Short-range atomic structure of ${\mathrm{Nd}}_{2\mathrm{-}\mathit{x}}$${\mathrm{Ce}}_{\mathit{x}}$${\mathrm{CuO}}_{4\mathrm{-}\mathit{y}}$ determined by real-space refinement of neutron-powder-diffraction data

The local structure of ${\mathrm{Nd}}_{2\mathrm{-}\mathit{x}}$ ${\mathrm{Ce}}_{\mathit{x}}$ ${\mathrm{CuO}}_{4\mathrm{-}\mathit{y}}$, for x=0.165 and 0.2, has been examined in detail. The technique used is the refinement of the atomic pair density function (PDF), which was obtained from neutron-powder-diffraction data. This is a nonstandard technique and thus it is described in some detail in this paper. We find that the ${\mathrm{CuO}}_2$ planes in these materials are not flat but are buckled and distorted by oxygen displacements of magnitude ≲0.1 Å. The displacements cannot be explained simply by the presence of different-sized impurity dopant ions in the lattice. The local structure is best explained if the ${\mathrm{CuO}}_2$ planes are spatially inhomogeneous. There are two types of local regions, or domains, one heavily distorted and the other relatively undistorted. The structure within the distorted regions is well ordered with a distinct symmetry that is lower than that of the parent structure. A model for this local order is presented. From the PDF we estimate the size of these domains to be ∼6 Å. Ion-size arguments suggest that the ${\mathrm{CuO}}_2$ plane is in tension in this material and plane-buckling distortions are not expected from steric arguments. We present a mechanism whereby the buckling could be stabilized by a strong coupling to the electronic system via narrow-band Op states. This gives rise to lattice-induced hole states that coexist with the usual, impurity-doped, electrons. We speculate on the possible implications this has for the superconductivity of this material.