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


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.

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Fig. 1: Strain dependence of the upper critical field of Sr2RuO4.
Fig. 2: Knight shift K versus temperature T, measured at the van Hove singularity (εaa = εv).
Fig. 3: Zero-strain 17O NMR spectra of Sr2RuO4 for varying pulse energy.
Fig. 4: Transient effects following radiofrequency pulses for εaa = 0.

Data availability

The data that support the findings of this study can be accessed at Additional information is available from the corresponding authors upon reasonable request.


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We thank M. Ikeda and S. Kivelson for conversations. We particularly appreciate discussions with K. Ishida and Y. Maeno about the implications of our findings, and K. Ishida for reproducing our results. A.P. acknowledges support by the Alexander von Humboldt Foundation through a Feodor Lynen Fellowship. Y.L. acknowledges support by the 1000 Youth Talents Plan of China. N.K. acknowledges support from JSPS KAKENHI (number JP18K04715) and JST-Mirai Program (number JPMJMI18A3) in Japan. S.R. is supported in part by the US Department of Energy, Office of Basic Energy Sciences, contract DEAC02-76SF00515. This work was supported in part by the National Science Foundation (DMR-1709304) and by the Laboratory Directed Research and Development (LDRD) programme of Los Alamos National Laboratory under project number 20170204ER.

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Y.L., A.P., A.P.M. and S.E.B. conceived and designed the experiments. D.A.S., N.K., F.J., C.W.H. and A.P.M. prepared the crystal. E.D.B. characterized the sample and performed the spin labelling. A.P. and Y.L. performed the NMR measurements, supported by Y.-S.S. and A.C.; A.P., Y.L., C.W.H., A.P.M., S.R. and S.E.B. discussed the data, interpreted the results and wrote the paper with input from all authors. The time-synchronous reflection experiments were performed by S.E.B., A.P. and A.C.

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Correspondence to A. Pustogow or Yongkang Luo or S. E. Brown.

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Peer review information Nature thanks Catherine Kallin, Guo-qing Zheng and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Extended data figures and tables

Extended Data Fig. 1 RuO2 plane, with dxyp hybridizing orbitals and experimental setup.

a, Ru dxy and hybridizing O p orbitals at the Y point, which dominate the formation of the γ band. NMR shifts are measured at the O(1) and O(1′) sites. b, Compressive a-axis stress shifts the γ-band Fermi surface to the zone boundary at Y. vHs, van Hove singularity. c, Strain device. The enlarged view highlights the Sr2RuO4 single crystal mounted between the piezoelectric actuators, with B0 parallel to the b axis and the compressive stress along the a axis, εaa. The NMR coil covers the free part of ~1 mm length.

Extended Data Fig. 2 Estimation of strain gradients.

a, Power reflected from the tank circuit during magnetic-field sweeps. The steepest slope of δρT(B0) corresponds to the Bc2 values shown in Fig. 1. The broadening of the superconducting transition was modelled by a Gaussian strain distribution of half-width δε/εaa ≈ 10% (pink lines). b, The fitting curves also match with the corresponding derivative d(δρT)/dB0. For clarity, only a subset of the measured fields is shown.

Extended Data Fig. 3 Tuning of the crystal to zero strain.

a, Measurements of the reflected power δρT at low strain indicate that Bc2 has a minimum near UPiezo = 0 V. b, The derivative d(δρT)/dB0 illustrates that the Bc2 value associated with the largest rate of change at the transition midpoint first decreases when reducing the compression (UPiezo changing from −20 V to 0 V), followed by a slight increase upon tensile strain (UPiezo changing from 0 V to +12 V). c, The coil impedance was measured at the transition midpoint (B0 fixed at Bc2, as indicated in the inset), providing a sensitive measure of modifications upon changing the strain. Bc2 was determined by a field sweep at intervals of 20 V or less, and then B0 was set to the new transition midpoint. The results (solid blue squares) were corrected for the different B0 values, yielding one half of a parabola centred around [−10 V, 10 V], very similar to the strain dependence of Tc reported in ref. 3 (dashed black line).

Extended Data Fig. 4 Transient effects associated with normal-state response.

a, The transient components of the reflected power are plotted as a function of pulse energy E and time τ after the pulse (see Fig. 4). CW, continuous wave; IP, in-phase; Q, quadrature. b, The magnetic-field dependence of the reflected power was recorded at E = 0.8 μJ. The changes in δρT(B0) for increasing B0 from the measurement field (0.7107 T) to B0 > Bc2 match well with the time-dependent recovery in a, as indicated by the horizontal dotted lines. Both channels (IP and Q) indicate a variation in δρT that results from a transition between normal and superconducting states around τ ≈ 100 μs.

Extended Data Fig. 5 Strain dependence of 17O Knight shifts in the superconducting and normal states.

Comparison of shifts in the normal and superconducting states for strains covering the range εaa = [0, εv]. The top and bottom parts of the figure show the O(1′) and O(1) sites, respectively. The normal-state results (indicated by black and red solid symbols) were recorded at 4.3 K and two different field strengths19. Open symbols correspond to an equilibrium temperature of 20 mK, which is within the superconducting state for sufficiently high Tc, realized by large strain and small magnetic field. Blue and orange symbols correspond to field strengths of 0.7107 T and 1.1573 T, respectively. The results for B0 = 1.9980 T are shown in green (εaa = εv; see Fig. 2).

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Pustogow, A., Luo, Y., Chronister, A. et al. Constraints on the superconducting order parameter in Sr2RuO4 from oxygen-17 nuclear magnetic resonance. Nature 574, 72–75 (2019).

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