Antiferromagnetic Correlations Research Articles

Directly imaging spin polarons in a kinetically frustrated Hubbard system.

The emergence of quasiparticles in quantum many-body systems underlies the rich phenomenology in many strongly interacting materials. In the context of doped Mott insulators, magnetic polarons are quasiparticles that usually arise from an interplay between the kinetic energy of doped charge carriers and superexchange spin interactions1-8. However, in kinetically frustrated lattices, itinerant spin polarons-bound states of a dopant and a spin flip-have been theoretically predicted even in the absence of superexchange coupling9-14. Despite their important role in the theory of kinetic magnetism, a microscopic observation of these polarons is lacking. Here we directly image itinerant spin polarons in a triangular-lattice Hubbard system realized with ultracold atoms, revealing enhanced antiferromagnetic correlations in the local environment of a hole dopant. In contrast, around a charge dopant, we find ferromagnetic correlations, a manifestation of the elusive Nagaoka effect15,16. We study the evolution of these correlations with interactions and doping, and use higher-order correlation functions to further elucidate the relative contributions of superexchange and kinetic mechanisms. The robustness of itinerant spin polarons at high temperature paves the way for exploring potential mechanisms for hole pairing and superconductivity in frustrated systems10,11. Furthermore, our work provides microscopic insights into related phenomena in triangular-lattice moiré materials17-20.

Using Kondo entanglement to induce spin correlations between disconnected quantum dots

We investigate the entanglement between the spins of two quantum dots that are not simultaneously connected to the same system. Quantum entanglement among localized spins is a crucial property for the advancement of quantum computing and quantum information. Generating and controlling an entangled state between quantum dots have garnered significant attention in recent years for this reason. In this study, we demonstrate that information about the spin orientation of a quantum dot can be preserved, utilizing Kondo entanglement, within a reservoir of electrons. Subsequently, this information can be transmitted to another dot after the initial dot has been decoupled from the reservoirs. We employ a double quantum dot system in a parallel geometry to establish the initial state, where each dot interacts with reservoirs of different symmetries. A specific phase in the couplings is chosen to induce antiferromagnetic spin correlation between the dots. The time evolution of the initial state is analyzed using the time-dependent density matrix renormalization group method. Our findings reveal that a partially entangled state between the dots can be achieved, even when they are not simultaneously connected. This entangled state arises transiently and dissipates in the stationary state. The stability of the state observed during the transient phase is demonstrated. To comprehend the details of these phenomena, we employ a canonical transformation of real space.

Electron Glass Phase with Resilient Zhang-Rice Singlets in LiCu_{3}O_{3}.

LiCu_{3}O_{3} is an antiferromagnetic mixed valence cuprate where trilayers of edge-sharing Cu(II)O (3d^{9}) are sandwiched in between planes of Cu(I) (3d^{10}) ions, with Li stochastically substituting Cu(II). Angle-resolved photoemission spectroscopy (ARPES) and density functional theory reveal two insulating electronic subsystems that are segregated in spite of sharing common oxygen atoms: a Cu d_{z^{2}}/O p_{z} derived valence band (VB) dispersing on the Cu(I) plane, and a Cu 3d_{x^{2}-y^{2}}/O 2p_{x,y} derived Zhang-Rice singlet (ZRS) band dispersing on the Cu(II)O planes. First-principle analysis shows the Li substitution to stabilize the insulating ground state, but only if antiferromagnetic correlations are present. Li further induces substitutional disorder and a 2D electron glass behavior in charge transport, reflected in a large 530meV Coulomb gap and a linear suppression of VB spectral weight at E_{F} that is observed by ARPES. Surprisingly, the disorder leaves the Cu(II)-derived ZRS largely unaffected. This indicates a local segregation of Li and Cu atoms onto the two separate corner-sharing Cu(II)O_{2} sub-lattices of the edge-sharing Cu(II)O planes, and highlights the ubiquitous resilience of the entangled two hole ZRS entity against impurity scattering.

Coherent THz spin dynamics in antiferromagnets beyond the approximation of the Néel vector

Controlled generation of coherent spin waves with highest possible frequencies and shortest possible wavelengths is a cornerstone of spintronics and magnonics. Here, using Heisenberg antiferromagnet RbMnF3, we demonstrate that laser-induced THz spin dynamics corresponding to pairs of mutually coherent counter-propagating spin waves with the wavevectors up to the edge of the Brillouin zone cannot be understood in terms of magnetization and antiferromagnetic (Néel) vectors, conventionally used to describe spin waves. Instead, we propose to model such spin dynamics using the spin correlation function. We derive a quantum-mechanical equation of motion for the latter and emphasize that unlike the magnetization and antiferromagnetic vectors the spin correlations in antiferromagnets do not exhibit inertia.

