  Hole doping in Nd${}_{2}$NiO${}_{4.00}$ can be either achieved by
substituting the trivalent Nd atoms by bivalent alkaline earth metals or by
oxygen doping, yielding Nd${}_{2}$NiO${}_{4+\delta}$. In this study, we
investigated the interplay between oxygen and spin ordering for a low oxygen
doping concentration i.e. Nd${}_{2}$NiO${}_{4.10}$. Although the extra oxygen
doping level remains rather modest with only one out of 20 possible
interstitial tetrahedral lattice sites occupied, we observed by single crystal
neutron diffraction the presence of a complex 3D modulated structure related to
oxygen ordering already at ambient, the modulation vectors being
$\pm$2/13\textit{\textbf{a*}}$\pm$3/13\textit{\textbf{b*}},
$\pm$3/13\textit{\textbf{b*}}$\pm$2/13\textit{\textbf{b*}} and
$\pm$1/5\textit{\textbf{a*}}$\pm$1/2\textit{\textbf{c*}} and satellite
reflections up to fourth order. Temperature dependent neutron diffraction
studies indicate the coexistence of oxygen and magnetic ordering below
T${}_{N}$ $\simeq$ 48 K, the wave vector of the Ni sublattice being
\textbf{\textit{k}}=(100). In addition, magnetic satellite reflections adapt
exactly the same modulation vectors as found for the oxygen ordering,
evidencing a unique coexistence of 3D modulated ordering for spin and oxygen
ordering in Nd${}_{2}$NiO${}_{4.10}$. Temperature dependent measurements of
magnetic intensities suggest two magnetic phase transitions below 48 K and 20
K, indicating two distinct onsets of magnetic ordering for the Ni and Nd
sublattice, respectively.
