruthenate (Sr2RuO4) continues to present an important test of our understanding of unconventional superconductivity, because while its normal-state electronic structure is known with precision, its superconductivity remains unexplained. There is evidence that its order parameter is chiral, but reconciling this with recent observations of the spin part of the pairing requires an order parameter that is either finely tuned or implies a new form of pairing. Therefore, a definitive resolution of whether the superconductivity of Sr2RuO4 is chiral is important for the study of superconductivity. Here we report the measurement of zero-field muon spin relaxation—a probe sensitive to weak magnetism—on samples under uniaxial stresses. We observe stress-induced splitting between the onset temperatures of superconductivity and time-reversal symmetry breaking—consistent with the qualitative expectations for a chiral order parameter—and argue that this observation cannot be explained by conventional magnetism. In addition, we report the appearance of bulk magnetic order under higher uniaxial stress, above the critical pressure at which a Lifshitz transition occurs in Sr2RuO4. Postprint

We report resistance and elastoresistance measurements on $({\mathrm{Ba}}_{0.5}{\mathrm{K}}_{0.5}){\mathrm{Fe}}_{2}{\mathrm{As}}_{2}$, ${\mathrm{CaKFe}}_{4}{\mathrm{As}}_{4}$, and ${\mathrm{KCa}}_{2}{\mathrm{Fe}}_{4}{\mathrm{As}}_{4}{\mathrm{F}}_{2}$. The Fe-site symmetry is ${D}_{2d}$ in the first compound but ${C}_{2v}$ in the latter two, which lifts the degeneracy of the Fe ${d}_{xz}$ and ${d}_{yz}$ orbitals. The temperature dependence of the resistance and elastoresistance is similar between the three compounds. Especially, the [110] elastoresistance is enhanced with decreasing temperature irrespective of the Fe-site symmetry. This appears to be in conflict with recent Raman scattering studies on ${\mathrm{CaKFe}}_{4}{\mathrm{As}}_{4}$, which suggest the absence of nematic fluctuations. We consider possible ways of reconciliation and suggest that the present result is important in elucidating the origin of in-plane resistivity anisotropy in iron-based superconductors.

Sr2RuO4 has stood as the leading candidate for a spin-triplet superconductor for 26 years1. However, recent NMR experiments have cast doubt on this candidacy2,3 and it is difficult to find a theory of superconductivity that is consistent with all experiments. The order parameter symmetry for this material therefore remains an open question. Symmetry-based experiments are needed that can rule out broad classes of possible superconducting order parameters. Here, we use resonant ultrasound spectroscopy to measure the entire symmetry-resolved elastic tensor of Sr2RuO4 through the superconducting transition. We observe a thermodynamic discontinuity in the shear elastic modulus c66, which implies that the superconducting order parameter has two components. A two-component p-wave order parameter, such as px + ipy, naturally satisfies this requirement. As this order parameter appears to have been precluded by recent NMR experiments, we suggest that two other two-component order parameters, namely $$\{{d}_{xz},{d}_{yz}\}$$ and $$\{{d}_{{x}^{2}-{y}^{2}},{g}_{xy({x}^{2}-{y}^{2})}\}$$ , are now the prime candidates for the order parameter of Sr2RuO4. Ultrasound measurements show that the superconducting order parameter in strontium ruthenate must have two components.

