Incommensurate spin-density wave and multiband superconductivity in Na$_{x}$FeAs as revealed by nuclear magnetic resonance

TL;DR

This study uses NMR to reveal incommensurate spin-density wave order and multiband superconductivity in Na$_{x}$FeAs, showing coexistence and competition between magnetic order and superconductivity across different compositions.

Contribution

It provides the first NMR evidence of incommensurate SDW coexisting with superconductivity in Na$_{x}$FeAs, highlighting the role of multiband effects and partial Fermi surface gapping.

Findings

Incommensurate SDW order is confirmed by NMR lineshape analysis.

Superconductivity coexists with gapless excitations in the SDW state.

The SDW order parameter inversely correlates with the superconducting fraction.

Abstract

We report a $^{23}$Na and $^{75}$As nuclear magnetic resonance (NMR) investigation of Na$_{x}$FeAs series ($x=1$, 0.9, 0.8) exhibiting a spin-density wave (SDW) order below $T_{\rm SDW}=45$, 50 and 43 K for $x=1$, 0.9, 0.8, respectively, and a bulk superconductivity below $T_c\approx 12$ K for x=0.9. Below $T_{\rm SDW}$, a spin-lattice relaxation reveals the presence of gapless particle-hole excitations in the whole $x$ range, meaning that a portion of the Fermi surface remains gapless. The superconducting fraction as deduced from the bulk susceptibility scales with this portion, while the SDW order parameter as deduced from the NMR linewidth scales inversely with it. The NMR lineshape can only be reproduced assuming an incommensurate (IC) SDW. These findings qualitatively correspond to the mean-field models of competing interband magnetism and intraband superconductivity, which lead to an IC SDW order coexisting with superconductivity in part of the phase diagram.