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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.

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At least 289 records · Page 16
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Exploration of Rayleigh-Taylor seeding mechanisms in laser- and pulsed-power-driven inertial fusion

The ubiquitous Rayleigh-Taylor instability (RTI) has been observed in fluids and plasmas in a wide range of parameter regimes from astrophysical to laboratory plasmas. In high-energy-density (HED) laboratory plasmas, such as laser-driven inertial confinement fusion (ICF) plasmas, the RTI can have a detrimental impact on achieving fusion ignition through the generation of hydrodynamic mix. Hence, an understanding of the seeding mechanisms that produce the RTI and identifying ways to mitigate hydrodynamic mix is of critical importance. Appropriately aligned magnetic fields have been known to stabilize short-wavelength RTI. A number of numerical and experimental studies have demonstrated the benefits of using imposed magnetic fields in laser-driven ICF to achieve higher ion temeratures, higher neutron yields, and a relaxation of the ignition criteria. This work addresses seeding mechanisms in laser-driven implosions to understand critical early-stage physics that ultimately leads to substantial growth of the RTI along with mechanisms for mitigation of this growth. Surface perturbations due to machining tolerances and single-feature seeds (for example due to fill tubes) can produce substantial RTI growth in the ignition-relevant high-convergence ratio targets for laser- driven ICF implosions. RTI growth from single-feature seeding in laser-based implosions has the potential to be mitigated through appropriately aligned externally applied magnetic fields and the goal of this work has been to quantify that numerically and experimentally. Resistive-magnetohydrodynamic (MHD) simu- lations are used to study the seeding and evolution of the RTI leveraging previous support from the DOE HEDLP program. Furthermore, experimental data has been obtained and applied towards code validation of unmagnetized and magnetized evolution of single-feature seeded RTI growth.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Coherent population trapping and spin relaxation of a silicon vacancy center in diamond at millikelvin temperatures

Here, we report experimental studies of coherent population trapping (CPT) and spin relaxation in a temperature range 4 K–100 mK in a silicon vacancy (SiV) center subject to a transverse magnetic field. The spin linewidth, which is determined by spin dephasing, is extracted from power dependent CPT linewidths. Near and below 1 K, phonon-induced spin dephasing becomes negligible compared with that induced by the spin bath of naturally abundant 13 C atoms. The temperature dependence of the spin dephasing rates agrees with the theoretical expectation that phonon-induced spin dephasing arises primarily from orbital relaxation induced by first order electron-phonon interactions. A nearly 100-fold increase in spin lifetime is observed when the temperature is lowered from 4 K to slightly below 1 K, indicating that two-phonon spin-flip transitions play an essential role in the spin relaxation of SiV ground states.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Magnetic order and spin liquid behavior in [Mo 3 ] 11+ molecular magnets

Molecular magnets based on [Mo 3 ] 11+ units with one unpaired electron per trimer have attracted recent interest due to the identification of quantum spin liquid candidacy in some family members. Here, we present comprehensive measurements on polycrystalline samples of ZnScMo 3 O 8 , MgScMo 3 O 8 , and Na 3 Sc 2 Mo 5 O 16 with the same Mo 3 O 13 magnetic building blocks. In this work, the crystal structures are characterized with x-ray or neutron powder diffraction and the magnetic ground states are determined by performing ac and dc susceptibility, specific heat, neutron powder diffraction, and muon spin relaxation measurements. Our work indicates that ZnScMo 3 O 8 and MgScMo 3 O 8 have ferromagnetic Curie-Weiss temperatures of 18.5 and 11.9 K, ordered ground states with net moments (low-moment ferromagnetism or canted antiferromagnetism), and zero field ordering temperatures of $T_c$ = 6 K and $T_c$ < 2 K, respectively. On the other hand, Na 3 Sc 2 Mo 5 O 16 hosts a dynamical magnetic ground state with no evidence for magnetic ordering or spin freezing down to 20 mK despite an antiferromagnetic Curie-Weiss temperature of –36.2 K, and therefore is a candidate for quantum spin liquid behavior. By comparing the present results to past work on the same family of materials, we construct a phase diagram which illustrates that the magnetic ground states of these Mo-based molecular magnets are very sensitive to small changes in the nearest-neighbor Mo-Mo distance.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Room temperature colossal superparamagnetic order in aminoferrocene–graphene molecular magnets