Phases of matter are usually identified through spontaneous symmetry breaking, especially regarding unconventional superconductivity and the interactions from which it originates. In that context, the superconducting state of the quasi-two-dimensional and strongly correlated perovskite Sr2RuO4 is considered to be the only solid-state analogue to the superfluid 3He-A phase1,2, with an odd-parity order parameter that is unidirectional in spin space for all electron momenta and breaks time-reversal symmetry. This characterization was recently called into question by a search for an expected ‘split’ transition in a Sr2RuO4 crystal under in-plane uniaxial pressure, which failed to find any such evidence; instead, a dramatic rise and a peak in a single-transition temperature were observed3,4. Here we use nuclear magnetic resonance (NMR) spectroscopy of oxygen-17, which is directly sensitive to the order parameter via hyperfine coupling to the electronic spin degrees of freedom, to probe the nature of superconductivity in Sr2RuO4 and its evolution under strain. A reduction of the Knight shift is observed for all strain values and at temperatures below the critical temperature, consistent with a drop in spin polarization in the superconducting state. In unstrained samples, our results contradict a body of previous NMR work reporting no change in the Knight shift5 and the most prevalent theoretical interpretation of the order parameter as a chiral p-wave state. Sr2RuO4 is an extremely clean layered perovskite and its superconductivity emerges from a strongly correlated Fermi liquid, and our work imposes tight constraints on the order parameter symmetry of this archetypal system. Postprint

We perform de Haas-van Alphen measurements and quasiparticle self-consistent \textit{GW} (QS\textit{GW}) calculations on FeS. The calculated Fermi surface (FS) consists of two hole and two electron cylinders. We observe all the eight predicted FS cross sections experimentally. With momentum-independent band-energy adjustments of less than 0.1 eV, the maximum deviation between the calculated and observed cross sections is less than 0.2\% of the Brillouin zone area for $B \parallel c$. The carrier density is $\sim$0.5 carriers/Fe. The mass enhancements are nearly uniform across the FS cylinders and moderate, $\sim$2. The absence of a third hole cylinder with $d_{xy}$ character is favorable for the formation of a nodal superconducting gap., 7 pages, 3 figures

We report magnetic torque measurements on iron-pnictide superconductors ${\mathrm{Ba}}_{1\ensuremath{-}x}{\mathrm{K}}_{x}{\mathrm{Fe}}_{2}{\mathrm{As}}_{2}$ ($x\ensuremath{\approx}$ 0.69 and 0.76) to an applied field of ${B}_{a}=45$ T. The peak effect is observed in torque-vs-field curves below the irreversibility field. It is enhanced and becomes asymmetric as the field is tilted from the $c$ axis. For field directions close to the $ab$ plane, increasing- and decreasing-field curves peak at markedly different fields and exhibit a sharp jump, suggestive of a first-order phase transition, on the high- and the low-field sides of the peak, respectively. Complicated history dependence of the torque is observed in the peak-effect region. We construct and discuss the temperature-- ($T$) applied-magnetic-field (${B}_{a}$) phase diagram. Since the upper critical field for the $ab$-plane direction is comparable to the Pauli limit, we also consider possible influence of the spin paramagnetic effect on the anomalous peak effect.

High-quality single crystals are essentially needed for the investigation of the novel bulk properties of unconventional superconductors. The availability of such crystals grown by the floating-zone method has helped to unveil the unconventional superconductivity of the layered perovskite Sr$_2$RuO$_4$, which is considered as a strong candidate of a topological spin-triplet superconductor. Yet, recent progress of investigations urges further efforts to obtain ultimately high-quality crystalline samples. In this paper, we focus on the method of preparation of feed rods for the floating-zone melting and report on the improvements of the crystal growth. We present details of the improved methods used to obtain crystals with superconducting transition temperatures $T_\mathrm{c}$ that are consistently as high as 1.4 K, as well as the properties of these crystals., 9 pages, 6 figures

