Dynamic Parallel Spin Stripes from the 1/8 anomaly to the End of Superconductivity in La$_{1.6-x}$Nd$_{0.4}$Sr$_x$CuO$_4$*

Incommensurate magnetic structures based on spin stripes are known to be present across the phase diagram for hole-doped cuprates. These have been extensively studied in the 214 family of cuprates at low hole doping. The dynamic spectral weight associated with spin stripes has also been studied using inelastic neutron scattering and RIXS, with somewhat conflicting conclusions including a dimunition of spectral weight near (pi,pi) wavevectors and persistant paramagnon scattering at smaller wavevctors..  We have recently carried out inelastic neutron scattering experiments on four single crystals of Nd-LSCO with relatively high hole doping between x = 0.12 to 0.26 using time-of-flight techniques. Samples at these hole-doping levels are known to display static parallel spin stripes at low temperature, with onset temperatures and intensities which decrease rapidly with increasing x [1]. We report remarkably similar dynamic spectral weight for the corresponding dynamic parallel spin stripes, from the 1/8 anomaly near x=0.12,  to near x=0.26. Our new results are therefore consistent with persistent parallel spin stripe fluctuations around (pi, pi) across a wide range of Sr doping. These neutron scattering results, both the persistent  parallel spin stripe fluctuations and the rapid fall off with doping of the signal from the static parallel spin stripes show a remarkable similarity to the results of recent calculations for a quantum spin glass, based on a random t-J model [2].