Intensive studies are published for graphene-based molecular magnets due to their remarkable electric, thermal, and mechanical properties. However, to date, most of all produced molecular magnets are ligand based and subject to challenges regarding the stability of the ligand(s). The lack of long-range coupling limits high operating temperature and leads to a short-range magnetic order. Herein, we introduce an aminoferrocene-based graphene system with room temperature superparamagnetic behavior in the long-range magnetic order that exhibits colossal magnetocrystalline anisotropy of 8 × 10 5 and 3 × 10 7 J/m 3 in aminoferrocene and graphene-based aminoferrocene, respectively. These values are comparable to and even two orders of magnitude larger than pure iron metal. Aminoferrocene [C 10 H 11 FeN] + is synthesized by an electrophilic substitution reaction. It was then reacted with graphene oxide that was prepared by the modified Hammers method. The phase structure and functionalization of surface groups were characterized and confirmed by XRD, FT-IR, and Raman spectroscopy. To model the behavior of the aminoferrocene between two sheets of hydroxylated graphene, we have used density functional theory by placing the aminoferrocene molecule between two highly ordered hydroxylated sheets and allowing the structure to relax. Here, the strong bowing of the isolated graphene sheets suggests that the charge transfer and resulting magnetization could be strongly influenced by pressure effects. In contrast to strategies based on ligands surface attachment, our present work that uses interlayer intercalated aminoferrocene opens routes for future molecular magnets as well as the design of qubit arrays and quantum systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Vertex dominated superconductivity in intercalated FeSe

Bulk FeSe becomes superconducting below 9 K, but the critical temperature (T c ) is enhanced almost universally by a factor of ~4–5 when it is intercalated with alkali elements. How intercalation modifies the structure is known from in-situ X-ray and neutron scattering techniques, but why T c changes so dramatically is not known. Here we show that there is one-to-one correspondence between the enhancement in magnetic instabilities at certain q vectors and superconducting pairing vertex, even while the nuclear spin relaxation rate 1/(T 1 T) may not reflect this enhancement. Intercalation modifies electronic screening both in the plane and also between layers. We disentangle quantitatively how superconducting pairing vertex gains from each such changes in electronic screening. Intercalated FeSe provides an archetypal example of superconductivity where information derived from the single-particle electronic structure appears to be insufficient to account for the origins of superconductivity, even when they are computed including correlation effects. We show that the five-fold enhancement in T c on intercalation is not sensitive to the exact position of the d xy at Γ point, as long as it stays close to E F . Finally, we show that intercalation also significantly softens the collective charge excitations, suggesting the electron-phonon interaction could play some role in intercalated FeSe.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Methods and systems for low to ultra-low magnetic field nuclear magnetic resonance for detecting chemical nerve agents

A nuclear magnetic resonance (NMR) system is configured to detect chemical threat material. The system comprises a magnet configured to generate a magnetic field of about 300 millitesla or less; and a probe configured to detect nuclear relaxation of at least two nuclei selected from the group consisting of 1H, 19F, 31P and 14N, and detect the spin density of nuclei selected from the group consisting of 1H, 19F, 31P and 14N, following excitation.

Williams, Robert F.↗
DOE OSTI2022

Deformed spin- 1 2 square lattice in antiferromagnetic NaZnVOPO 4 ( HPO 4 )

