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At least 1,009 records · Page 56

The ATLAS experiment at the CERN Large Hadron Collider: a description of the detector configuration for Run 3

The ATLAS detector is installed in its experimental cavern at Point 1 of the CERN Large Hadron Collider. During Run 2 of the LHC, a luminosity of ℒ = 2 × 10 34 cm -2 s -1 was routinely achieved at the start of fills, twice the design luminosity. For Run 3, accelerator improvements, notably luminosity levelling, allow sustained running at an instantaneous luminosity of ℒ = 2 × 10 34 cm -2 s -1 , with an average of up to 60 interactions per bunch crossing. The ATLAS detector has been upgraded to recover Run 1 single-lepton trigger thresholds while operating comfortably under Run 3 sustained pileup conditions. A fourth pixel layer 3.3 cm from the beam axis was added before Run 2 to improve vertex reconstruction and b-tagging performance. New Liquid Argon Calorimeter digital trigger electronics, with corresponding upgrades to the Trigger and Data Acquisition system, take advantage of a factor of 10 finer granularity to improve triggering on electrons, photons, taus, and hadronic signatures through increased pileup rejection. The inner muon endcap wheels were replaced by New Small Wheels with Micromegas and small-strip Thin Gap Chamber detectors, providing both precision tracking and Level-1 Muon trigger functionality. Trigger coverage of the inner barrel muon layer near one endcap region was augmented with modules integrating new thin-gap resistive plate chambers and smaller-diameter drift-tube chambers. Tile Calorimeter scintillation counters were added to improve electron energy resolution and background rejection. Upgrades to Minimum Bias Trigger Scintillators and Forward Detectors improve luminosity monitoring and enable total proton-proton cross section, diffractive physics, and heavy ion measurements. These upgrades are all compatible with operation in the much harsher environment anticipated after the High-Luminosity upgrade of the LHC and are the first steps towards preparing ATLAS for the High-Luminosity upgrade of the LHC. This paper describes the Run 3 configuration of the ATLAS detector.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Canted antiferromagnetic order in the monoaxial chiral magnets V 1/3 TaS 2 and V 1/3 NbS 2

The Dzyaloshinskii-Moriya (DM) interaction is present in the transition metal dichalcogenides (TMDC) magnets of form M 1 / 3 T S 2 ( M = 3 d transition metal, T ϵ { Nb , Ta } ), given that the intercalants M form 3 × 3 superlattices within the structure of the parent materials T S 2 and break the centrosymmetry. Competition between DM and ferromagnetic exchange interactions has been shown to stabilize a topological defect known as a chiral soliton in select intercalated TMDCs, initiating interest both in terms of fundamental physics and the potential for technological applications. In the current article we report on our study of the materials V 1 / 3 TaS 2 and V 1 / 3 NbS 2 , using a combination of x-ray powder diffraction, magnetization, and single crystal neutron diffraction. Historically identified as ferromagnets, our diffraction results instead reveal that vanadium spins in these compounds are arranged into an A-type antiferromagnetic configuration at low temperatures. Refined moments are 1.37(6) and 1.50(9) μ B for V 1 / 3 TaS 2 and V 1 / 3 NbS 2 , respectively. Transition temperatures T c = 32 K for V 1 / 3 TaS 2 and 50 K for V 1 / 3 NbS 2 are obtained from the magnetization and neutron diffraction results. We attribute the small net magnetization observed in the low-temperature phases to a subtle ( ~ 2 ° ) canting of XY spins in the out-of-plane direction. These new results are indicative of dominant antiferromagnetic exchange interactions between the vanadium moments in adjacent a b planes, likely eliminating the possibility of identifying stable chiral solitons in the current materials.

