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

Interdependent scaling of long-range oxygen and magnetic ordering in non-stoichiometric Nd${}_2$NiO${}_{4.10}$