In this work, we report the structural and magnetic properties of a new spin-$\frac{1}{2}$ antiferromagnet NaZnVOPO 4 (HPO 4 ) studied via x-ray diffraction, magnetic susceptibility, high-field magnetization, specific heat, and 31 P nuclear magnetic resonance (NMR) measurements, as well as density-functional band-structure calculations. While thermodynamic properties of this compound are well described by the J 1 – J 2 square-lattice model, ab initio calculations suggest a significant deformation of the spin lattice. From fits to the magnetic susceptibility we determine the averaged nearest-neighbor and second-neighbor exchange couplings of $\bar{J}$ 1 ≃ – 1.3 K and $\bar{J}$ 2 ≃ 5.6 K , respectively, resulting in the effective frustration ratio α = $\bar{J}$ 2 – $\bar{J}$ 1 ≃ – 4.3 that implies columnar antiferromagnetic order as the ground state. Experimental saturation field of 15.3 T is consistent with these estimates if 20% spatial anisotropy in J 1 is taken into account. Specific heat data signal the onset of a magnetic long-range order at T N ≃ 2.1 K , which is further supported by a sharp peak in the NMR spin-lattice relaxation rate. The NMR spectra mark the superposition of two P lines due to two nonequivalent P sites where the broad line with the strong hyperfine coupling and short T 1 is identified as the P(1) site located within the magnetic planes, while the narrow line with the weak hyperfine coupling and long T 1 is designated as the P(2) site located between the planes.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Magnetic ground state of the one-dimensional ferromagnetic chain compounds M (NCS) 2 (thiourea) 2 (M=Ni,Co)

The magnetic properties of the two isostructural molecule-based magnets— Ni ( NCS ) 2 ( thiourea ) 2 , S = 1 [ thiourea = SC ( NH 2 ) 2 ] and Co ( NCS ) 2 ( thiourea ) 2 , S = 3 / 2 —are characterized using several techniques in order to rationalize their relationship with structural parameters and to ascertain magnetic changes caused by substitution of the spin. Zero-field heat capacity and muon-spin relaxation measurements reveal low-temperature long-range ordering in both compounds, in addition to Ising-like ( D < 0 ) single-ion anisotropy ( D Co ~ - 100 K, D Ni ~ - 10 K). Crystal and electronic structure, combined with dc-field magnetometry, affirm highly quasi-one-dimensional behavior, with ferromagnetic intrachain exchange interactions J Co ≈ + 4 K and J Ni ~ + 100 K and weak antiferromagnetic interchain exchange, on the order of J ' ~ - 0.1 K. Furthermore, electron charge- and spin-density mapping reveals through-space exchange as a mechanism to explain the large discrepancy in J -values despite, from a structural perspective, the highly similar exchange pathways in both materials. Both species can be compared to the similar compounds M Cl 2 ( thiourea ) 4 , M = Ni(II) (DTN) and Co(II) (DTC), where DTN is known to harbor two magnetic-field-induced quantum critical points. Direct comparison of DTN and DTC with the compounds studied here shows that substituting the halide Cl - ion for the NCS - ion results in a dramatic change in both the structural and magnetic properties.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Extending the family of reduced [Mn 12 O 12 (O 2 CR) 16 (H 2 O) x ] n- complexes, and their sensitivity to environmental factors

Here, the family of reduced [Mn 12 O 12 (O 2 CR) 16 (H 2 O) 4 ] n- (n = 1, 2) single-molecule magnets (SMMs) has been expanded with the synthesis of new members using I - as a stoichiometric one-electron reducing agent of the neutral n = 0 complexes. Electrochemical data, 1 H NMR spectra of the [Mn 12 O 12 (O 2 CCH 2 Cl) 16 (H 2 O) 3 ] 0,-,2- salts, and the crystal structures of two complexes, (PPh 4 )[Mn 12 O 12 (O 2 CCHCl 2 ) 16 (H 2 O) 4 ] and (PPh 4 ) 2 [Mn 12 O 12 (O 2 CCH 2 Cl) 16 (H 2 O) 3 ] have been obtained. For (PPh 4 ) 2 [Mn 12 O 12 (O 2 CCH 2 Cl) 16 (H 2 O) 3 ], the data confirm an S = 10 ground state, and magnetization vs dc field scans on a pristine crystal exhibit hysteresis loops possessing steps due to quantum tunneling of magnetization (QTM). In addition, two forms of the cluster have been identified in the crystal with distinctly different relaxation barriers, with the faster-relaxing form being the majority one in pristine crystals from mother liquor, and the slower-relaxing one becoming the majority one in vacuum-dried samples. Similar behavior is seen for (PPh 4 )[Mn 12 O 12 (O 2 CCHCl 2 ) 16 (H 2 O) 4 ] with an S = 19 / 2 ground state, which shows three forms to be present in the hysteresis loops of a pristine crystal, all converting to a slow-relaxing form on vacuum-drying. High-frequency EPR spectra of the latter confirm a high axial anisotropy with $\mathcal{D}$ = -0.477 cm -1 and rationalize its effective relaxation barrier U eff = 57 K. The combined work emphasizes a high sensitivity of such ultra-small nanomagnets to environmental influences, affecting their properties significantly, especially their quantum properties that are so important to many potential new 21st century applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Ferrimagnetism in EuFe 4 As 12 revealed by 153 Eu NMR and 75 As NQR measurements