36 MATERIALS SCIENCE↗

On the subject of large-scale pool fires and turbulent boundary layer interactions

The role to which a realistic inflow turbulent boundary layer (TBL) influences transient and mean large-scale pool fire quantities of interest (QoIs) is numerically investigated. High-fidelity, low-Mach large-eddy simulations that activate low-dissipation, unstructured numerics are conducted using an unsteady flamelet combustion modeling approach with mutiphysics coupling to soot and participating media radiation transport. Three inlet profile configurations are exercised for a large-scale, high-aspect rectangular pool that is oriented perpendicular to the flow direction: a time-varying, TBL inflow profile obtained from a periodic precursor simulation, the time-mean of the transient TBL, and a steady power-law inflow profile that replicates the mean TBL crosswind velocity of 10.0 m/s at a vertical height of 10 m. Results include both qualitative transient flame evolution and quantitative flame shape with ground-level temperature and convective/radiative heat flux profiles. While transient fire events, which are driven by burst-sweep TBL coupling, such as blow-off and reattachment are vastly different in the TBL case (contributing to increased root mean square QoI fluctuation prediction and disparate flame lengths), mean surface QoI magnitudes are similar. Quadrant analysis demonstrates that the TBL configuration modifies burst-sweep phenomena at windward pool locations, while leeward recovery is found. In conclusion, positive fluctuations of convective heat flux correlate with fast moving fluid away from the pool surface due to intermittent combustion events.

97 MATHEMATICS AND COMPUTING↗

Opportunities for an Integrated Web-Based Workbench for Data Access and Analysis - 20244

Management of environmental issues can require integration of multiple types of data and information, conducting data analysis and interpretation, and providing data visualization for effective communications. These data elements are important for site management to support regulator interactions and provide defensibility for remedial decisions. Databases and information repositories are core elements of managing data; however, efficient data access and analysis also enable effective site management. The U.S. Department of Energy (DOE) Hanford Site is an example of a complex site with a voluminous quantity of environmental data and a need for efficient site management. Different tiers of data and information tools have been developed and deployed to address site needs. These tools are configured for ready access via the web site interfaces and meet the rigorous quality requirements for environmental site management. Evolving efforts are focused on an integrated platform to meet site environmental management needs. In this platform, users can access site information at multiple levels of detail based on their need and permissions, so that data and associated analyses are presented within the context of the site mission and the user's management or technical needs. This concept is not only applicable at individual sites like Hanford but also applicable at other sites within the DOE complex. An integrated web-based architecture that links data visualization, data analytics, and management tools can provide holistic access to large data sets, minimize complexity, and maximize interactivity and technical communication. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

A gas dynamic perspective on particle lifting in electrostatic discharge-like devices using multiphase particle-in-cell approach

Although particle–laden electrostatic discharges are widely used in laboratories as well as in industrial applications, the mechanism of particle lifting for particles initially at rest in such highly unsteady systems is not well understood. A multiphase gas–particle solver is developed using the multiphase particle-in-cell (MP-PIC) approach to emulate the interaction of a compressible shock-dominated gas phase with the dense particle phase. First, the two-way coupled solver is initially used to study the interaction of a planar traveling shock with a vertical curtain of particulates. The gas and particle phase evolution was found to be in good agreement with a similar experimental study in Ling et al. [Phys. Fluids 24, 113301 (2012)]. Second, the MP-PIC code is used to study the interaction of an expanding blast wave with a thick bed of particles. The simulation considered forces such as quasi-steady drag, pressure-gradient, added-mass, Saffman, and Magnus forces. We observe that the vertical liftoff particles close to the shock impingement point in this configuration are associated with the quasi-steady drag, pressure gradient, and added-mass forces. Also, the Saffman lift and Magnus forces contribute to lifting particles located radially farther away from the shock impingement point. In addition, the study finds a decrease in particle lifting efficiency with decreasing plasma kernel length and shock strength.

42 ENGINEERING↗

Wavelength conversion for single-photon polarization qubits through continuous-variable quantum teleportation

A quantum internet connects remote quantum processors that need to interact and exchange quantum signals over a long distance through photonic channels. However, these quantum nodes operate at the wavelength ranges unsuitable for long-distance transmission. Therefore, quantum wavelength conversion to telecom bands is crucial for long-distance quantum networks based on optical fiber. Here, we propose wavelength conversion devices for single-photon polarization qubits using continuous-variable quantum teleportation that can efficiently convert qubits between near-infrared (780–795 nm suitable for interacting with atomic quantum nodes) and telecom wavelength (1300–1500 nm suitable for long-distance transmission). The teleportation uses entangled photon fields (i.e., nondegenerate two-mode squeezed state) that can be generated by four-wave mixing in a rubidium atomic gas using a diamond configuration of atomic transitions. The entangled fields can be emitted in two orthogonal polarizations with locked relative phase, making them especially suitable for interfacing with single- photon polarization qubits. Furthermore, our work may pave the way for the realization of long-distance quantum networks.

