Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “superconducting fluctuations”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 397 records · Page 22
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Observation of a critical charge mode in a strange metal

Understanding the strange metallic behavior that develops at the brink of localization in quantum materials requires probing the underlying electronic charge dynamics. Using synchrotron radiation–based Mössbauer spectroscopy, we studied the charge fluctuations of the strange metal phase of β-YbAlB 4 as a function of temperature and pressure. We found that the usual single absorption peak in the Fermi-liquid regime splits into two peaks upon entering the critical regime. Here, we interpret this spectrum as a single nuclear transition, modulated by nearby electronic valence fluctuations whose long time scales are further enhanced by the formation of charged polarons. These critical charge fluctuations may prove to be a distinct signature of strange metals.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Enhancing superconductivity of Y 5 Rh 6 Sn 18 by atomic disorder

Here, we investigate the effect of enhancement of superconducting transition temperature $T_c$ by nonmagnetic atom disorder in the filled skutterudite-related tetragonal Y 5 Rh 6 Sn 18 compound doped with Ca. We documented experimentally that Y 5 Rh 6 Sn 18 and its Ca-doped alloys are electronically inhomogeneous at the nanoscale, when Ca content is smaller than ~1.5 in the Y 5– x Ca x Rh 6 Sn 18 system, while for $\textit{x}$ ≥ 1.5 much stronger chemical phase inhomogeneity is observed with an about 20% volume fraction of the second 3:4:13 cubic phase, which we interpret as a fluctuation of stoichiometry within the bulk sample. Then the enhancement of $T_c$ vs $\textit{x}$ could be modeled by a mechanism proposed in recent theoretical reports for increasing the mean-field transition temperature $T_c$ in the presence of nonmagnetic disorder. The increase in disorder with doping increases the sample inhomogeneity and causes a systematic increase in $T_c$, while for two-phase $\textit{x}$ ≥ 1.5 samples the critical temperature $T^{\star}_c ≈ 2 × T_c$ rapidly increases. Based on band structure calculations performed under pressure, we demonstrate how the change in density of states would affect $T_c$ of Y 5 Rh 6 Sn 18 . We obtained the Grüneisen parameter $γ_G$ larger for the inhomogeneous phase with respect to $γ_G$ of the bulk $T_c$ phase and attribute the enhancement of $T_c$ to larger stiffening of the high-temperature $T^{\star}_c$ phase.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Nonsuperconducting electronic ground state in pressurized BaFe 2 S 3 and BaFe 2 S 2.5 Se 0.5

In this work, we report a comprehensive study of the spin ladder compound BaFe 2 S 2.5 Se 0.5 using neutron diffraction, inelastic neutron scattering, high pressure synchrotron diffraction, and high pressure transport techniques. We find that BaFe 2 S 2.5 Se 0.5 possesses the same C m c m structure and stripe antiferromagnetic order as does BaFe 2 S 3 , but with a reduced Néel temperature of T N = 98 K compared to 120 K for the undoped system, and a slightly increased ordered moment of 1.40 μ B per iron. Additionally, the low-energy spin excitations in BaFe 2 S 2.5 Se 0.5 are likewise similar to those observed in BaFe 2 S 3 . However, unlike the reports of superconductivity in BaFe 2 S 3 below T c ~ 14 K under pressures of 10 GPa or more, we observe no superconductivity in BaFe 2 S 2.5 Se 0.5 at any pressure up to 19.7 GPa. In contrast, the resistivity exhibits an upturn at low temperature under pressure. Furthermore, we show that additional high-quality samples of BaFe 2 S 3 synthesized for this study likewise fail to become superconducting under pressure, instead displaying a similar upturn in resistivity at low temperature. These results demonstrate that microscopic, sample-specific details play an important role in determining the ultimate electronic ground state in this spin ladder system. We suggest that the upturn in resistivity at low temperature in both BaFe 2 S 3 and BaFe 2 S 2.5 Se 0.5 may result from Anderson localization induced by S vacancies and random Se substitutions, enhanced by the quasi-one-dimensional ladder structure.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Magnetic properties of the itinerant ferromagnet LaCrGe 3 under pressure studied by La 139 NMR