Filled skutterudite compound EuFe 4 As 12 shows the highest magnetic ordering temperature of T C =154K among Eu-based skutterudite compounds, but its magnetic ground state has not been determined yet. In this study, we performed 153 Eu nuclear magnetic resonance (NMR) and 75 As nuclear quadrupole resonance (NQR) measurements on EuFe 4 As 12 to reveal its magnetic ground state as well as the physical properties from a microscopic point of view. From the temperature and magnetic field dependence of 153 Eu NMR spectrum in the magnetically ordered state, we found that the Eu ions are in Eu 2+ state with a nearly 7 μB corresponding to S=7/2 spins. Combined with the magnetization measurements, which show the reduced saturation moments of 4.5 μB/f.u., we determined the ground magnetic structure in EuFe 4 As 12 to be ferrimagnetic where the Eu 2+ 4f and the Fe 3d ordered moments are ferromagnetically aligned in each sublattice but the moments between the sublattices are antiferromagnetically aligned. We also found the local distortion at the Eu site from the cubic symmetry in the magnetically ordered state. The relationship between the rattling motion of Eu atoms and the local symmetry of the Eu ions is discussed. From the 75 As NQR nuclear spin-lattice relaxation time measurements as well as 153 Eu NMR measurements, we found that the 4f electrons of the Eu ions are well described by the local moment picture in both the magnetic and paramagnetic metallic states.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Local atomic and magnetic structure of multiferroic (Sr,Ba)⁢(Mn,Ti)⁢O 3

Here, we present a detailed study of the local atomic and magnetic structure of the type-I multiferroic perovskite system (Sr,Ba)(Mn,Ti)O 3 using x-ray and neutron pair distribution function (PDF) analysis, polarized neutron scattering, and muon spin relaxation (μSR) techniques. The atomic PDF analysis reveals widespread nanoscale tetragonal distortions of the crystal structure even in the paraelectric phase with average cubic symmetry, corresponding to incipient ferroelectricity in the local structure. Magnetic PDF analysis, polarized neutron scattering, and μSR likewise confirm the presence of short-range antiferromagnetic correlations in the paramagnetic state, which grow in magnitude as the temperature approaches the magnetic transition. We show that these short-range magnetic correlations coincide with a reduction of the tetragonal (i.e., ferroelectric) distortion in the average structure, suggesting that short-range magnetism can play an important role in magnetoelectric and/or magnetostructural phenomena even without genuine long-range magnetic order. The reduction of the tetragonal distortion scales linearly with the local magnetic order parameter, pointing to spontaneous linear magnetoelectric coupling in this system. These findings provide greater insight into the multiferroic properties of (Sr,Ba)(Mn,Ti)O 3 and demonstrate the importance of investigating the local atomic and magnetic structure to gain a deeper understanding of the intertwined degrees of freedom in multiferroics.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