74 ATOMIC AND MOLECULAR PHYSICS↗

Model simulations of Plum Island Ecosystems LTER low marsh site using ELM-PFLOTRAN

Model simulations using the E3SM Land Model (ELM) coupled to the PFLOTRAN reactive transport model via the Alquimia interface. The simulations were conducted for a tidal salt marsh at the Plum Island Ecosystems LTER near Rowley, Massachusetts, USA. Model simulations were forced using site-specific tidal cycles and salinity, and the simulations used a biogeochemical reaction network including aerobic decomposition, sulfate reduction, iron reduction, and methanogenesis. Model outputs include simulated carbon stocks, carbon dioxide and methane fluxes, and porewater concentrations of key solutes related to sulfur, iron, and carbon cycling. The model simulations included a saline simulation (with tidal sulfate inputs), a fresh simulation (with low salinity and low sulfate inputs), and a saline simulation with lower vegetation productivity to represent the effect of salinity on vegetation. These simulations were conducted to demonstrate that a new model framework incorporating subsurface redox and biogeochemical interactions into a land surface model could reproduce measured surface greenhouse gas fluxes and biogeochemical dynamics in tidal marsh ecosystems, and to test whether including redox interactions in a land surface model would allow the model to resolve contrasts in biogeochemical cycling and greenhouse gas production between saline and freshwater wetlands.The data package includes gzipped tar archives (which can be expanded using standard tar and gzip utilities) of model outputs from three model configurations: saline subsurface and reduced vegetation productivity related to salinity; saline subsurface with vegetation productivity not reduced; and freshwater. Also included are code for the modified E3SM model, Alquimia interface, and PFLOTRAN reactive transport simulator in gzipped tar format; plain text parameter and configuration files; python code files for visualizing model output and defining model configurations; and model output, tide and salinity forcing, and configuration files in netCDF format. See the README.md file in the data package for a detailed description of all files contained in the package. All files are in netCDF (.nc), gzipped tar archive (.tar.gz or .tgz), or text (all other files).Updated: May 13, 2024. Model output, E3SM code, PFLOTRAN input files, and python codes for visualizing results were updated to reflect changes made for the manuscript revision. The updated archive reflects the code and model output from the final accepted manuscript. Changes included updated reaction parameters reflecting improved parameterization and additional comparisons with field measurements. E3SM code changes included better support for multiple grid cells and improved flow and transport parameterization.

54 ENVIRONMENTAL SCIENCES↗

High-Resolution WRF-Based Downscaling of Earth System Model Projections for Energy Applications across CONUS

Evaluating energy resources under future scenarios requires meteorological information that adequately resolves regional-scale variability and is suitable for regional energy system studies. Although Earth system model (ESM) outputs provide essential large-scale context, their coarse resolution and inherent biases limit direct use in energy system applications. This work presents a high-resolution dynamical downscaling framework using the Weather Research and Forecasting (WRF) model to generate energy-relevant regional fields for future scenarios over the contiguous United States (CONUS). The framework first identifies an optimal WRF configuration through sensitivity experiments, then evaluates raw and bias-corrected ESM initial and boundary conditions, with soil moisture and soil temperature bias correction implemented as an integral component of the bias-corrected ESM atmospheric forcing prior to WRF dynamical downscaling to improve land-atmosphere interactions. Simulations performed at 4-km resolution show that uncorrected ESM forcing leads to systematically dry and cold soil states, which propagate into elevated near-surface air temperature and solar irradiance biases, particularly during summer for the period 2000-2014. Incorporating bias-corrected atmospheric forcing together with soil state bias correction substantially reduces these errors and improves the representation of surface energy processes in WRF simulations. The results highlight the importance of bias-aware initialization strategies in high-resolution dynamical downscaling for future energy system analysis and planning.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Dynamical instability of collapsed dark matter halos