139 La nuclear magnetic resonance (NMR) measurements under pressure (p = 0 – 2.64 GPa) have been carried out to investigate the static and dynamic magnetic properties of the itinerant ferromagnet LaCrGe 3 . 139 La -NMR spectra for all measured pressures in the ferromagnetically ordered state show a large shift due to the internal field induction |B int | ~ 4 T at the La site produced by Cr ordered moments. The change in B int by less than 5% with p up to 2.64 GPa indicates that the Cr 3d moments are robust under pressure. The temperature dependence of NMR shift and B int suggest that the ferromagnetic order develops below ~50 K under higher pressures in a magnetic field of ~7.2 T. Based on the analysis of NMR data using the self-consistent-renormalization (SCR) theory, the spin fluctuations in the paramagnetic state well above T C are revealed to be three-dimensional ferromagnetic throughout the measured p region.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

From nonmetal to strange metal at the stripe-percolation transition in La 2 - x Sr x CuO 4

The nature of the normal state of cuprate superconductors continues to stimulate considerable speculation. Of particular interest has been the linear temperature dependence of the in-plane resistivity in the low-temperature limit, which violates the prediction for a Fermi liquid. We present measurements of anisotropic resistivity in La$_{2–x}$Sr$_x$CuO$_4$ that confirm the strange-metal behavior for crystals with doped-hole concentration $p = x > p^* \sim 0.19$ and contrast with the nonmetallic behavior for $p < p^*$. We propose that the changes at $p^*$ are associated with a first-order transition from doped Mott insulator to conventional metal; the transition appears as a crossover due to intrinsic dopant disorder. We consider results from the literature that support this picture; in particular, we present a simulation of the impact of the disorder on the first-order transition and the doping dependence of stripe correlations. Below $p^*$, the strong electronic interactions result in charge and spin stripe correlations that percolate across the CuO 2 planes; above $p^*$, residual stripe correlations are restricted to isolated puddles. Here we suggest that the $T$-linear resistivity results from scattering of quasiparticles from antiferromagnetic spin fluctuations within the correlated puddles. This is a modest effect compared to the case at $p < p^*$, where the data suggest that there are no coherent quasiparticles in the normal state.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Energy Frontier Research Centers: Center for the Computational Design of Functional Layered Materials (CCDM) August 1, 2014 - July 31, 2018; Center for Complex Materials from First Principles (CCM) August 1, 2018 - July 31, 2021 (Final Report)

The mission of the DOE Energy Frontier Research Centers CCDM (2014-2018) and CCM (2018-2021) was to theoretically develop, computationally apply, and experimentally validate electronic structure methods for all materials, with a focus on the complex materials, especially layered and two-dimensional materials, strongly-correlated materials, and liquid water. This was achieved by over 200 published journal articles authored by about 17 senior investigators from physics and chemistry and from theory, computation, and experiment, plus their collaborators. In particular, the Centers confirmed the predictive power of the SCAN (strongly constrained and appropriately normed) density functional, which was constructed to satisfy 17 known exact constraints and several appropriate norms. Without being fitted to real bonded systems, and at a modest computational cost, SCAN correctly predicted covalent, ionic, metallic, hydrogen, and van der Waals bonds in many challenging materials. SCAN gave an improved description of defects in semiconductors, surface properties of metals, seven phases of ice, liquid water, liquid and supercooled silicon, subtle structural distortions in ferroelectrics, formation energies and structural predictions for solids, and critical pressures for structural phase transitions. Perhaps most remarkably, SCAN correctly described some strongly-correlated materials that were previously believed to be beyond the reach of density-functional approximations. SCAN is the only density functional that correctly predicts the band gap closing under chemical doping of the cuprate high-temperature superconducting materials. SCAN also predicts a landscape of competing stripe and magnetic phases in the cuprates. For some materials with some codes, SCAN has convergence problems that are greatly reduced by the CCM-developed r 2 SCAN, without loss of accuracy or rigor. SCAN and r 2 SCAN still make some self-interaction error, which is greatly reduced by the CCDM/ CCM-developed local orbital scaling correction (LOSC). These Centers further proved that the fundamental energy gaps of a solid from an orbital energy difference and from total energy differences are the same for a large class of generalized Kohn-Sham (GKS) functionals, including SCAN and standard hybrid functionals, and that symmetry breaking arises when a dynamic density fluctuation drops to zero frequency. The Centers identified new mechanisms for catalysis in layered materials with ions intercalated between the layers, investigated charge density waves both in model systems and in real layered materials, studied changes of band gap with the number of layers, and explored topological ultrathin films, bent nanoribbons, and defects.

