Local octahedral tilts in ${\mathrm{La}}_{2\mathrm{-}\mathit{x}}$${\mathrm{Ba}}_{\mathit{x}}$${\mathrm{CuO}}_4$: Evidence for a new structural length scale

The short-range structure in ${\mathrm{La}}_{2\mathrm{-}\mathit{x}}$ ${\mathrm{Ba}}_{\mathit{x}}$ ${\mathrm{CuO}}_4$ is examined by obtaining the pair distribution function from neutron powder diffraction data. In contrast to the predictions of the crystal structure models, locally, the ${\mathrm{CuO}}_6$ octahedra do not change their tilt direction at the low-temperature tetragonal (LTT) to low-temperature orthorhombic (LTO) phase transition: they always tilt in the [110] (LTT) directions. The long-range structures of the high-temperature phases result from coherent superpositions of the local LTT variants. The local tilt order extends over ∼1 nm. We discuss the implications of this local structure for the properties.