A self-interacting dark matter halo can experience gravothermal collapse, resulting in a central core with an ultrahigh density. It can further contract and collapse into a black hole, a mechanism proposed to explain the origin of supermassive black holes. We study dynamical instability of the core in general relativity. Here we use a truncated Maxwell-Boltzmann distribution to model the dark matter distribution and solve the Tolman-Oppenheimer-Volkoff equation. For given model parameters, we obtain a series of equilibrium configurations and examine their dynamical instability based on considerations of total energy, binding energy, fractional binding energy, and adiabatic index. Our numerical results indicate that the core can collapse into a black hole when the fractional binding energy reaches 0.035 with a central gravitational redshift of 0.5. We further show for the instability to occur in the classical regime, the boundary temperature of the core should be at least 10% of the mass of dark matter particles; for a 10 9 M ⊙ seed black hole, the particle mass needs to be larger than a few keV. These results can be used to constrain different collapse models, in particular, those with dissipative dark matter interactions.

79 ASTRONOMY AND ASTROPHYSICS↗

Understanding the Structure and Dynamics of Complex Biomembrane Interactions by Neutron Scattering Techniques

The membrane is one of the key structural materials of biology at the cellular level. Composed predominantly of a bilayer of lipids with embedded and bound proteins, it defines the boundaries of the cell and many organelles essential to life and therefore is involved in almost all biological processes. Membrane-specific interactions, such as drug binding to a membrane receptor or the interactions of an antimicrobial compound with the lipid matrix of a pathogen membrane, are of interest across the scientific disciplines. Herein we present a review, aimed at nonexperts, of the major neutron scattering techniques used in membrane studies: small-angle neutron scattering, neutron membrane diffraction, neutron reflectometry, quasielastic neutron scattering, and neutron spin echo. Neutron scattering techniques are well suited to studying biological membranes. The nondestructive nature of cold neutrons means that samples can be measured for long periods without fear of beam damage from ultraviolet, electron, or X-ray radiation, and neutron beams are highly penetrating, thus offering flexibility in samples and sample environments. Most important is the strong difference in neutron scattering lengths between the two most abundant forms of hydrogen, protium and deuterium. Changing the relative amounts of protium/deuterium in a sample allows the production of a series of neutron scattering data sets, enabling the observation of differing components within complex membrane architectures. This approach can be as simple as using the naturally occurring neutron contrast between different biomolecules to study components in a complex by changing the solution H 2 O/D 2 O ratio or as complex as selectively labeling individual components with hydrogen isotopes. This review presents an overview of each experimental technique with the neutron instrument configuration, related sample preparation and sample environment, and data analysis, highlighted by a special emphasis on using prominent neutron contrast to understand structure and dynamics. This review gives researchers a practical introduction to the often enigmatic suite of neutron beamlines, thereby lowering the barrier to taking advantage of these large-facility techniques to achieve new understandings of membranes and their interactions with other molecules.

59 BASIC BIOLOGICAL SCIENCES↗

Role of Hydrogen-bonded Bimolecular Formic Acid–Formate Complexes for Formic Acid Decomposition on Copper: A Combined First-Principles and Microkinetic Modeling Study

Hydrogen bonding interactions alter the nanoscale reaction mechanisms of many chemistries. Yet, it remains unclear how they affect heterogeneously catalyzed decomposition of formic acid (FA), a reaction of intense interest since FA is a promising hydrogen carrier. In this work, we elucidate how hydrogen bonding affects the reaction mechanisms for FA decomposition on Cu(111) by combining first-principles density functional theory calculations to calculate reaction energetics, Latin-hypercube sampling to elucidate stable high-coverage adsorbate configurations, and coverage self-consistent mean-field microkinetic models to predict reaction kinetics. We demonstrate that hydrogen-bonded complexes of FA with formate (bimolecular FA–HCOO complexes) can play a dominant role in FA decomposition. Specifically, our first-principles calculations show that hydrogen bonding of FA with HCOO may stabilize the crucial monodentate HCOO intermediate and the transition states for HCOO decomposition, especially at low coverages. We predict that, depending on the reaction conditions, 40–80% of the reaction flux goes through pathways involving the bimolecular FA–HCOO complexes. Additionally, the active site for FA decomposition on Cu(111) involves a high coverage (~0.4 monolayers (ML)) of these complexes, which unexpectedly stabilize intermediates and transition states via van der Waals interactions. Our work provides molecular insights consistent with previous experimental observations on supported Cu/Al 2 O 3 catalysts. This paves the way toward the development of novel catalysts for FA decomposition as well as for other industrially important chemistries with intermediates capable of hydrogen bonding, such as ammonia electrooxidation and CO 2 hydrogenation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

