Constraints on the superconducting order parameter in Sr2RuO4 from oxygen-17 nuclear magnetic resonance

Abstract

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

Properties of the H−T phase diagram of the 3−K phase in eutectic Sr2Kaneyasu1, Enokida2, Nomura3 et al. 2019Phys. Rev. B7190View full textAdd to dashboardCite

“…The former is a spin-singlet state based on interlayer pairing, and the latter corresponds to in-plane equal-spin pairing (spin triplet with S z = 0), where the paired electrons lie in the same plane. While the NMR-Knight-shift data appeared to clearly support the in-plane equal-spin pairing state [17,18], recent experiments have shown that the susceptibility is reduced in the superconducting phase for in-plane fields because it is more compatible with the even-parity spin-singlet phase [19,20]. The in-plane upper critical field displays features analogous to paramagnetic limiting, which is in agreement with the above-mentioned result [4,[21][22][23].…”

Distinct reduction of Knight shift in superconducting state of Sr2RuO4 under uniaxial strain

“…1, leading to a larger drop in the spin-polarization along the b axis than that of the unstrained case, as reported in Ref. [12]. With the same strain condition, the a-axis polarization drop should be smaller.…”

“…Since the no-change Knight shift across T c has been the strong piece of evidence of a spin triplet, this observation may rule out several spin-triplet pairings including the d vector along the c axis, and potentially in the ab plane, depending on the magnitude of the decrease observed, as listed in Ref. [12].…”

“…Recently, Pustogow et al [12] made an important breakthrough in determining the spin component of the order parameter, as they reported a 20%-50% drop, depending on the field strength, in the spin polarization M s below T c in unstrained samples in contrast to the earlier NMR reports [5]. When the sample is strained along the a axis, the spin polarization along the b axis drops almost 75%.…”

Exploring Topological Superconductivity in Topological Materials

“…First, the evidence of a superconducting gap in Sr 2 RuO 4 is inconclusive, although a gap node has been evidenced by measurements of the specific heat, thermal conductivity, and 1/T 1 as well as by the temperature dependence of the penetration depth . A recent NMR study on Sr 2 RuO 4 found a substantially suppressed spin susceptibility, which could cause considerable controversy over its superconducting order paramenter . According to a theoretical work, topological edge states may exist in nodal gap superconductors, but the edge state is weaker than that in fully gapped systems .…”