Extended Honeycomb Metal Chloride with Tunable Antiferromagnetic Correlations

Extended Honeycomb Metal Chloride with Tunable Antiferromagnetic Correlations

Tuneable Short-Range Antiferromagnetic Correlation in Fe-Containing Entropy Stabilized Oxides.

To elucidate the impact of a high entropy elemental distribution of the lattice site on the magnetic properties in oxide compounds, a series of complex perovskites BaBO3 (B = Y, Fe, Ti, Zr, Hf, Nb, and Ta) with different Fe content ratios (0, 0.2, 0.3, and 0.4) have been synthesized and thoroughly characterized. In this complex oxide series, superconducting quantum interference device magnetometry reveals a gradual change of a well-defined magnetic phase transition and B-site magnetic moment, which correlates with the Fe content. More importantly, a comprehensive analysis of the sample with a 0.4-Fe content (40% on the B-site) including magnetization, heat capacity, neutron diffraction, and muon-spin rotation measurements suggests that in the low-temperature state, a short-range antiferromagnetic correlation may exist, which could result from the magnetic interaction of Fe ions and consequent redistribution of associated d-electrons.

Observation of the Anomalous Hall Effect in a Layered Polar Semiconductor

AbstractProgress in magnetoelectric materials is hindered by apparently contradictory requirements for time‐reversal symmetry broken and polar ferroelectric electronic structure in common ferromagnets and antiferromagnets. Alternative routes can be provided by recent discoveries of a time‐reversal symmetry breaking anomalous Hall effect (AHE) in noncollinear magnets and altermagnets, but hitherto reported bulk materials are not polar. Here, the authors report the observation of a spontaneous AHE in doped AgCrSe2, a layered polar semiconductor with an antiferromagnetic coupling between Cr spins in adjacent layers. The anomalous Hall resistivity 3 is comparable to the largest observed in compensated magnetic systems to date, and is rapidly switched off when the angle of an applied magnetic field is rotated to ≈80° from the crystalline c‐axis. The ionic gating experiments show that the anomalous Hall conductivity magnitude can be enhanced by modulating the p‐type carrier density. They also present theoretical results that suggest the AHE is driven by Berry curvature due to noncollinear antiferromagnetic correlations among Cr spins, which are consistent with the previously suggested magnetic ordering in AgCrSe2. The results open the possibility to study the interplay of magnetic and ferroelectric‐like responses in this fascinating class of materials.

Dichotomy of heavy and light pairs of holes in the t−J model

A key step in unraveling the mysteries of materials exhibiting unconventional superconductivity is to understand the underlying pairing mechanism. While it is widely agreed upon that the pairing glue in many of these systems originates from antiferromagnetic spin correlations, a microscopic description of pairs of charge carriers remains lacking. Here we use state-of-the art numerical methods to probe the internal structure and dynamical properties of pairs of charge carriers in quantum antiferromagnets in four-legged cylinders. Exploiting the full momentum resolution in our simulations, we are able to distinguish two qualitatively different types of bound states: a highly mobile, meta-stable pair, which has a dispersion proportional to the hole hopping t, and a heavy pair, which can only move due to spin exchange processes and turns into a flat band in the Ising limit of the model. Understanding the pairing mechanism can on the one hand pave the way to boosting binding energies in related models, and on the other hand enable insights into the intricate competition of various phases of matter in strongly correlated electron systems.

Quasi-particle functional renormalisation group calculations in the two-dimensional t-t'-Hubbard model

We extend and apply a recently introduced quasi-particle functional renormalisation group scheme to the two-dimensional Hubbard model with next-nearest-neighbour hopping and away from half filling. We confirm the generation of superconducting correlations in some regions of the phase diagram, but also find that the inclusion of self-energy feedback by means of a decreasing quasi-particle weight can suppress superconducting tendencies more than anti-ferromagnetic correlations by which they are generated. As a supplement, we provide sample results for the self-energy in second-order perturbation theory and address some conceptual matters.