First saturation correction in high energy proton-nucleus collisions. Part III. Ensemble averaging

In high energy proton-nucleus collisions, the gluon saturation effects from the nucleus are fully incorporated into the light-like Wilson lines. The gluon saturation effects from the proton, which are anticipated to be important either in the extreme high energy limit or towards the dense-dense (nucleus-nucleus) collision regimes, have been studied perturbatively within the Color Glass Condensate effective theory in previous papers of this series. A configuration-by-configuration expression for the single inclusive semi-hard gluon production including the first saturation correction was obtained. In this paper, we perform ensemble averaging in the McLerran-Venugopalan model and the Dipole Approximation. We find that, in the saturation correction, the effects of the initial state interactions are negligible while the final state interactions play most important role and give a positive-valued contribution to the semi-hard gluon spectrum. Furthermore, we show that the single gluon spectrum scales approximately 1/$k$$^{4}_{⊥}$ at small k ⊥ , suggesting that a resummation of higher order saturation corrections is required to regulate the infrared region of the gluon spectrum.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Study of the deformed halo nucleus 31 Ne with Glauber model based on microscopic self-consistent structures

In this work, the exotic deformed nucleus 31 Ne is studied with an approach that combines self-consistent structure and reaction theories. The deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc) is utilized to demonstrate that deformation and pairing correlations give rise to a halo structure with a large-amplitude p-wave configuration in 31 Ne. Then the valence nucleon wave functions and angle-averaged density distributions of 30 Ne from this theory are used as input for the Glauber reaction model to study the observables of neutron-rich neon isotopes to search halo signatures. With NL1 effective interaction, our predictions of the reaction cross sections for these exotic neon isotopes on a carbon target can better reproduce the experimental data than those from the relativistic mean field model for a spherical shape with resonances and pairing correlation contributions, and are roughly 3.3% (~ 50 mb) larger than those with Gaussian function-fitted densities of the core nuclei. The calculated one-neutron removal cross section at 240 MeV/nucleon, and the inclusive longitudinal momentum distribution of the 30 Ne residues from the 31Ne breakup reaction are largely improved over previous theoretical predictions and agree well with data. These reaction evaluations indicate a dilute density distribution in coordinate space and are a canonical signature of a halo structure. Moreover, our predictions with the NL3 and PK1 effective interactions give slightly better descriptions of reaction observables for exotic neon isotopes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Increased panel height enhances cooling for photovoltaic solar farms

We report solar photovoltaic (PV) systems suffer substantial efficiency loss due to environmental and internal heating. However, increasing the canopy height of these systems promotes surface heat transfer and boosts production. This work represents the first wind tunnel experiments to explore this concept in terms of array flow behavior and relative convective heat transfer, comparing model solar arrays of varied height arrangements - a nominal height, extended height, and a staggered height configuration. Analyses of surface thermocouple data show average Nusselt number (Nu) to increase with array elevation, where panel convection at double height improved up to 1.88 times that of the nominal case. This behavior is an effect of sub-array entrainment of high velocity flow and panel interactions as evidenced through flow statistics and mean kinetic energy budgets on particle image velocimetry (PIV) data. The staggered height arrangement encourages faster sub-panel flow than in the nominal array. Despite sub-array blockage due to the lower panel interaction, heat shedding at panel surfaces promotes improvements on over 1.3 times that of the nominal height case.