08 HYDROGEN↗
NASA NTRS1985

The superconducting cavity stability ruby maser oscillator

Analysis of an application of the rudy maser to a superconducting Cavity Stabilized oscillator shows many attractive features. These derive from the mechancial stability inherent in an all-cryogenic design and from the properties of the ruby maser itself. A multiple-cavity design has been developed to allow physical separation of the high-Q superconducting cavity and the ruby element with its requried applied magnetic field. Mode selection is accomplished in this design by tuning the ruby by means of the applied field. We conclude that such an oscillator would perform well, even with cavity Q's as low as 10 to the 8th power allowing the use of a superconductor-on-sapphire resonator with its greater rigidity and lower thermal expansion. A first test of the Superconducting Cavity Stabilized Maser Oscillator (SCSMO) confirms the efficacy of the multiple-cavity design and the applicability of the ruby maser. Frequency variation less than 4x10 to the minus 11th power was measured in the stabilized mode and is attributed to the reference oscillator and to instabilities in the pump source. Variation of 10 to the minus 10th power was observed in the low-Q unstabilized mode, again attributable to pump fluctuations. Even so, direct scaling to a Q of 10 the 9th power predicts a stability better than 10 to the minus 15th power. Together with results showing the lowest losses to date in sapphire at microwave frequencies, and preliminary experiments on superconductor-on-sapphire resonators, frequency stability, levels as low as 10 to the minus 17th power are indicated.

Dick, G. J.↗
NASA NTRS1991

Oxide superconductors under magnetic field

One of the current most serious problems for the oxide superconductors from the standpoint of practical application is the various novel features derived mainly from their extremely short coherence. In particular, the coherence length so far observed in the cuprate superconductors is in the range of 0.1 nm perpendicular to the CuO2 plane. This seems to be creating most of the difficulties in the device fabrication and in the performance under the magnetic field. Some of the superconducting properties under the magnetic field will be discussed in terms of the short coherence length. A model will be presented based on the gradual strengthening of the pinning force with decrease in temperature and the weak coupling at the grain boundaries. Secondly, the broadening of the superconducting transition under the magnetic field is discussed. This is observed significantly only when the field is applied perpendicular to the basal plane and the relative orientation of the current to the field is insignificant in determining the extent of broadening. Besides, the change in the strength of the pinning force does not affect the width of the broadening. From these observations discussions will be made on a model based on the giant fluctuation. Based on this model, it is predicted that the coherence length along the c-axis will be the single most important material parameter to determine the performance of the superconductor under a strong magnetic field. It seems that BYCO is superior in this regard to Bi- or Tl-systems as far as the performance at 77 K is considered, although another material with the coherence length slightly longer along the c-axis is still highly desired.

Kitazawa, K.↗
DOE OSTI2024

Quantum fluctuations lead to glassy electron dynamics in the good metal regime of electron doped KTaO 3

One of the central challenges in condensed matter physics is to comprehend systems that have strong disorder and strong interactions. In the strongly localized regime, their subtle competition leads to glassy electron dynamics which ceases to exist well before the insulator-to-metal transition is approached as a function of doping. Here, we report on the discovery of glassy electron dynamics deep inside the good metal regime of an electron-doped quantum paraelectric system: KTaO 3 . We reveal that upon excitation of electrons from defect states to the conduction band, the excess injected carriers in the conduction band relax in a stretched exponential manner with a large relaxation time, and the system evinces simple aging phenomena—a telltale sign of glassy dynamics. Most significantly, we observe a critical slowing down of carrier dynamics below 35 K, concomitant with the onset of quantum paraelectricity in the undoped KTaO 3 . Our combined investigation using second harmonic generation technique, density functional theory and phenomenological modeling demonstrates quantum fluctuation-stabilized soft polar modes as the impetus for the glassy behavior. This study addresses one of the most fundamental questions regarding the potential promotion of glassiness by quantum fluctuations and opens a route for exploring glassy dynamics of electrons in a well-delocalized regime.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1990

