Charge-stripe ordering from local octahedral tilts: Underdoped and superconducting ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{CuO}}_4(0\mathrm{}<~x<~0.30)$

The local structure of ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{CuO}}_4,$ for $0<~x<~0.30,$ has been investigated using the atomic pair distribution function (PDF) analysis of neutron powder-diffraction data. The local octahedral tilts are studied to look for evidence of [110] symmetry [i.e., low-temperature tetragonal (LTT) symmetry] tilts locally, even though the average tilts have [010] symmetry [i.e., low-temperature orthorhombic (LTO) symmetry] in these compounds. We argue that this observation would suggest the presence of local charge-stripe order. We show that the tilts are locally LTO in the undoped phase, in agreement with the average crystal structure. At nonzero doping the PDF data are consistent with the presence of local tilt disorder in the form of a mixture of LTO and LTT local tilt directions and a distribution of local tilt magnitudes. We present topological tilt models which qualitatively explain the origin of tilt disorder in the presence of charge stripes and show that the PDF data are well explained by such a mixture of locally small and large amplitude tilts.