Statistics of the cuprate pairon states on a square lattice

In this paper the fundamental parameters of high-Tc superconductivity are shown to be connected to the statistics of pairons (hole pairs in their antiferromagnetic (AF) environment) on a square lattice. In particular, we study the density fluctuations and the distribution of the area surrounding each pairon on the scale of the AF correlation length , for the complete range of hole concentration. We show that the key parameters of the phase diagram, the Tc dome, and the pseudogap (PG) temperature , emerge from the statistical properties of the pairon disordered state. In this approach, the superconducting and the PG states appear as inseparable phenomena. The condensation energy, which fixes the critical temperature, is directly proportional to the correlation energy between pairons and not to the energy gap, contrary to conventional superconductors. When the correlation energy between pairons is suppressed by fluctuations, either thermally, by disorder, or in the vortex core, the PG state of disordered pairons is obtained. We attribute the unique features of cuprate superconductivity to this order–disorder transition in real space, which clearly differs from the Bardeen–Cooper–Schrieffer mechanism. Our predictions are in quantitative agreement with low-temperature tunneling and photoemission spectroscopy experiments.

Frustration- and doping-induced magnetism in a Fermi-Hubbard simulator.

Geometrical frustration in strongly correlated systems can give rise toa plethora of novel ordered states and intriguing magnetic phases, such as quantum spin liquids1-3. Promising candidate materials for such phases4-6 can be described by the Hubbard model on an anisotropic triangular lattice, a paradigmaticmodel capturing the interplay between strong correlations and magnetic frustration7-11. However, the fate of frustrated magnetism in the presence of itinerant dopants remains unclear, as well as its connection to the doped phases of the square Hubbard model12. Here we investigate the local spin order of a Hubbard model with controllable frustration and doping, using ultracold fermions in anisotropic optical lattices continuously tunable from a square to a triangular geometry. At half-filling and strong interactions U/t ≈ 9, we observe at the single-site level how frustration reduces the range of magnetic correlations and drives a transition from a collinear Néel antiferromagnet to a short-range correlated 120° spiral phase. Away from half-filling, the triangular limit shows enhanced antiferromagnetic correlations on the hole-doped side and a reversal to ferromagnetic correlations at particle dopings above 20%, hinting at the role of kinetic magnetism in frustrated systems. This work paves the way towards exploring possible chiral ordered or superconducting phases in triangular lattices8,13 and realizing t-t' square lattice Hubbard models that may be essential to describe superconductivity in cuprate materials14.

Evolution of magnetic correlation in an inhomogeneous square lattice

We explore the magnetic properties of a two-dimensional Hubbard model on an inhomogeneous square lattice, which provides a platform for tuning the bandwidth of the flat band. In its limit, this inhomogeneous square lattice turns into a Lieb lattice, and it exhibits abundant properties due to the flat band structure at the Fermi level. By using the determinant quantum Monte Carlo simulation, we calculate the spin susceptibility, double occupancy, magnetization, spin structure factor, and effective pairing interaction of the system. It is found that the antiferromagnetic correlation is suppressed by the inhomogeneous strength and that the ferromagnetic correlation is enhanced. Both the antiferromagnetic correlation and ferromagnetic correlation are enhanced as the interaction increases. It is also found that the effective $d$-wave pairing interaction is suppressed by the increasing inhomogeneity. In addition, we also study the thermodynamic properties of the inhomogeneous square lattice, and the calculation of specific heat provides good support for our point. Our intensive numerical results provide a rich magnetic phase diagram over both the inhomogeneity and interaction.

Structural, optical and magnetic properties of ErxZn1-xO nanoparticles: The impact of the Er-content

In this study we report on both the successful synthesis of ErxZn1-xO nanoparticles (x = 0.000, 0.005, 0.010, 0.030, 0.050, 0.075, and 0.100) and characterization (structural, optical, and magnetic) of the as-produced nanomaterials. The nanoparticles were produced by the polymeric precursor method (Pechini’s method). X-ray diffraction and Raman spectroscopy showed formation of hexagonal wurtzite phase in all samples. Meanwhile, only samples with a high Er-content (x = 0.075 and x = 0.100) exhibited a minority (up to 7 % w/w) secondary crystalline phase (Er2O3). The Rietveld refinement method was employed to assess details of the structural parameters. It was demonstrated that the increase of the Er-content leads to systematic mean crystalline size reduction (from ∼80 to ∼13 nm) and band gap shrinking (from ∼3.17 to ∼3.00 eV). The UV-Vis spectra showed the presence of characteristic Er3+-ion absorption bands. Likewise, emission peaks associated with Er3+-ion 4S3/2 → 4I15/2 electronic transition were verified by room temperature photoluminescence (PL). Strong differences in the PL spectra profiles of the ErxZn1-xO nanoparticles with respect to the PL spectrum of a reference Er2O3 sample, suggested that the majority of Er3+-ions replace Zn2+-ions in the wurtzite hosting matrix. Magnetic measurements show a paramagnetic behavior in all doped samples. The χ×T and M×Hcurves were successfully fitted to Curie-Weiss law and Brillouin modified model, showing the existence of short-range antiferromagnetic correlation.