Oxide superconductors under magnetic field

One of the current most serious problems for the oxide superconductors from the standpoint of practical application is the various novel features derived mainly from their extremely short coherence. In particular, the coherence length so far observed in the cuprate superconductors is in the range of 0.1 nm perpendicular to the CuO2 plane. This seems to be creating most of the difficulties in the device fabrication and in the performance under the magnetic field. Some of the superconducting properties under the magnetic field will be discussed in terms of the short coherence length. A model will be presented based on the gradual strengthening of the pinning force with decrease in temperature and the weak coupling at the grain boundaries. Secondly, the broadening of the superconducting transition under the magnetic field is discussed. This is observed significantly only when the field is applied perpendicular to the basal plane and the relative orientation of the current to the field is insignificant in determining the extent of the broadening. Besides, the change in the strength of the pinning force does not affect the width of the broadening. From these observations discussions will be made on a model based on the giant fluctuation. Based on this model, it is predicted that the coherence length along the c-axis will be the single most important material parameter to determine the performance of the superconductor under a strong magnetic field. It seems that BYCO is superior in this regard to Bi- or Tl-systems as far as the performance at 77 K is considered, although another material with the coherence length slightly longer along the c-axis is still highly desired.

Kitazawa, K.↗
DOE OSTI2020

Ferromagnetic cluster-glass phase in Ca(Co 1-x Ir x ) 2-y As 2 crystals

In this study, single crystals of Ca(Co 1-x Ir x ) 2-y As 2 with 0≤x≤0.35 and 0.10≤y≤0.14 have been grown using the self-flux technique and characterized by single-crystal x-ray diffraction (XRD), energy-dispersive x-ray spectroscopy, magnetization M, and magnetic susceptibility χ measurements versus temperature T, magnetic field H, and time t, and heat-capacity C p (H,T) measurements. The XRD refinements reveal that all the Ir-substituted crystals crystallize in a collapsed-tetragonal structure as does the parent CaCo 2-y As 2 compound. A small 3.3% Ir substitution for Co in CaCo 1.86 As 2 drastically lowers the A-type antiferromagnetic (AFM) transition temperature T N from 52 to 23 K with a significant enhancement of the Sommerfeld electronic heat-capacity coefficient. The A-type AFM structure consists of ab-plane layers of spins ferromagnetically aligned along the c axis with AFM alignment of the spins in adjacent layers along this axis. The positive Weiss temperatures obtained from Curie-Weiss fits to the χ(T>T N ) data indicate that the dominant magnetic interactions are ferromagnetic (FM) for all x. A magnetic phase boundary is inferred to be present between x=0.14 and x=0.17 from a discontinuity in the x dependencies of the effective moment and Weiss temperature in the Curie-Weiss fits. FM fluctuations that strongly increase with increasing x are also revealed from the χ(T) data. Furthermore, the magnetic ground state for x≥0.17 is a spin glass as indicated by hysteresis in χ(T) between field-cooled and zero-field-cooled measurements and from the relaxation of M in a small field that exhibits a stretched-exponential time dependence. The spin glass has a small FM component to the ordering and is hence inferred to be comprised of small FM clusters. The competing AFM and FM interactions along with crystallographic disorder associated with Ir substitution are inferred to be responsible for the development of a FM cluster-glass phase. A logarithmic T dependence of Cp at low T for x=0.14 is consistent with the presence of significant FM quantum fluctuations. This composition is near the T=0 boundary at x≈0.16 between the A-type AFM phase containing ferromagnetically-aligned layers of spins and the FM cluster-glass phase.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Benchmarking a Tunable Quantum Neural Network on Trapped-Ion and Superconducting Hardware

