Elastic neutron scattering measurements have been carried out on a single crystal of ${\mathrm{La}}_{1.6-x}{\mathrm{Nd}}_{0.4}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$ at optimal doping for superconductivity, $x$ = 0.19, in magnetic fields up to 8 T, applied $\parallel c$. At zero magnetic field, these measurements of the intensity of parallel spin stripe quasi-Bragg peaks show a departure from a weak sloping background below $T_N$ = 40 K, with a $\sim$ linear growth in intensity that is bounded between superconducting $T_c^{\text{(onset)}}$ = 26 K and $T_c^{\text{(mid)}}$ = 13 K. Below $T_c^{\text{(mid)}}$, the order parameter plateaus and subsequently displays a strong increase below $T_{\text{Nd}}\sim$ 8 K. This strong, low-temperature increase is due to weak coupling between the magnetism in the ${\mathrm{CuO}}_2$ planes and that of ${\mathrm{Nd}}^{3+}$ moments between the planes. A magnetic field $\parallel c>$ 1.5 T suppresses this low-temperature rise of the order parameter, as the ${\mathrm{Nd}}^{3+}$ moments polarize in the field, and the coupled ${\mathrm{Nd}}^{3+}\text{−}{\mathrm{CuO}}_2$ magnetism can no longer participate in the incommensurate, parallel spin stripe structure. At $T=10\mathrm{K}$, above $T_{\text{Nd}}$ but below $T_c^{\text{(mid)}}$, the stripe intensity weakly decreases with field, consistent with vortex-induced disorder of short-range stripes in $d$-wave superconducting regions. For $T\ge 17\mathrm{K}$, no measurable field dependence is observed, showing that a uniform $H\parallel c<8$ T does not perturb ${\mathrm{CuO}}_2$ stripe magnetism. A plateau at $T_c^{\text{(mid)}}$ persists across all fields. These results are discussed in the context of earlier studies of the magnetic field dependence on parallel spin stripes in ${\mathrm{La}}_{1.6-x}{\mathrm{Nd}}_{0.4}{\mathrm{Sr}}_x{\mathrm{CuO}}_4, {\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$, and ${\mathrm{La}}_{2-x}{\mathrm{Ba}}_x{\mathrm{CuO}}_4$.

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• Pair density wave
• Stripes
• Cuprates
• Inelastic neutron scattering