Horizontal Line Nodes in Sr₂RuO₄ Proved by Spin Resonance

Abstract

We investigated the low-energy incommensurate (IC) magnetic fluctuations in Sr2RuO4 by the high-resolution inelastic neutron scattering measurements and random phase approximation (RPA) calculations. We observed a spin resonance with energy of ωres = 0.56 meV centered at a characteristic wavevector Qres = (0.3, 0.3, 0.5). The resonance energy corresponds well to the superconducting gap 2∆ = 0.56 meV estimated by the tunneling spectroscopy. The spin resonance shows the L modulation with a maximum at around L = 0.5. The L modulated intensity of the spin resonance and our RPA calculations indicate that the superconducting gaps regarding the quasi-one-dimensional α and β sheets at the Fermi surfaces have the horizontal line nodes. These results may set a strong constraint on the pairing symmetry of Sr2RuO4. We also discuss the implications on possible superconducting order parameters.

Neutron scattering studies on spin fluctuations in Sr2RuO4

“…However, the anisotropy of the gap function and interactions can strongly modify the magnetic response in the superconducting state. A more recent time-of-flight (TOF) inelastic neutron scattering experiment confirms the absence of a large gap but reports weak evidence for suppression of spectral weight at very low energies [53]. This experiment also claims the occurrence of a spin resonance mode at the nesting position with a finite perpendicular wave-vector component, which would point to an essential modulation of the superconducting gap perpendicular to the RuO 2 layers but which is inconsistent with the results of this work.…”

“…The opening of a superconductivity-induced gap in the spectrum of magnetic fluctuations would have a strong impact on the discussion of the superconducting character in Sr 2 RuO 4 . Previous INS experiments using a TAS revealed the clear absence of a large gap at the nesting position [52], whereas a recent TOF experiment reports a tiny gap, although the statistics remained very poor [53]. Studying the magnetic response of Sr 2 RuO 4 in its superconducting phase by INS is challenging, because one needs to focus on small energies of the order of 0.2-0.5 meV.…”

“…Following the claim of Iida et al [53], the TOF data are also analyzed in terms of a possible resonance mode appearing at a finite value of the L component, i.e., at (0.3,0.3,0.5). Therefore, the L dependence of the magnetic signal at (0.3, 0.3, L) is determined by background subtraction and compared for the two temperatures (see Fig.…”

“…The different panels represent the energy ranges from Ref. [53], where a resonance appearing at 0.56 meV is proposed for L = 0.5. In our data shown in Fig.…”

Superconducting subphase and substantial Knight shift in Sr2RuO4

“…It should be noted that the experimental specific heat may be captured by either horizontal or vertical line nodes, or simply deep minima on the gap function. Recent experiments are in conflict on this matter: whereas the thermal conductivity measurements show that the gap structure of Sr 2 RuO 4 consists of vertical line nodes 40 with no evidence of deep minima, both spin resonance in inelastic neutron scattering measurements 41 and fieldangle-dependent specific heat capacity measurements 42 provided evidence of horizontal line nodes.…”