We implement a quantum generalization of a neural network on trapped-ion and IBM superconducting quantum computers to classify MNIST images, a common benchmark in computer vision. The network feedforward involves qubit rotations whose angles depend on the results of measurements in the previous layer. The network is trained via simulation, but inference is performed experimentally on quantum hardware. The classical-to-quantum correspondence is controlled by an interpolation parameter, $a$, which is zero in the classical limit. Increasing $a$ introduces quantum uncertainty into the measurements, which is shown to improve network performance at moderate values of the interpolation parameter. We then focus on particular images that fail to be classified by a classical neural network but are detected correctly in the quantum network. For such borderline cases, we observe strong deviations from the simulated behavior. We attribute this to physical noise, which causes the output to fluctuate between nearby minima of the classification energy landscape. Such strong sensitivity to physical noise is absent for clear images. We further benchmark physical noise by inserting additional single-qubit and two-qubit gate pairs into the neural network circuits. Our work provides a springboard toward more complex quantum neural networks on current devices: while the approach is rooted in standard classical machine learning, scaling up such networks may prove classically non-simulable and could offer a route to near-term quantum advantage.

FOS: Physical sciences↗
DOE OSTI2023

Ultrafast lattice disordering can be accelerated by electronic collisional forces

In the prevalent picture of ultrafast structural phase transitions, the atomic motion occurs in a slowly varying potential energy surface determined adiabatically by the fast electrons. However, this ignores non-conservative forces caused by electron-lattice collisions, which can significantly influence atomic motion. Most ultrafast techniques only probe the average structure and are less sensitive to random displacements, and therefore do not detect the role played by non-conservative forces in phase transitions. Here we show that the lattice dynamics of the prototypical insulator-to-metal transition of VO 2 cannot be described by a potential energy alone. We use the sample temperature to control the preexisting lattice disorder before ultrafast photoexcitation across the phase transition and our ultrafast diffuse scattering experiments show that the fluctuations characteristic of the rutile metal develop equally fast (120 fs) at initial temperatures of 100 K and 300 K. This indicates that additional non-conservative forces are responsible for the increased lattice disorder. In conclusion, these results highlight the need for more sophisticated descriptions of ultrafast phenomena beyond the Born-Oppenheimer approximation as well as ultrafast probes of spatial fluctuations beyond the average unit cell measured by diffraction.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Observation of weakly damped modes using high resolution measurement of turbulence in a dipole confined plasma

When plasma is confined by a levitated superconducting current ring, the turbulent radial particle flux changes the direction depending upon the gradient of the particle number within tubes of equal magnetic flux [Garnier et al., Phys. Plasmas 24, 012506 (2017)]. When the density profile is highly peaked, the particle flux is outward. When the density profile is less peaked, turbulence drives an inward “particle pinch.” This change in the direction of particle flux coincides with a reversal of the mean toroidal propagation direction of turbulent fluctuations. Previously, only the mean wavenumber of the fluctuations was reported. The mean wavenumber was computed from the ensemble correlation between two probes. Here, the full frequency-wavenumber power spectrum of the saturated turbulence is calculated by applying Capon’s “maximum likelihood method” to floating potential measurements from an array of probes. The power spectrum shows that the highest intensity modes are due to unstable entropy modes, and the less intense modes coincide with weakly damped convective cells, which rotate toroidally in the direction opposite to the unstable modes. Because the weakly damped modes make up a significant fraction of the fluctuating power, these measurements imply that saturated turbulence in a dipole-confined plasma involves the excitation of weakly damped rotating convective cells.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Low-Frequency Correlated Charge-Noise Measurements Across Multiple Energy Transitions in a Tantalum Transmon

Transmon qubits fabricated with tantalum metal have been shown to possess energy relaxation times greater than 400 𝜇⁢s and, as such, present an attractive platform for high precision, correlated noise studies across multiple higher-energy transitions. Tracking the multilevel fluctuating qudit frequencies with a precision enabled by the high coherence of the device allows us to extract the charge offset and quasiparticle dynamics. We observe qualitatively different charge-offset behavior in the tantalum device than those measured in previous low-frequency charge-noise studies. In particular, we find the charge-offset dynamics are dominated by rare, discrete jumps between a finite number of quasistationary charge configurations, a previously unobserved charge-noise process in superconducting qubits.