Resistance and magnetic torque measurements are reported in a layered organic superconductor, $\ensuremath{\beta}''\ensuremath{-}{(\mathrm{BEDT}\ensuremath{-}\mathrm{TTF})}_{4}[({\mathrm{H}}_{3}\mathrm{O})\mathrm{Ga}{({\mathrm{C}}_{2}{\mathrm{O}}_{4})}_{3}]{\mathrm{C}}_{6}{\mathrm{H}}_{5}{\mathrm{NO}}_{2}$ with ${T}_{c}=4.8$ K, where BEDT-TTF stands for bis(ethylenedithio)tetrathiafulvalene. Because of the large anion between the BEDT-TTF conducting layers, the superconductivity of this salt is highly anisotropic. In magnetic fields parallel to the conducting layers for $T=0.4$ K, the magnetic torque shows a large diamagnetic signal associated with hysteresis up to $\ensuremath{\sim}21$ T, suggesting the upper critical field ${H}_{c2}\ensuremath{\gtrsim}21$ T at 0.4 K. The large reduction of the diamagnetic signal is observed above 16 T, which shows a Fulde and Ferrell and Larkin and Ovchinnikov (FFLO) phase transition. For $T=0.5$ K, the interlayer resistance has nonzero value in a wide field region up to ${H}_{c2}$, arising from the Josephson vortex dynamics. Successive dips in the second derivative curves of the resistance are observed between 16 T and ${H}_{c2}$, which are ascribed to the commensurability effect between the Josephson vortex lattice and the order parameter oscillation of the FFLO phase. The commensurability effect is observed only in nearly parallel fields, showing that the FFLO phase is stable in a very limited field angle region. The temperature-field phase diagram is determined.

Magnetic torque measurements using a microcantilever have been performed to investigate the superconducting phase of ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$ down to 40 mK. For high-quality single crystals with the transition temperature $({T}_{\mathrm{c}})$ of 1.48--1.49 K, an abrupt jump of the torque signal is found near 1.5 T in field parallel to the conducting ${\mathrm{RuO}}_{2}$ planes below $\ensuremath{\sim}0.8\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. The jump corresponds to the first order transition recently revealed by magnetocaloric and magnetization measurements [Yonezawa et al., Phys. Rev. Lett. 110, 077003 (2013); Kittaka et al., Phys. Rev. B 90, 220502(R) (2014)]. Furthermore, weak diamagnetic and irreversible signals are found to persist above the first order transition up to 1.85 T. The result indicates the presence of a subphase boundary separating low- and high-field phases in the superconducting phase. The high-field subphase disappears when the field is tilted from the conducting planes only by a few degrees. Quantum oscillation measurements are also reported to clarify the strong sample-quality dependence of the high-field subphase.

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$_4$., Comment: 5 pages, 3 figures (main text) + 3 pages, 3 figures (supplemental material), accepted for publication in J. Phys. Soc. Jpn

We have investigated the magnetic field and temperature dependence of the tunneling spectra of the eutectic system Sr2RuO4-Ru. Electric contacts to individual Ru lamellae embedded in Sr2RuO4 enable the tunneling spectra at the interface between ruthenate and a Ru microinclusion to be measured. A zero bias conductance peak (ZBCP) was observed in the bias voltage dependence of the differential conductance, suggesting that Andreev bound states are present at the interface. The ZBCP starts to appear at a temperature well below the superconducting transition temperature. The onset magnetic field of the ZBCP is also considerably smaller than the upper critical field when the magnetic field is parallel to the ab-plane. We propose that the difference between the onset of the ZBCP and the onset of superconductivity can be understood in terms of the existence of the single-component state predicted by Sigrist and Monien., Comment: 4 pages, 4 figures, to appear in J. Phys. Soc. Jpn. vol. 74 no. 2

Hard X-ray photoemission studies are carried out to evaluate the electronic structure of iron-based superconductors BaFe2(As1−xPx)2 in a wide range of the P content 0 ≤ x ≤ 0.61. As x increases, th...

