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DOE OSTI2023

Challenges and Prospects of Sodium‐Ion and Potassium‐Ion Batteries for Mass Production

The exponential growth of the lithium‐ion (LIB) market is causing a significant disparity between the supply chain and demand for its resources. In this regard, sodium‐ion and potassium‐ion batteries are promising alternatives to LIBs due to their low cost. However, the larger sizes of Na + and K + ions create challenges that prevent them from achieving energy densities comparable to LIBs while maintaining an acceptable cycle life. Here, in this perspective, the aim is to evaluate the status of Na‐ion and K‐ion batteries and the challenges associated with them on both fundamental and commercial levels. The focus is on the structural instability arising from phase transitions during cycling, intricate chemical degradation processes, and potential avenues for enhancing their performance with a specific goal of improving their viability for grid‐scale energy storage. Materials production and abundance limitations for the chemistries of the state‐of‐the‐art materials and account for critical parameters from both the perspective of researchers and investors are analyzed. This analysis aims to provide insights into the strategic trade‐offs required to effectively implement the technology in real‐world applications, such as grid‐scale storage and other areas. Furthermore, the utilization of metals with low or no supply‐chain problems as an important aspect of these trade‐offs is considered.

25 ENERGY STORAGE↗

DOE OSTI2026

Phase Stability and Electrochemical Performance of La-Site-Doped Li6La3Zr0.5Nb0.5Ta0.5Hf0.5O12 High-Entropy Garnets

We investigate La-site substitution in the high-entropy garnet Li6La3Zr0.5Nb0.5Ta0.5Hf0.5O12 (LLZNTH) using Ba2+, Sr2+, and Sm3+ to elucidate how dopant governs phase stability, Li-site distribution, and electrochemical behavior. X-ray diffraction shows that Sr2+ is incorporated homogeneously into the garnet lattice, whereas the larger Ba2+ and smaller Sm3+ ions partially exceed the structural tolerance, generating secondary phases. Nevertheless, the Sm-doped composition (x = 0.05) exhibits the highest room-temperature ionic conductivity (2.7 × 10–4 S cm–1). Neutron powder diffraction reveals that Sm substitution drives a redistribution of Li+ from the tetrahedral 24 d sites into the higher-mobility 96 h positions, enhancing the connectivity of the three-dimensional Li-ion migration network. A Sm-doping series (x = 0.01–0.05) further shows that only sufficiently high Sm levels induce this redistribution, whereas lower concentrations retain Li arrangements similar to the undoped garnet. Critical current density measurements demonstrate that La-site dopants also influence interfacial stability against Li metal, underscoring a trade-off between bulk transport enhancement and mechanical robustness. Collectively, these findings reveal that in high-entropy garnets improved ionic conductivity can originate not only from phase-pure structures but also from targeted modification of the Li sublattice, even when accompanied by secondary phases, offering a compositional design principle for garnet electrolytes.

Li, Chang [Mechanical Engineering, School of Scien↗

DOE OSTI2026

Eddy Covariance Theory: A Review

Eddy covariance (EC), the gold standard for measuring ecosystem scale gas and heat exchanges, has transformed our understanding of the breathing of the biosphere, and thus global change biology. Despite numerous methodological improvements and insights gained from the technique, the community faces persistent challenges that have been present since the first EC measurements. Here, we review the theoretical developments underpinning EC. We present theoretical developments in four important areas that have relevance to EC measurements of the net ecosystem exchanges (NEE) of gases and heat from a single tower: (i) measuring the total vertical flux density, (ii) flux attenuation, (iii) coordinate rotations, and (iv) energy balance closure. Persistent problems with EC measurements, such as the inability to close the energy budget, led us to identify two priorities for revisiting the theory underlying: (i) sensible heat flux calculations, and (ii) constraining the mean vertical wind velocity. We present a framework for improved calculation of sensible heat flux derived from first principles of fluid mechanics and thermodynamics that considers coupled heat and mass transfer so that conservation of both is obeyed. These refinements are motivated by the need for unbiased measurements of energy and mass transfer between the land surface and atmosphere for ecosystem research and to validate satellite observations and land surface models.

ecosystem fluxes↗

DOE OSTI2025

High‐Performance Rechargeable Lithium‐Chlorine Batteries with ALD Conformal Starburst Porous Graphene Positive Electrodes