How spin relaxes and dephases in bulk halide perovskites

Abstract Spintronics in halide perovskites has drawn significant attention in recent years, due to their highly tunable spin-orbit fields and intriguing interplay with lattice symmetry. Here, we perform first-principles calculations to determine the spin relaxation time ( T 1 ) and ensemble spin dephasing time ( $${T}_{2}^{*}$$ T 2 * ) in a prototype halide perovskite, CsPbBr 3 . To accurately capture spin dephasing in external magnetic fields we determine the Landé g -factor from first principles and take it into account in our calculations. These allow us to predict intrinsic spin lifetimes as an upper bound for experiments, identify the dominant spin relaxation pathways, and evaluate the dependence on temperature, external fields, carrier density, and impurities. We find that the Fröhlich interaction that dominates carrier relaxation contributes negligibly to spin relaxation, consistent with the spin-conserving nature of this interaction. Our theoretical approach may lead to new strategies to optimize spin and carrier transport properties.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2021

Universal spin wave damping in magnetic Weyl semimetals

We analyze the decay of spin waves into Stoner excitations in magnetic Weyl semimetals. The lifetime of a mode is found to have a universal dependence on its frequency and momentum, and on a few parameters that characterize the relativistic Weyl spectrum. At the same time, uniform Gilbert damping by Weyl electrons is absent. Here, the decay rate of spin waves is calculated perturbatively using the s-d model of itinerant Weyl or Dirac electrons coupled to local moments. We show that many details of the Weyl spectrum, such as the momentum-space locations, dispersions, and sizes of the Weyl Fermi pockets, can be deduced indirectly by probing the spin waves of local moments using inelastic neutron scattering.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Structural, magnetic, and electronic evolution of the spin-ladder system BaFe 2 S 3-x Se x with isoelectronic substitution

We reWe report experimental studies of a series of BaF e 2 S 3 - x Se x ( 0 ≤ $x$ ≤ 3 ) single crystals and powder specimens using x-ray diffraction, neutron-diffraction, muon-spin-relaxation, and electrical transport measurements. A structural transformation from $C$ $mcm$ ( BaFe 2 Se 3 ) to $P$ $nma$ ( BaFe 2 Se 3 ) was identified around $x$ = 0.7 - 1 . Neutron-diffraction measurements on the samples with $x$ = 0.2, 0.4, and 0.7 reveal that the Néel temperature of the stripe antiferromagnetic order is gradually suppressed from ~120 to 85 K, while the magnitude of the ordered Fe 2+ moments shows very little variation. Similarly, the block antiferromagnetic order in BaFe 2 Se 3 remains robust for 1.5 ≤ $x$ ≤ 3 with negligible variation in the ordered moment and a slight decrease of the Néel temperature from 250 K ( $x$ = 3 ) to 225 K ( $x$ = 1.5 ). The sample with $x$ = 1 near the $C$ $mcm$ and $P$ $nma$ border shows coexisting, two-dimensional, short-range stripe- and block-type antiferromagnetic correlations. The system remains insulating for all $x$ , but the thermal activation gap shows an abrupt increase when traversing the boundary from the $C$ $mcm$ stripe phase to the $P$ $nma$ block phase. The results demonstrate that the crystal structure, magnetic order, and electronic properties are strongly coupled in the BaFe 2 S 3-x Se x system.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Spin injection by spin–charge coupling in proximity induced magnetic graphene

Abstract Within the field of spintronics major efforts are directed towards developing applications for spin-based transport devices made fully out of two-dimensional materials. In this work we present an experimental realization of a spin-valve device where the generation of the spin signal is exclusively attributed to the spin-dependent conductivity of the magnetic graphene resulting from the proximity of an interlayer antiferromagnet, chromium sulfide bromide (CrSBr). We clearly demonstrate that the usage of the conventional air-sensitive 3D magnetic contacts can be fully avoided when graphene/CrSBr heterostructures are employed. Moreover, apart from providing exceptionally long spin relaxation length, the usage of graphene for both generation and transport of the spin allows to automatically avoid the conductivity mismatch between the source and the channel circuits that has to be considered when using conventional low-resistive contacts. Our results address a necessary step in the engineering of spintronic circuitry out of layered materials and precede further developments in the area of complex spin-logic devices. Moreover, we introduce a fabrication procedure where we designed and implemented a recipe for the preparation of electrodes via a damage-free technique that offers an immediate advantage in the fields of air-sensitive and delicate organic materials.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Vertically Aligned Single-Crystalline CoFe 2 O 4 Nanobrush Architectures with High Magnetization and Tailored Magnetic Anisotropy