The crystal structure, superconducting properties, and electronic structure of a novel superconducting 122-type antimonide, BaPt$_2$Sb$_2$, have been investigated by measurements of powder X-ray diffraction patterns, electrical resistivity, ac magnetic susceptibility, specific heat as well as ab-initio calculations. This material crystallizes in a new-type of monoclinic variant of the CaBe$_2$Ge$_2$-type structure, in which Pt$_2$Sb$_2$ layers consisting of PtSb$_4$ tetrahedra and Sb$_2$Pt$_2$ layers consisting of SbPt$_4$ tetrahedra are stacked alternatively and Ba atoms are located between the layers. Measurements of electrical resistivity, ac magnetic susceptibility and specific heat revealed that BaPt$_2$Sb$_2$ is a superconducting material with a $T_{\rm c}$ of 1.8 K. The electronic heat capacity coefficient $\gamma_{\rm n}$ and Debye temperature $\theta_{\rm D}$ were 8.6(2) mJ/mol K$^2$ and 146(4) K, where the figures in parentheses represent the standard deviation. The upper critical field $\mu_{\rm 0}H_{\rm c2}(0)$ and the Ginzburg-Landau coherent length $\xi(0)$ were determined to be 0.27 T and 35 nm. Calculations showed that it has two three-dimensional Fermi surfaces (FSs) and two two-dimensional FSs, leading to anisotropic transport properties. The d-states of the Pt atoms in the Pt2Sb2 layers mainly contribute to $N(E_{\rm F})$. A comparison between experimental and calculated results indicates that BaPt$_2$Sb$_2$ is a superconducting material with moderate coupling., Comment: 24 pages, 9 figures

We report measurements of ac magnetic susceptibility ${\ensuremath{\chi}}_{\text{ac}}$ and de Haas--van Alphen (dHvA) oscillations in ${\mathrm{KFe}}_{2}$${\mathrm{As}}_{2}$ under high pressure up to 24.7 kbar. The pressure dependence of the superconducting transition temperature ${T}_{c}$ changes from negative to positive across ${P}_{c}\ensuremath{\sim}18$ kbar, as previously reported. The ratio of the upper critical field to ${T}_{c}$, i.e., ${B}_{c2}/{T}_{c}$, is enhanced above ${P}_{c}$, and the shape of the ${\ensuremath{\chi}}_{\text{ac}}$ versus field curves qualitatively changes across ${P}_{c}$. dHvA oscillations smoothly evolve across ${P}_{c}$, indicating no drastic change in the Fermi surface up to 24.7 kbar. Three dimensionality increases with pressure, while effective masses show decreasing trends. We suggest a crossover from a nodal to a full-gap $s$ wave as a possible explanation.

We have observed hysteresis in superconducting resistive transition curves of Ba${}_{0.07}$K${}_{0.93}$Fe${}_{2}$As${}_{2}$ (${T}_{c}\ensuremath{\sim}8$ K) below about 1 K for in-plane fields. The hysteresis is not observed as the field is tilted away from the $ab$ plane by 20${}^{\ensuremath{\circ}}$ or more. The temperature and angle dependencies of the upper critical field indicate a strong paramagnetic effect for in-plane fields. We suggest that the hysteresis can be attributed to a first-order superconducting transition due to the paramagnetic effect. Magnetic torque data are also shown.

We report measurements of resistance and ac magnetic susceptibility on FeSe single crystals under high pressure up to 27.2 kbar. The structural phase transition is quickly suppressed with pressure, and the associated anomaly is not seen above $\sim$18 kbar. The superconducting transition temperature evolves nonmonotonically with pressure, showing a minimum at $\sim12$ kbar. We find another anomaly at 21.2 K at 11.6 kbar. This anomaly most likely corresponds to the antiferromagnetic phase transition found in $\mu$SR measurements [M. Bendele \textit{et al.}, Phys. Rev. Lett. \textbf{104}, 087003 (2010)]. The antiferromagnetic and superconducting transition temperatures both increase with pressure up to $\sim25$ kbar and then level off. The width of the superconducting transition anomalously broadens in the pressure range where the antiferromagnetism coexists., Comment: 3 figures

