Phases of matter are usually identified through the lens of spontaneous symmetry breaking, which particularly applies to unconventional superconductivity and the interactions it originates from. In that context, the superconducting state of the quasi-two-dimensional and strongly correlated Sr 2 RuO 4 is uniquely held up as a solid-state analog to superfluid 3 He-A 1, 2 , with an odd-parity vector order parameter that is unidirectional in spin space for all electron momenta and also breaks time-reversal symmetry. This characterization was recently * These authors contributed equally to this work. 1 called into question by a search for, and failure to find, evidence for an expected "split" transition while subjecting a Sr 2 RuO 4 crystal to in-plane uniaxial pressure; instead a dramatic rise and peak in a single transition temperature was observed 3, 4. NMR spectroscopy, which is directly sensitive to the order parameter via the hyperfine coupling to the electronic spin degrees of freedom, is exploited here to probe the nature of superconductivity in Sr 2 RuO 4 and its evolution under strained conditions. A reduction of Knight shifts K is observed for all strain values and temperatures T < T c , consistent with a drop in spin polarization in the superconducting state. In unstrained samples, our results are in contradiction with a body of previous NMR work 5 , and with the most prominent previous proposals for the order parameter. Sr 2 RuO 4 is an extremely clean layered perovskite, and the superconductivity emerges from a strongly correlated Fermi Liquid. The present work imposes tight constraints on the order-parameter symmetry of this archetypal system. The normal state of Sr 2 RuO 4 is based on three bands crossing the Fermi level 6, 7 , with pronounced strong-correlation characteristics linked to Hund's Rule coupling of the partially filled Ru t 2g orbitals dominating the Fermi surface. The transition to a superconducting ground state at T c =1.5 K 8 , with indirect evidence for proximity to ferromagnetism, led to the suggestion that the pair wave functions of the superconducting state likely exhibit a symmetric spin part, i.e., triplet 1. Crucial support for the existence of a triplet order parameter rested on NMR spectroscopy, which showed no change in Knight shift between normal and superconducting states 5. Later, several experiments produced evidence for time-reversal symmetry breaking (TRSB) 9, 10. Together, these reports aligned well to the above-mentioned proposal that Sr 2 RuO 4 is a very clean, quasi two

Sr & RuO ' is an unconventional superconductor that has attracted widespread study because of its high purity and the possibility that its superconducting order parameter has odd parity. We study the dependence of its superconductivity on anisotropic strain. Applying uniaxial pressures of up to ~1 GPa along a 〈100〉 direction ( -axis) of the crystal lattice results in . increasing from 1.5 K in the unstrained material to 3.4 K at compression by ≈0.6%, and then falling steeply. Calculations give evidence that the observed maximum . occurs at or near a Lifshitz transition when the Fermi level passes through a Van Hove singularity, and open the possibility that the highly strained, . =3.4 K Sr & RuO ' has an even-rather than an odd-parity order parameter.The formation of superconductivity by the condensation of electron pairs into a coherent

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The effects of uniaxial compressive stress on the normal state 17 O nuclear magnetic resonance properties of the unconventional superconductor Sr2RuO4 are reported. The paramagnetic shifts of both planar and apical oxygen sites show pronounced anomalies near the nominal a-axis strain εaa ≡ εv, that maximizes the superconducting transition temperature, Tc. The spin susceptibility weakly increases on lowering the temperature below T 10 K, consistent with an enhanced density of states associated with passing the Fermi energy through a van Hove singularity. Although such a Lifshitz transition occurs in the γ band, formed by the Ru dxy states hybridized with in-plane O pπ orbitals, the large Hund's coupling renormalizes the uniform spin susceptibilty, which, in turn, affects the hyperfine fields of all nuclei. We estimate this "Stoner" renormalization, S, by combining the data with first-principles calculations and conclude that this is an important part of the strain effect, with implications for superconductivity.

A key question regarding the unconventional superconductivity of Sr2RuO4 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 percent of that of the primary superconducting transition. The normalized jump in heat capacity, ΔC/C, grows smoothly as a function of uniaxial pressure, favoring 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 Sr2RuO4.

Unambiguous identification of the superconducting order parameter symmetry in Sr2RuO4 has remained elusive for more than a quarter century. While a chiral p-wave ground state analogue to superfluid 3He-A was ruled out only very recently, other proposed triplet-pairing scenarios are still viable. Establishing the condensate magnetic susceptibility reveals a sharp distinction between even-parity (singlet) and odd-parity (triplet) pairing since the superconducting condensate is magnetically polarizable only in the latter case. Here field-dependent 17O Knight shift measurements, being sensitive to the spin polarization, are compared to previously reported specific heat measurements for the purpose of distinguishing the condensate contribution from that due to quasiparticles. We conclude that the shift results can be accounted for entirely by the expected field-induced quasiparticle response. An upper bound for the condensate magnetic response of <10% of the normal state susceptibility is sufficient to exclude all purely odd-parity candidates.

One of the main developments in unconventional superconductivity in the past two decades has been the discovery that most unconventional superconductors form phase diagrams that also contain other strongly correlated states. Many systems of interest are therefore close to more than one instability, and tuning between the resultant ordered phases is the subject of intense research1. In recent years, uniaxial pressure applied using piezoelectric-based devices has been shown to be a particularly versatile new method of tuning2,3, leading to experiments that have advanced our understanding of the fascinating unconventional superconductor Sr2RuO4 (refs. 4–9). Here we map out its phase diagram using high-precision measurements of the elastocaloric effect in what we believe to be the first such study including both the normal and the superconducting states. We observe a strong entropy quench on entering the superconducting state, in excellent agreement with a model calculation for pairing at the Van Hove point, and obtain a quantitative estimate of the entropy change associated with entry to a magnetic state that is observed in proximity to the superconductivity. The phase diagram is intriguing both for its similarity to those seen in other families of unconventional superconductors and for extra features unique, so far, to Sr2RuO4.

We perform nuclear magnetic resonance (NMR) measurements of the oxygen-17 Knight shifts for Sr2RuO4, while subjected to uniaxial stress applied along [100] direction. The resulting strain is associated with a strong variation of the temperature and magnetic field dependence of the inferred magnetic response. A quasiparticle description based on density-functional theory calculations, supplemented by many-body renormalizations, is found to reproduce our experimental results, and highlights the key role of a van-Hove singularity. The Fermi-liquid coherence scale is shown to be tunable by strain, and driven to low values as the associated Lifshitz transition is approached.