BaMn2P2 : Highest magnetic ordering temperature 122-pnictide compound

We report the growth of high-quality single crystals of ${\mathrm{ThCr}}_{2}{\mathrm{Si}}_{2}$-type tetragonal ${\mathrm{BaMn}}_{2}{\mathrm{P}}_{2}$ and investigation of its structural, electrical transport, thermal, and magnetic properties. Our results of basal plane electrical resistivity and heat capacity measurements show that the compound has an insulating ground state with a small band gap. Anisotropic susceptibility ${\ensuremath{\chi}}_{ab,c}(T)$ data infer a collinear local-moment N\'eel-type antiferromagnetic (AFM) ground state below the ordering temperature ${T}_{\mathrm{N}}=795(15)\phantom{\rule{0.28em}{0ex}}\mathrm{K}$, which is highest among all the ${\mathrm{ThCr}}_{2}{\mathrm{Si}}_{2}$- and ${\mathrm{CaAl}}_{2}{\mathrm{Si}}_{2}$-type 122-pnictide compounds reported so far suggesting that the strength of magnetic exchange interactions is strongest in this material. The magnetic transition temperatures of ${\mathrm{BaMn}}_{2}P{n}_{2}$ ($Pn=\mathrm{P}$, As, Sb, Bi) compounds exhibit a monotonic decrease with the increase of tetragonal unit cell parameters $a$ and $c$, suggesting a strong dependence of the strength of the decisive magnetic exchange interactions on the separation between the localized spins residing on the Mn ions. The observed monotonic increase of both ${\ensuremath{\chi}}_{ab}$ and ${\ensuremath{\chi}}_{c}$ for $T>{T}_{\mathrm{N}}$ suggests that short-range dynamic quasi-two-dimensional AFM correlations persist above the ${T}_{\mathrm{N}}$ up to the highest temperature of the measurements. The large ${T}_{\mathrm{N}}$ of ${\mathrm{BaMn}}_{2}{\mathrm{P}}_{2}$ demands for systematic hole-doping studies on this material as similar investigations on related ${\mathrm{BaMn}}_{2}{\mathrm{As}}_{2}$ with ${T}_{\mathrm{N}}=618\phantom{\rule{0.28em}{0ex}}\mathrm{K}$ have led to the discovery of an outstanding ground state where AFM of localized Mn spins and itinerant half-metallic ferromagnetism with ${T}_{\mathrm{c}}\ensuremath{\approx}100\phantom{\rule{0.28em}{0ex}}\mathrm{K}$ originating from the doped holes coexist together.

Rare-earth control of phase transitions in infinite-layer nickelates.

Perovskite nickelates RNiO3 (R = rare-earth ion) exhibit complex rare-earth ion dependent phase diagram and high tunability of various appealing properties. Here, combining first- and finite-temperature second-principles calculations, we explicitly demonstrate that the superior merits of the interplay among lattice, electron, and spin degrees of freedom can be passed to RNiO2, which recently gained significant interest as superconductors. We unveil that decreasing the rare-earth size directly modulates the structural, electronic, and magnetic properties and naturally groups infinite-layer nickelates into two categories in terms of the Fermi surface and magnetic dimensionality: compounds with large rare-earth sizes (La, Pr) closely resemble the key properties of CaCuO2, showing quasi-two-dimensional (2D) antiferromagnetic (AFM) correlations and strongly localized orbitals around the Fermi level; the compounds with small rare-earth sizes (Nd-Lu) are highly analogous to ferropnictides, showing three-dimensional (3D) magnetic dimensionality and strong dispersion of electrons at the Fermi level. Additionally, we highlight that RNiO2 with R = Nd-Lu exhibit on cooling a structural transition with the appearance of oxygen rotation motion, which is softened by the reduction of rare-earth size and enhanced by spin-rotation couplings. The rare-earth control of dispersion and structural phase transition might be the key factors differentiating the distinct upper critical field and resistivity in different compounds. The established original phase diagram summarizing the temperature and rare-earth controlled structural, electronic, and magnetic transitions in RNiO2 compounds provides rich structural and chemical flexibility to tailor the superconducting property.