We report the results of a study of the Hall effect and magnetoresistance in single crystals of ${\mathrm{Sr}}_{2}\mathrm{Ru}{\mathrm{O}}_{4}$ in which ${\mathrm{Sr}}^{2+}$ has been substituted by ${\mathrm{La}}^{3+}$ $({\mathrm{Sr}}_{2\ensuremath{-}y}{\mathrm{La}}_{y}\mathrm{Ru}{\mathrm{O}}_{4})$ or ${\mathrm{Ru}}^{4+}$ by ${\mathrm{Ti}}^{4+}$ $({\mathrm{Sr}}_{2}{\mathrm{Ru}}_{1\ensuremath{-}x}{\mathrm{Ti}}_{x}{\mathrm{O}}_{4})$. For undoped ${\mathrm{Sr}}_{2}\mathrm{Ru}{\mathrm{O}}_{4}$, the purity is so high that the strong-field Hall coefficient can be measured for fields above $4\phantom{\rule{0.3em}{0ex}}\mathrm{T}$. The conventional weak-field Hall coefficient as a function of doping shows a sharp jump and sign change at $y\ensuremath{\sim}0.01$ that is unrelated to either a sharp change in Fermi-surface topography or a magnetic instability. The implications of these results are discussed.

We report a study of magnetic, thermal, and transport properties of ${\mathrm{La}}^{3+}$ substituted ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$, performed in order to investigate the effects of additional electron doping in this correlated metal. A gradual enhancement of the electronic part of specific heat and a more drastic increase of the static magnetic susceptibility were observed in ${\mathrm{Sr}}_{2\ensuremath{-}y}{\mathrm{La}}_{y}{\mathrm{RuO}}_{4}$ with increasing $y$. Furthermore, the quasi-two-dimensional Fermi-liquid behavior seen in pure ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$ breaks down near the critical concentration ${y}_{\mathrm{c}}\ensuremath{\sim}0.20$. Combined with a realistic tight-binding model with rigid-band shift of Fermi level, the enhancement of the density of states can be ascribed to the elevation of the Fermi energy toward a van Hove singularity of the thermodynamically dominant $\ensuremath{\gamma}$ Fermi-surface sheet. On approaching the van Hove singularity, the effective nesting vector of the $\ensuremath{\gamma}$ band shrinks and further enhances the susceptibility near the wave vector $q\ensuremath{\sim}0$. We attribute the non-Fermi-liquid behavior to two-dimensional ferromagnetic fluctuations with short range correlations at the van Hove singularity. The observed behavior is in sharp contrast to that of ${\mathrm{Ti}}^{4+}$ substitution in ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$ which enhances antiferromagnetic fluctuations and subsequently induces incommensurate magnetic ordering associated with the nesting between the other Fermi-surface sheets ($\ensuremath{\alpha}$ and $\ensuremath{\beta}$). We thus establish that substitution of appropriate chemical dopants can band selectively modify the spin-fluctuation spectrum in the spin-triplet superconductor ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$.

We report a systematic study of electron doping of ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$ by nonisovalent substitution of ${\mathrm{La}}^{3+}$ for ${\mathrm{Sr}}^{2+}$. Using a combination of de Haas-van Alphen oscillations, specific heat, and resistivity measurements, we show that electron doping leads to a rigid-band shift of the Fermi level corresponding to one doped electron per $\mathrm{La}$ ion, with constant many-body quasiparticle mass enhancement over the band mass. The susceptibility spectrum is substantially altered and enhanced by the doping but this has surprisingly little effect on the strength of the unconventional superconducting pairing.

We describe transport measurements in single-crystal, high-purity Ca 3 Ru 2 O 7 . The observation of a large linear magnetoresistance together with low frequency quantum oscillations is shown to be consistent with a small volume Fermi surface incompletely gapped by density wave formation. This complements previous ARPES experiments. The quantum oscillations are more pronounced in the Hall signal than in the longitudinal resistivity. This unusual observation is also explained by the peculiar electronic structure in this material. We remark on the similarity between our observations in Ca 3 Ru 2 O 7 and the observations of quantum oscillations in the underdoped cuprate superconductors.