Micrometer-tall vertically aligned single-crystalline CoFe 2 O 4 nanobrush architectures with extraordinarily large aspect ratio have been achieved by the precise control of a kinetic and thermodynamic non-equilibrium pulsed laser epitaxy process. Direct observations by scanning transmission electron microscopy reveal that the nanobrush crystal is mostly defect-free by nature, and epitaxially connected to the substrate through a continuous 2D interface layer. In contrast, periodic dislocations and lattice defects such as anti-phase boundaries and twin boundaries are frequently observed in the 2D interface layer, suggesting that interface misfit strain relaxation under a non-equilibrium growth condition plays a critical role in the self-assembly of such artificial architectures. Further, magnetic property measurements have found that the nanobrushes exhibit a saturation magnetization value of 6.16 μB/f.u., which is much higher than the bulk value. The discovery not only enables insights into an effective route for fabricating unconventional high-quality nanostructures, but also demonstrates a novel magnetic architecture with potential applications in nanomagnetic devices.

36 MATERIALS SCIENCE↗
DOE OSTI2026

MnRhBi3: A Cleavable Antiferromagnetic Metal

This dataset contains DFT input and output files supporting the theoretical modeling in the associated publication (Chem. Mater. 2024, 36, 11306-11316). The calculations characterize MnRhBi3, an orthorhombic (Cmmm) van der Waals-layered intermetallic compound that cleaves easily between neighboring Bi layers. The dataset is organized into three calculation types: (i) Bulk: Structural relaxations of the periodic MnRhBi3 crystal in antiferromagnetic (AFM) and ferromagnetic (FM) configurations, using the vdW-DF-optB86b functional. These provide the equilibrium lattice constants, magnetic energy differences (AFM is 0.5 meV/f.u. lower than FM), and magnetic moments (4.4 µB/Mn, 0.17 µB/Rh, 0.18 µB/Bi) reported in Table 1 of the main text. (ii) Slab: Same magnetic configurations computed with an 18 Ang vacuum layer introduced between Bi layers, used to calculate the cleavage energy Ec = 0.56 J/m2 (AFM) and 0.57 J/m2 (FM), establishing MnRhBi3 as a van der Waals-layered material comparable to graphite, MoS2, and CrI3. (iii) ELF: Single-point calculation on the relaxed bulk AFM geometry with LELF=.TRUE., producing the ELFCAR file used to generate electron localization function isosurfaces and contour maps (Fig. 2, main text) showing Bi lone pairs directed into the van der Waals gaps. All folders contain CONTCAR, INCAR, KPOINTS, OUTCAR, and POSCAR. The ELF/ folder additionally contains ELFCAR. Calculations were performed using VASP 6.3.2 with PBE + vdW-DF-optB86b, PAW potentials, and an energy cutoff of 800 eV.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Quantum utility in simulating the real-time dynamics of the Fermi–Hubbard model using superconducting quantum computers

The Fermi–Hubbard model is a fundamental model in condensed matter physics that describes strongly correlated electrons. On the other hand, quantum computers are emerging as powerful tools for exploring the complex dynamics of these quantum many-body systems. In this work, we demonstrate the quantum simulation of the one-dimensional Fermi–Hubbard model using IBM's superconducting quantum computers, employing over 100 qubits. We introduce a first-order Trotterization scheme and extend it to an optimized second-order Trotterization for the time evolution in the Fermi–Hubbard model, specifically tailored for the limited qubit connectivity of quantum architectures, such as IBM's platforms. Notably, both Trotterization approaches are scalable and maintain a constant circuit depth at each Trotter step, regardless of the qubit count, enabling us to precisely investigate the relaxation dynamics in the Fermi–Hubbard model by measuring the expectation value of the Néel observable (staggered magnetization) for time-evolved quantum states. Lastly, our successful measurement of expectation values in such large-scale quantum many-body systems, especially at longer time scales with larger entanglement, highlights the quantum utility of superconducting quantum platforms over conventional classical approximation methods.

97 MATHEMATICS AND COMPUTING↗