3-dimensional systems↗
DOE OSTI2025

General trends of superconducting pairing and magnetic correlations in the Ruddlesden-Popper nickelate 𝑚-layered superconductors La 𝑚+1 ⁢Ni 𝑚 ⁢O 3⁢𝑚+1

Here, we report a comprehensive theoretical analysis of the Ruddlesden-Popper layered nickelates La 𝑚+1 ⁢Ni 𝑚 ⁢O 3⁢𝑚+1 (𝑚 = 1 to 6) under pressure. These materials have recently received significant attention due to the discovery of superconductivity in some nickelates under pressure. Our results suggest that, while these Ruddlesden-Popper layered nickelates display many similarities, they also show noticeable differences. One of the common features of La 𝑚+1 ⁢Ni 𝑚 ⁢O 3⁢𝑚+1 is that the electronic states near the Fermi level are mainly contributed by Ni 3⁢𝑑 orbitals, slightly hybridized with O 2⁢𝑝 orbitals. The Ni 𝑑 3⁢𝑧 2 −𝑟 2 orbitals display bonding-antibonding, or bonding-antibonding-nonbonding, characteristic splittings, depending on the even or odd number of stacking layers 𝑚. In addition, the ratio of the in-plane interorbital hopping between 𝑑 3⁢𝑧 2 −𝑟 2 and 𝑑 𝑥 2 −𝑦 2 orbitals and in-plane intraorbital hopping between 𝑑 𝑥 2 −𝑦 2 orbitals was found to be large in La 𝑚+1 ⁢Ni 𝑚 ⁢O 3⁢𝑚+1 (𝑚 = 1 to 6), and this ratio increases from 𝑚 = 1 to 𝑚 = 6, suggesting that the in-plane hybridization will increase as the layer number 𝑚 increases. In contrast to the dominant 𝑠 ± -wave state driven by spin fluctuations in the bilayer La 3 ⁢Ni 2⁢ O 7 and trilayer La 4 ⁢Ni 3 ⁢O 10 , two nearly degenerate 𝑑 𝑥 2 −𝑦 2 -wave and 𝑠 ± -wave leading states were obtained in the four-layer stacking La 5⁢ Ni 4 ⁢O 13 and five-layer stacking La 6 ⁢Ni 5 ⁢O 16 . The leading 𝑠 ± -wave state was recovered in the six-layer material La 7 ⁢Ni 6 ⁢O 19 with slightly higher calculated pairing strength 𝜆 than that of the 𝑑 𝑥 2 −𝑦 2 -wave state. All this evidence suggests that both 𝑠 ± -wave and 𝑑 𝑥 2 −𝑦 2 -wave channels are strongly competing in the high-order niceklates based on our random-phase approximation calculations. In general, at the level of the random-phase approximation treatment, the superconducting transition temperature 𝑇 𝑐 decreases in stoichiometric bulk systems from the bilayer La 3 ⁢Ni 2 ⁢O 7 to the six-layer La 7 ⁢Ni 6 ⁢O 19 , despite the 𝑚-dependent dominant pairing. Both in-plane and out-of-plane magnetic correlations are found to be quite complex. Within the in-plane direction, we obtained the peak of the magnetic susceptibility at 𝐪 = (0.6⁢𝜋, 0.6⁢𝜋) for La 5 ⁢Ni 4 ⁢O 13 (𝑚 = 4) and La 7 ⁢Ni 6 ⁢O 19 (𝑚 = 6) and at 𝐪 = (0.7⁢𝜋, 0.7⁢𝜋) for La 6⁢ Ni 5⁢ O 16 (𝑚 = 5). Along the out-of-plane direction, four layers are coupled as ↓−↑−↑−↓ in La 5 ⁢Ni 4⁢ O 13 , five layers are coupled as ↑−↑−↓−↑−↑ in La 6 ⁢Ni 5 ⁢O 16 , and six layers are coupled as ↑−↓−↓−↑−↑−↓ in La 7 ⁢Ni 6 ⁢O 19 .

Zhang, Yang [Univ. of Tennessee, Knoxville, TN (Un↗