14 SOLAR ENERGY↗

Developing a microwave-driven reactor for ammonia synthesis: insights into the unique challenges of microwave catalysis

Rapid development of new ammonia (NH 3 ) synthesis techniques that enable modular, intermittent production is essential to actualizing NH 3 's potential as a clean energy carrier, since contemporary methods are configured to centralized, continuous production methods with high emissions and are incompatible with renewable sources. Here, in this mission, microwave-driven catalysis is promising for its ability to enhance reaction kinetics and apply targeted heating for efficient energy use. However, owing to an incomplete understanding of the interaction between microwave fields and catalyst beds, the development of such microwave-catalysis systems remains underexplored and challenging. This paper investigates the 10× scale-up of a microwave-based NH 3 synthesis reactor using numerical and experimental approaches, achieving the largest reported microwave-driven NH 3 reactor to date. Results elucidate phenomena unique to microwave processes that are only predictable through numerical modeling, including how a catalyst's dielectric properties influence microwave field distribution by affecting penetration depth and how energy utilization can be poor even with sufficient attenuation. These dynamics change with scale, constrain reactor geometry, and potentially hamper performance. Nonetheless, we demonstrate a production rate of 56.6 g NH$_3$ per day, the highest reported NH 3 synthesis rate for laboratory-scale alternative techniques; correspondingly, the benchmark energy efficiency achieved in this paper (45.6 g NH$_3$ kW h -1 ) is the highest reported for such reactors of sufficient scale. Even with this exemplary energy efficiency, energy losses were found in excess of 50%, an issue resolvable through scale and reactor design. The efficiencies imparted by microwaves were key in these achievements, warranting further investigation toward development of microwave-driven NH 3 systems.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Ab Initio Study of Atomic and Electronic Structure of Promising Ba4XMn3O12 (X = Nb, Ce, Pr) Oxides for Solar Thermochemical Hydrogen Production

The two-step metal oxide water-splitting cycle is one of the most viable approach for Solar Thermochemical Hydrogen (STCH) production. Challenges exist in finding suitable oxides that can satisfy thermodynamics of the STCH redox cycle under viable range of temperatures and partial pressures. Recently, BXM family members, i.e., Ba4NbMn3O12 (BNM), Ba4CeMn3O12 (BCM), Ba4PrMn3O12 (BPM) are discovered to exhibit promising STCH performance. However, the magnetic degrees of freedom of their experimental crystal structures is not characterized, and only hypothetical models exist for their electronic structure. We performed Monte-Carlo sampling for the magnetic spin arrangement of Mn atoms to provide explicit atomic structure models for their ground state 12R polytype and determined the most stable spin configuration for each member after structure relaxation using density functional theory (DFT) calculations. We also elucidate the most stable charge configuration (Mn3+/Mn4+ arrangement) for BNM among the existing hypothesis in literature. We investigate these strongly correlated oxides using different levels of theory (DFT+U, Hybrid-DFT) to develop better understanding of their electronic structure. These calculations allowed us to develop a model based on molecular orbital interactions that help explain the observed changes in their experimental x-ray spectroscopy measurements. Thereby, help link differences in electronic structure of BXM family members to their varying water-splitting behavior. These structure models will further facilitate future in-depth defect studies to model STCH redox cycle of these oxides.

atomic and magnetic structure↗

Magnetic field effects on the quantum spin liquid behaviors of NaYbS 2

Spin-orbit coupling is an important ingredient to regulate the many-body physics, especially for many spin liquid candidate materials such as rare-earth magnets and Kitaev materials. The rare-earth chalcogenides NaYbCh 2 (Ch = O, S, Se) is a congenital frustrating system to exhibit the intrinsic landmark of spin liquid by eliminating both the site disorders between Na + and Yb 3+ ions with the big ionic size difference and the Dzyaloshinskii-Moriya interaction with the perfect triangular lattice of the Yb 3+ ions. The temperature versus magnetic-field phase diagram is established by the magnetization, specific heat, and neutron-scattering measurements. Notably, the neutron diffraction spectra and the magnetization curve might provide microscopic evidence for a series of spin configuration for in-plane fields, which include the disordered spin liquid state, 120° antiferromagnet, and one-half magnetization state. Furthermore, the ground state is suggested to be a gapless spin liquid from inelastic neutron scattering, and the magnetic field adjusts the spin orbit coupling. Therefore, the strong spin-orbit coupling in the frustrated quantum magnet substantially enriches low-energy spin physics. This rare-earth family could offer a good platform for exploring the quantum spin liquid ground state and quantum magnetic transitions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