Glassy nature of stripe ordering in ${\mathrm{La}}_{1.6-x}{\mathrm{Nd}}_{0.4}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$

We present the results of neutron-scattering studies on various aspects of crystalline and magnetic structure in single crystals of ${\mathrm{La}}_{1.6-x}{\mathrm{Nd}}_{0.4}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$ with $x=0.12\mathrm{}$ and 0.15. In particular, we have reexamined the degree of stripe order in an $x=0.12\mathrm{}$ sample. Measurements of the width for an elastic magnetic peak show that it saturates at a finite value below 30 K, corresponding to a spin-spin correlation length of $200\mathrm{\AA }\mathrm{}.$ A model calculation indicates that the differing widths of magnetic and (previously reported) charge-order peaks, together with the lack of commensurability, can be consistently explained by disorder in the stripe spacing. Above 30 K (i.e., above the point at which a recent muon spin-rotation study has found a loss of static magnetic order), the width of the nominally elastic signal begins to increase. Interpreting the signal as critical scattering from slowly fluctuating spins, the temperature dependence of the width is consistent with renormalized classical behavior of a two-dimensional anisotropic Heisenberg antiferromagnet. Inelastic scattering measurements show that incommensurate spin excitations survive at and above 50 K, where the elastic signal is negligible. Given that the stripe order is believed to be pinned by the low-temperature tetragonal (LTT) crystal structure, we have also investigated the transition near 70 K from the low-temperature orthorhombic (LTO) structure. We show that our $x=0.12\mathrm{}$ crystal passes through an intervening less-orthorhombic phase, before reaching the LTT at $\sim 40\mathrm{K},$ whereas the $x=0.15\mathrm{}$ crystal goes directly from LTO to LTT, with coexistence of the two phases over a range of $\sim 7\mathrm{K}.$ Sharp Bragg peaks in the LTT phase of the $x=0.15\mathrm{}$ crystal indicate a domain size of $\gtrsim 1000\mathrm{\AA }\mathrm{},$ with no obvious evidence for LTO domains; hence, the coexistence of stripe order and superconductivity in this sample cannot be explained by a mixture of crystalline phases. Finally, we present scattering evidence for small LTT-like domains in the LTO phase of the $x=0.15\mathrm{}$ sample. A correlation between the volume fraction of such domains and deviations of in-plane resistivity from linear T dependence suggest that charge stripes interact with these domains within the LTO matrix.