Combinatorial Synthesis of Cation-Disordered Manganese Tin Nitride MnSnN2 Thin Films with Magnetic and Semiconducting Properties

Magnetic semiconductors may soon improve the energy efficiency of microelectronics, but materials exhibiting these dual properties remain underexplored. Here, we report the computational prediction and realization of a new magnetic and semiconducting material, MnSnN2, via combinatorial sputtering of thin films. Grazing incidence wide-angle X-ray scattering and laboratory X-ray diffraction studies show MnSnN2 exhibits a wurtzite-like crystal structure with cation disorder. This new material has a wide composition tolerance, with a single-phase region ranging from 20% < Mn/(Mn + Sn) < 65%. Spectroscopic ellipsometry identifies an optical absorption onset of 1 eV, consistent with the computationally predicted 1.2 eV bandgap. Resistivity measurements as a function of temperature support the semiconducting nature of MnSnN2. Hall effect measurements show carrier density has a weak inverse correlation with temperature, indicating that the charge transport mechanisms are more complex than in a pristine semiconductor. Magnetic susceptibility measurements reveal a low-temperature magnetic ordering transition (≈10 K) for MnSnN2 and strong antiferromagnetic correlations. This finding contrasts with bulk, cation-ordered MnSiN2 and MnGeN2, which exhibited antiferromagnetic ordering above 400 K in previous studies. To probe the origin of this difference, we perform Monte Carlo simulations of cation-ordered and cation-disordered MnSnN2. They reveal that cation disorder lowers the magnetic transition temperature relative to the ordered phase. In addition to discovering a new compound, this work shows that future efforts could use cation (dis)order to tune magnetic transitions in semiconducting materials for precise control of properties in microelectronics.

Strong Magnetocaloric Coupling in Oxyorthosilicate with Dense Gd3+ Spins.

Searching for working refrigerant materials is the key element in the design of magnetic cooling devices. Herein, we report on the thermodynamic and magnetocaloric parameters of an X1 phase oxyorthosilicate, Gd2SiO5, by field-dependent static magnetization and specific heat measurements. An overall correlation strength of |J|S2 ≈ 3.4 K is derived via the mean-field estimate, with antiferromagnetic correlations between the ferromagnetically coupled Gd-Gd layers. The magnetic entropy change -ΔSm is quite impressive, reaches 0.40 J K-1 cm-3 (58.5 J K-1 kg-1) at T = 2.7 K, with the largest adiabatic temperature change Tad = 23.2 K for a field change of 8.9 T. At T = 20 K, the lattice entropy SL is small enough compared to the magnetic entropy Sm, Sm/SL = 21.3, which warrants its potential in 2 -20 K cryocoolers with both the Stirling and Carnot cycles. Though with relatively large exchange interactions, the layered A-type spin arrangement ultimately enhances the magnetocaloric coupling, raising the possibilities of designing magnetic refrigerants with a high ratio of cooling capacity to volume.

Magnetic properties of Ba2Y1-xCuxTaO6-δ solid solutions

We carried out a study of the structural and magnetic properties of Ba2Y1-xCuxTaO6-δ (0.0 ≤ x ≤ 0.5) compounds. The cubic rock-salt double perovskite structure of Ba2YTaO6 is retained upon the partial substitution of Cu for Y up to x = 0.50 and the lattice parameter a drops at the rate of da/dx ≈ −0.17 ± 0.01 Å/%Cu. While the effective moment μeff and the Curie-Weiss temperature θCW are nearly negligible in Ba2YTaO6, the partial substitution of Cu for Y results shows an increase in μeff at the rate of ≈ 1.9 ± 0.2 µB/%Cu, consistently with the paramagnetic behavior expected for Cu2+, and a decrease in θCW at the rate of −16 ± 2 K/%Cu. The drive of θCW towards more negative values is suggestive of the onset of antiferromagnetic correlations.

Magnetic impurities in a charge-ordered background

We investigate how magnetic impurities may affect a system exhibiting a charge-density wave (CDW) in its ground state. We consider a disordered Hubbard-Holstein model with a homogeneous electron-phonon interaction but with a (randomly chosen) fraction of sites displaying a nonzero Coulomb repulsion $U$ and perform state-of-the-art finite-temperature quantum Monte Carlo simulations. For a single magnetic impurity, charge-charge correlations hamper the spin-spin ones around the repulsive site, thus requiring a strong enough value of $U$ to create nonnegligible antiferromagnetic (AFM) correlations. As the number of magnetic impurities increases, these AFM correlations become deleterious to CDW order and its features. First, the critical temperature is drastically reduced and seems to vanish $\ensuremath{\sim}40%$ of impurities (for fixed $U/\ensuremath{\lambda}=2$), which we correlate with the classical percolation threshold. We also notice that just a small amount of disorder suffices to create a bad insulating state, with the suppression of both Peierls and spin gaps, even within the charge-ordered phase. Finally, we have also found that pairing correlations are enhanced at large doping, driven by the competition between CDW and AFM tendencies.

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.