Magnetic Field Tuning of Parallel Spin Stripe Order and Fluctuations near the Pseudogap Quantum Critical Point in La$_{1.36}$Nd$_{0.4}$Sr$_{0.24}$CuO$_4$

A quantum critical point in the single layer, hole-doped cuprate system La$_{1.6-x}$Nd$_{0.4}$Sr$_x$CuO$_4$ (Nd-LSCO), near $x$ = 0.23 has been proposed as an organizing principle for understanding high temperature superconductivity. Our earlier neutron diffraction work on Nd-LSCO at optimal and high doping revealed static parallel spin stripes to exist out to the QCP and slightly beyond, at $x$ = 0.24 and 0.26. We examine more closely the parallel spin stripe order parameter in Nd-LSCO in both zero magnetic field and fields up to 8 T for H // c in these single crystals. In contrast to earlier studies at lower doping, we observe that H //c in excess of $\sim$ 2.5 T eliminates the incommensurate quasi-Bragg peaks associated with parallel spin stripes. But this elastic scattering is not destroyed by the field; rather it is transferred to commensurate {\textbf{Q} = 0} Bragg positions, implying that the spins participating in the spin stripes have been polarized. Inelastic neutron scattering measurements at high fields show an increase in the low energy, parallel spin stripe fluctuations and evidence for a spin gap, $\Delta_{spin}$= 3 $\pm$ 0.5 meV for Nd-LSCO with $x$ = 0.24. This is shown to be consistent with spin gap measurements as a function of superconducting T$_C$ over five different families of cuprate superconductors, which follow the approximate linear relation, $\Delta_{spin}$ = 3.5 k$_B$T$_C$.