  Quasi-two dimensional quantum magnetism is clearly highly correlated with
superconducting ground states in cuprate-based High T$_c$ superconductivity.
Three dimensional, commensurate long range magnetic order in La$_2$CuO$_4$
quickly evolves to quasi-two dimensional, incommensurate correlations on doping
with mobile holes, and superconducting ground states follow for x as small as
0.05 in the La$_{2-x}$Sr$_x$/Ba$_x$CuO$_4$ family of superconductors. It has
long been known that the onset of superconducting ground states in these
systems is coincident with a remarkable rotation of the incommensurate spin
order from "diagonal stripes" below x = 0.05, to "parallel stripes" above.
However, little is known about the spin correlations at optimal and high doping
levels, where the dome of superconductivity draws to an end. Here we present
new elastic and inelastic neutron scattering measurements on single crystals of
La$_{1.6-x}$Nd$_{0.4}$Sr$_x$CuO$_4$ with x = 0.125, 0.19, 0.24 and 0.26, and
show that two dimensional, quasi-static, parallel spin stripes are observed to
onset at temperatures such that the parallel spin stripe phase envelopes all
superconducting ground states in this system. Parallel spin stripes stretch
across 0.05 < < 0.26, with rapidly decreasing moment size and onset
temperatures for x > 0.125. We also show that the low energy, parallel spin
stripe fluctuations for optimally doped x = 0.19 display dynamic spectral
weight which grows with decreasing temperature and saturates below its
superconducting T$_c$. The elastic order parameter for x = 0.19 also shows
plateau behavior coincident with the onset of superconductivity. This set of
observations assert the foundational role played by two dimensional parallel
spin stripe order and fluctuations in High T$_c$ cuprate superconductivity.
