Evidence of correlated incommensurate structural and magnetic order in highly oxygen-doped layered nickelate Nd2NiO4.23

$\mathrm{Nd}{}_{2}\mathrm{NiO}{}_{4+\ensuremath{\delta}}$ is a nonstoichiometric oxide, crystallizing in the Ruddlesden-Popper-type framework and exhibiting a wide range of oxygen nonstoichiometry $\ensuremath{\delta}$ with a complex structural phase diagram. Excess oxygen atoms insert holes, directly influencing the Ni valence state and associated electronic structure. We report here the existence of a correlated incommensurate structural and antiferromagnetic order below $T{}_{N}\phantom{\rule{4pt}{0ex}}\ensuremath{\approx}$ 150 K in highly oxygen-doped $\mathrm{Nd}{}_{2}\mathrm{NiO}{}_{4+\ensuremath{\delta}}$ with $\ensuremath{\delta} \ensuremath{\approx}$ 0.23. The crystal and magnetic structures are investigated by polarized and unpolarized single-crystal neutron diffraction studies together with synchrotron x-ray powder diffraction and macroscopic magnetization measurements. Due to the long-range ordering of excess oxygen atoms, the real structure of the compound is incommensurately modulated, represented by $\mathbf{Q}{}_{n}=\ifmmode\pm\else\textpm\fi{}0.813{\mathbf{a}}^{*}\ifmmode\pm\else\textpm\fi{}0.519{\mathbf{b}}^{*}$ wave vectors. The antiferromagnetic order is characterized by the presence of incommensurate Bragg peaks of type ($h\phantom{\rule{4pt}{0ex}}\ifmmode\pm\else\textpm\fi{}\phantom{\rule{4pt}{0ex}}\ensuremath{\varepsilon}$, 0, $l$/2), with $h$ and $l$ being odd-integer numbers and the magnetic incommensurability $\ensuremath{\varepsilon}\ensuremath{\approx}$ 0.36. The in-plane magnetic correlation length is found to be $\ensuremath{\xi}{}_{ab}$ = 184(1) \AA{} but is significantly reduced along the $c$ axis to $\ensuremath{\xi}{}_{c}$ = 39(2) \AA{}, indicating the quasi-two-dimensional nature of the antiferromagnetic correlations. Our study indicates that the excess oxygen atoms nevertheless strongly enhance the magnetic correlations between the ${\mathrm{NiO}}_{2}$ planes, resulting in a doubling of the magnetic unit cell along the $c$ axis. In contrast to $\mathrm{Nd}{}_{2}\mathrm{NiO}{}_{4.1}$, in which the incommensurate periodicity of oxygen and magnetic ordering was found to be identical, the structural and electronic orderings in heavily oxygen-doped ${\mathrm{Nd}}_{2}{\mathrm{NiO}}_{4.23}$ show two independent modulation vectors. Our study thus unravels a strong correlation between structural and electronic orderings in the highly oxygen-doped $\mathrm{Ln}{}_{2}\mathrm{NiO}{}_{4+\ensuremath{\delta}}$ system.