Interdependent scaling of long-range oxygen and magnetic ordering in nonstoichiometric ${\mathrm{Nd}}_2{\mathrm{NiO}}_{4.10}$

Hole doping in ${\mathrm{Nd}}_2{\mathrm{NiO}}_{4.00}$ can be achieved either by substituting the trivalent Nd atoms by bivalent alkaline-earth metals or by oxygen doping, yielding ${\mathrm{Nd}}_2{\mathrm{NiO}}_{4+\delta }$. While the alkaline-earth-metal atoms are statistically distributed on the rare-earth sites, the extra oxygen atoms in the interstitial lattice remain mobile down to ambient temperature and allow complex ordering scenarios depending on $\delta$ and $T$. Thereby the oxygen ordering, usually setting in far above room temperature, adds an additional degree of freedom on top of charge, spin, and orbital ordering, which appear at much lower temperatures. In this study, we investigated the interplay between oxygen and spin ordering for a low oxygen doping concentration, i.e., ${\mathrm{Nd}}_2{\mathrm{NiO}}_{4.10}$. Although the extra oxygen doping level remains rather modest with only 1 out of 20 possible interstitial tetrahedral lattice sites occupied, we observed by single-crystal neutron diffraction the presence of a complex three-dimensional (3D) modulated structure related to oxygen ordering already at ambient, the modulation vectors being $\pm 2/13$a*$\pm 3/13$b*, $\pm 3/13$b*$\pm 2/13$b*, and $\pm 1/5$a*$\pm 1/2$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 $\mathit{k}=\left(100\right)$. 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 ${\mathrm{Nd}}_2{\mathrm{NiO}}_{4.10}$. Temperature-dependent measurements of magnetic intensities suggest two magnetic phase transitions below 48 and 20 K, indicating two distinct onsets of magnetic ordering for the Ni and Nd sublattices, respectively.

Figure 1

The proposed LTT crystal structure of ${\mathrm{Nd}}_2{\mathrm{NiO}}_{4.10}$ at room temperature (space group $P{4}_2/ncm$). (a) The tetragonal unit cell consists of alternate stacking of ${\mathrm{NiO}}_2$ and ${\mathrm{Nd}}_2{\mathrm{O}}_2$ layers along the $c$ axis. (b) Two different tetrahedral sites with Wyckoff symmetry b and 4e. Excess oxygen atoms selectively occupy only the 4b Wyckoff sites as observed with powder and single-crystal neutron-diffraction studies.

Figure 2

The $\omega$-scan profiles ($\omega$ values around ${\theta }_{hkl}$) of (a) (104) and (b) (101) Bragg peaks recorded at different temperatures on a ${\mathrm{Nd}}_2{\mathrm{NiO}}_{4.10}$ single crystal. Temperature evolution of the integrated intensities of (c) (104) and (d) (101) Bragg peaks. Vertical blue dashed lines at $T\sim 48$ K and $T\sim 18$ K indicate the magnetic ordering temperature of the Ni sublattice and the onset of magnetic polarization of the Nd sublattice, respectively. Thick solid lines are only to guide the eye. The measurements were carried out on HEiDi, MLZ, with $\lambda =0.793\left(1\right)$ Å.

Figure 3

Reconstructed single-crystal neutron-diffraction plane maps of ${\mathrm{Nd}}_2{\mathrm{NiO}}_{4.10}$. Excerpts of (a–c) ($h0l$) and (d–f) ($hk0$) reciprocal planes measured at 300, 55, and 2 K. The dashed blue circles show the reflections that emerged from the NiO impurity phase while the squares and solid circles represent characteristic superstructure reflections appearing from the ordering of excess oxygen atoms and spins in ${\mathrm{Nd}}_2{\mathrm{NiO}}_{4.10}$, respectively. Rectangular boxes in orange in the 2 K maps display the sections which are magnified in Fig. 4. The measurements were carried out on DMC at SINQ, PSI, with $\lambda =2.4586\left(3\right)$ Å.

Figure 4

Magnified zones of the (a) experimentally measured ($h0l$) plane presented together with the (b) simulated zone. Magnified sections of the (c) experimentally measured ($hk0$) plane presented along with the (d) simulated zone. Integer numbers represent different orders of the satellites corresponding to a Bragg peak. Q scans through the superstructure peaks observed in the ($hk0$) and ($h0l$) plane maps of ${\mathrm{Nd}}_2{\mathrm{NiO}}_{4.10}$. (e) The Q scan in is starting from (102) along the blue line up to the fourth-order satellite as shown in (a); (f) the cut is starting from (110) along the green line up to the fourth-order satellite as shown in (c). A constant $y$ offset is used to plot the 55 and 2 K data.

Figure 5

Powder-diffraction patterns of ${\mathrm{Nd}}_2{\mathrm{NiO}}_{4.11}$. Excerpts of the Le Bail fit of the (a) NPD data at 2 K and (b) XRPD data at 5 K with the $\mathbf{q}$ vectors obtained from the reciprocal space plane mappings. Observed (blue circles) and calculated (red line) patterns resulting from the profile analysis of the powder data. Both insets represent the temperature dependence of two superstructure reflections as marked by colored arrows in the powder patterns. The NPD data were measured on DMC at SINQ, PSI, with $\lambda =2.4586\left(3\right)$ Å. The XRPD data were measured on MS-X04SA at SLS, PSI, with $\lambda =0.62104\left(3\right)$ Å. Both sets of powder data are identical to those reported in Ref. [18].