Three-dimensional, commensurate long-range magnetic order in ${\mathrm{La}}_2{\mathrm{CuO}}_4$ quickly evolves to quasi-two-dimensional, incommensurate correlations upon doping with mobile holes, and superconductivity follows for $x$ as small as 0.05 in the ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x/{\mathrm{Ba}}_x{\mathrm{CuO}}_4$ family of superconductors. The onset of superconductivity in these systems is known to be 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, around and beyond the proposed quantum critical point for the pseudogap phase, $p^{*}$. Here, we present elastic and inelastic neutron scattering measurements on single crystals of ${\mathrm{La}}_{1.6-x}{\mathrm{Nd}}_{0.4}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$ with $x$ = 0.125, 0.19, 0.24, and 0.26 and show that two-dimensional, quasistatic, parallel spin stripes have an onset at temperatures such that the parallel spin stripe phase extends beyond $p^{*}$ and envelops the entirety of superconducting ground states in this system. We also show that the elastic order parameter for parallel spin stripes at optimum doping, $x$ = 0.19, displays an inflection point at superconducting $T_c$, while the low-energy dynamic spectral weight of parallel stripe fluctuations grows with decreasing temperature and saturates below $T_c$.

• Received 2 September 2020
• Revised 12 March 2021
• Accepted 29 April 2021

DOI:https://doi.org/10.1103/PhysRevResearch.3.023151

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Published by the American Physical Society