[Paper Review] Pronounced drop of $^{17}$O NMR Knight shift in superconducting state of Sr$_2$RuO$_4$

Andrej Pustogow, Yongkang Luo+10 more|arXiv (Cornell University)|Mar 29, 2019

Advanced Condensed Matter Physics12 references108 citations

TL;DR

This study uses 17O NMR under uniaxial strain to show a pronounced drop in spin polarization in Sr2RuO4 upon entering the superconducting state, challenging previous zero-strain interpretations of its order parameter.

ABSTRACT

The superconducting state in the quasi-two-dimensional and strongly correlated Sr$_2$RuO$_4$ is uniquely held up as a solid state analog to superfluid $^3$He-$A$, with an odd-parity order parameter that also breaks time reversal symmetry, and for which the vector order parameter has the same direction in spin space for all electron momenta. The recent discovery that uniaxial pressure causes a steep rise and maximum in transition temperature ($T_c$) in strained samples motivated the study of $^{17}$O nuclear magnetic resonance (NMR) that we describe in this article. A reduction of Knight shifts $K$ was observed for all strain values and temperatures $T

Motivation & Objective

• Motivate the search for the superconducting order parameter in Sr2RuO4 by testing spin susceptibility under strain.
• Use 17O NMR Knight shift to probe spin polarization across Tc under varying uniaxial strain.
• Investigate whether strain-induced Tc enhancement correlates with changes in order parameter symmetry.
• Evaluate potential artifacts in prior zero-strain Knight shift measurements and reconcile with TRSB observations.

Proposed method

• Apply uniaxial stress along the a-axis to tune Sr2RuO4 across Tc up to Tc,max ≈ 3.5 K.
• Perform 17O NMR central-transition measurements on three oxygen sites (O(1), O(1′), O(2)) at low fields B0 ≪ Bc2 to extract Knight shifts K.
• Analyze Knight shifts as a function of temperature across Tc for various strains, accounting for quadrupolar corrections in the central transition.
• Use pulse-energy dependent and time-synchronous RF measurements to assess possible heating and transient effects on the observed shifts.
• Compare strained zero-strain results to prior unstrained measurements to assess consistency with proposed order parameters.

Experimental results

Research questions

• RQ1 Does the spin susceptibility, as inferred from 17O Knight shifts, drop in Sr2RuO4 when entering the superconducting state under zero and strained conditions?
• RQ2 How does uniaxial strain (and the associated Tc enhancement) affect the Knight shift and hence the possible symmetry of the superconducting order parameter?
• RQ3 Are there experimental artifacts (e.g., pulse heating, transient states) that could reconcile zero-strain Knight shift results with strained measurements?
• RQ4 Do the strain-dependent results rule out chiral p-wave (out-of-plane d-vector) as the sole description of the pairing across the strain range?

Key findings

• Knight shifts for all three O sites show a pronounced reduction below Tc under strain, indicating a drop in spin polarization Ms in the superconducting state.
• Zero-strain measurements differ from prior reports, challenging the conventional chiral p-wave (out-of-plane d-vector) interpretation.
• At both zero strain and at the van Hove singularity (maximum Tc under strain), the spin susceptibility is substantially suppressed at 20 mK, with the extent depending on field, suggesting not all triplet states are compatible with the data.
• Lower applied fields (e.g., B0 ≈ 0.71 T) yield larger Knight shift reductions (up to ~75% in one strain case), implying stronger constraints on possible triplet states.
• Time-synchronous RF measurements reveal transient normal-like responses immediately after high-energy pulses, indicating heating effects and vortex dynamics that must be accounted for in interpreting Knight shifts.
• Across strains εaa ∈ [0, εv], the Knight shift changes vary smoothly with strain, with no observed first-order transition splittings that would indicate a clear symmetry change under uniaxial pressure.
• Overall, the results argue against a simple out-of-plane triplet (Eu with d-vector along z) and motivate consideration of alternative even- or odd-parity states, acknowledging that some odd-parity states with in-plane d-vectors may still be compatible within uncertainties.