Absence of a Large Superconductivity-Induced Gap in Magnetic Fluctuations of Sr_{2}RuO_{4}

Resonance from antiferromagnetic spin fluctuations for superconductivity in UTe2

Superconductivity originates from the formation of bound (Cooper) pairs of electrons that can move through the lattice without resistance below the superconducting transition temperature T_c (ref. ¹). Electron Cooper pairs in most superconductors form anti-parallel spin singlets with total spin S = 0 (ref. ²), although they can also form parallel spin-triplet Cooper pairs with S = 1 and an odd parity wavefunction³. Spin-triplet pairing is important because it can host topological states and Majorana fermions relevant for quantum computation^4,5. Because spin-triplet pairing is usually mediated by ferromagnetic (FM) spin fluctuations³, uranium-based materials near an FM instability are considered to be ideal candidates for realizing spin-triplet superconductivity⁶. Indeed, UTe₂, which has a T_c ≈ 1.6 K (refs. ^7,8), has been identified as a candidate for a chiral spin-triplet topological superconductor near an FM instability^7-14, although it also has antiferromagnetic (AF) spin fluctuations^15,16. Here we use inelastic neutron scattering (INS) to show that superconductivity in UTe₂ is coupled to a sharp magnetic excitation, termed resonance^17-23, at the Brillouin zone boundary near AF order. Because the resonance has only been found in spin-singlet unconventional superconductors near an AF instability^17-23, its observation in UTe₂ suggests that AF spin fluctuations may also induce spin-triplet pairing²⁴ or that electron pairing in UTe₂ has a spin-singlet component.

Incommensurate Spin Fluctuations in the Spin-Triplet Superconductor Candidate UTe_{2}

Spin-triplet superconductors are of extensive current interest because they can host topological state and Majorana fermions important for quantum computation. The uranium-based heavy-fermion superconductor UTe_{2} has been argued as a spin-triplet superconductor similar to UGe_{2}, URhGe, and UCoGe, where the superconducting phase is near (or coexists with) a ferromagnetic (FM) instability and spin-triplet electron pairing is driven by FM spin fluctuations. Here we use neutron scattering to show that, although UTe_{2} exhibits no static magnetic order down to 0.3 K, its magnetism in the [0,K,L] plane is dominated by incommensurate spin fluctuations near an antiferromagnetic ordering wave vector and extends to at least 2.6 meV. We are able to understand the dominant incommensurate spin fluctuations of UTe_{2} in terms of its electronic structure calculated using a combined density-functional and dynamic mean-field theory.

Superconducting Symmetries of Sr_{2}RuO_{4} from First-Principles Electronic Structure

Although correlated electronic-structure calculations explain very well the normal state of Sr_{2}RuO_{4}, its superconducting symmetry is still unknown. Here we construct the spin and charge fluctuation pairing interactions based on its correlated normal state. Correlations significantly reduce ferromagnetic in favor of antiferromagnetic fluctuations and increase interorbital pairing. From the normal-state Eliashberg equations, we find spin-singlet d-wave pairing close to magnetic instabilities. Away from these instabilities, where charge fluctuations increase, we find two time-reversal symmetry-breaking spin triplets: an odd-frequency s wave, and a doubly degenerate interorbital pairing between d_{xy} and (d_{yz},d_{xz}).

Spin Fluctuations in Sr_{2}RuO_{4} from Polarized Neutron Scattering: Implications for Superconductivity

Triplet pairing in Sr_{2}RuO_{4} was initially suggested based on the hypothesis of strong ferromagnetic spin fluctuations. Using polarized inelastic neutron scattering, we accurately determine the full spectrum of spin fluctuations in Sr_{2}RuO_{4}. Besides the well-studied incommensurate magnetic fluctuations, we do find a sizable quasiferromagnetic signal, quantitatively consistent with all macroscopic and microscopic probes. We use this result to address the possibility of magnetically driven triplet superconductivity in Sr_{2}RuO_{4}. We conclude that, even though the quasiferromagnetic signal is stronger and sharper than previously anticipated, spin fluctuations alone are not enough to generate a triplet state strengthening the need for additional interactions or an alternative pairing scenario.