Pinning of dynamic spin-density-wave fluctuations in cuprate superconductors

We present a theory of the pinning of dynamic spin-density-wave (SDW) fluctuations in a d-wave superconductor by local imperfections that preserve spin-rotation invariance, such as impurities or vortex cores. The pinning leads to static spatial modulations in spin-singlet observables, while the SDW correlations remain dynamic: these are the Friedel oscillations of a spin-gap antiferromagnet. We connect the spectrum of these modulations as observed by scanning tunnelling microscopy to the dynamic spin structure factor measured by inelastic neutron scattering.