Random Fields from Quenched Disorder in an Archetype for Correlated Electrons: the Parallel Spin Stripe Phase of La$_{1.6-x}$Nd$_{0.4}$Sr$_x$CuO$_4$ at the 1/8 Anomaly

The parallel stripe phase is remarkable both in its own right, and in relation to the other phases it co-exists with. Its inhomogeneous nature makes such states susceptible to random fields from quenched magnetic vacancies. We argue this is the case by introducing low concentrations of nonmagnetic Zn impurities (0-10%) into La$_{1.6-x}$Nd$_{0.4}$Sr$_x$CuO$_4$ (Nd-LSCO) with $x$ = 0.125 in single crystal form, well below the percolation threshold of $\sim$ 41% for two-dimensional (2D) square lattice. Elastic neutron scattering measurements on these crystals show clear magnetic quasi-Bragg peaks at all Zn dopings. While all the Zn-doped crystals display order parameters that merge into each other and the background at $\sim$ 68 K, the temperature dependence of the order parameter as a function of Zn concentration is drastically different. This result is consistent with meandering charge stripes within the parallel stripe phase, which are pinned in the presence of quenched magnetic vacancies. In turn it implies vacancies that preferentially occupy sites within the charge stripes, and hence that can be very effective at disrupting superconductivity in Nd-LSCO ($x$ = 0.125), and, by extension, in all systems exhibiting parallel stripes.