Abstract Rechargeable alkali metal‐chlorine batteries are emerging as a promising high‐energy‐density solution. However, they confront significant challenges, including the primary issue stemming from the weak binding affinity of cathode materials for Cl 2 , which leads to a sluggish and inadequate supply of Cl 2 during the redox reactions, resulting in a shortened cycle life and low Coulombic efficiency (CE), particularly when operating at ultrahigh specific capacity outputs. Herein, an Al 2 O 3 ‐skinned heterostructured starburst porous graphene with conformal metasurfaces (Al 2 O 3 @rGO) is reported, crafted from a hierarchical porous starburst graphene arranged in a unique layered structure by the PTFE microemulsion skin effect, leveraging subsequent fluidized bed atomic layer deposition (FBALD) of Al 2 O 3 groups. Al 2 O 3 @rGO features superhydrophilicity, effective adsorption, fast kinetics from stable dynamic respiratory interface, high electrical and thermal conductivity anisotropy, intelligent thermal management and safe operation over a wide temperature range. Consequently, the Li‐Cl 2 @Al 2 O 3 @rGO battery achieves an ultrahigh discharge specific capacity of 5000 mAh g −1 at ≈100% CE, and even delivers stable cycling over 200 cycles with 2000 mAh g −1 at an average CE of 99.8% under low temperature environment of ‐40 °C. The scalable heterostructure approach offers a sustainable perspective of the development of functionalized metamaterials and metasurfaces for next‐generation safe and energy‐dense batteries and broader applications.

Chemistry↗

DOE OSTI2026

Graphitization of banana peel – synergistic effect of Ca and other elements of the biomass on carbon structure transformation

Recently, growing interest has been observed in using calcium as an effective catalyst for graphitizing disordered carbon materials derived from biomass and bioprecursors, such as cellulose and lignin, at relatively low tem peratures (<2000 °C). Herein, it is demonstrated that in the presence of elements such as calcium, silicon, sulfur, and potassium, which are abundant in banana peel composed of cellulose and lignin base, graphitization occurs much more effectively. The addition of external calcium source, in the form of calcium carbonate, to the banana peel-derived carbon and heat-treatment of the mixture under protective atmosphere up to 1750 °C results in a significant increase in the degree of the graphitization order and local formation of graphite crystals, whereas the same preparation and heat-treatment procedure applied to carbon material derived from pristine cellulose does not lead to such effective graphitization. It is indicated that the graphitization of banana peel carbon occurs due to the synergistic effect of the external Ca-based catalyst and the internal elements present in the raw biomass, supporting the transformation of the disordered graphene-like layers into graphitic structures. These findings are important for the future production of green graphite from biomass

09 BIOMASS FUELS↗

DOE OSTI2026

Assembly and Testing of Scintillator Tile Modules for the CMS High-Granularity Calorimeter Upgrade

The High-Granularity Calorimeter (HGCAL), part of the upgrade to the Compact Muon Solenoid (CMS) experiment, employs silicon and scintillator tile modules in the endcaps to maintain detector performance during the High-Luminosity Large Hadron Collider (HL-LHC) era, scheduled to operate from 2030 to 2040. The upgraded calorimeter will provide highly segmented three-dimensional imaging, energy measurements, and precise timing for particle shower reconstruction. Approximately half of the HGCal plastic scintillator tile modules (1,834 total) will be assembled at Fermilab using an automated pick-and-place (PnP) machine. Following assembly, each tile module undergoes quality control (QC) procedures such as electrical validation, thermal testing, and physics validation using cosmic rays. This poster/talk presents the QC procedures and results from the tile module production in 2026, demonstrating the performance and quality of the assembled tile modules.

Bazimya, Jean Luc [Grambling State U.]↗

DOE OSTI2025

Detection of visible-wavelength aurora on Mars

Mars hosts various auroral processes despite the planet’s tenuous atmosphere and lack of a global magnetic field. To date, all aurora observations have been at ultraviolet wavelengths from orbit. We describe the discovery of green visible-wavelength aurora, originating from the atomic oxygen line at 557.7 nanometers, detected with the SuperCam and Mastcam-Z instruments on the Mars 2020 Perseverance rover. Near–real-time simulations of a Mars-directed coronal mass ejection (CME) provided sufficient lead-time to schedule an observation with the rover. The emission was observed 3 days after the CME eruption, suggesting that the aurora was induced by particles accelerated by the moving shock front. To our knowledge, detection of aurora from a planetary surface other than Earth has never been reported, nor has visible aurora been observed at Mars. This detection demonstrates that auroral forecasting at Mars is possible, and that during events with higher particle precipitation, or under less dusty atmospheric conditions, aurorae will be visible to future astronauts.

Science & Technology - Other Topics↗

DOE OSTI2026

Design Trade-Offs in Composite Fuel Cell Membranes: Effects of Reinforcement and Chemical Additives

Perfluorosulfonic acid (PFSA) membranes are critical components in proton exchange membrane fuel cells, where performance depends on balancing ionic conductivity, mechanical durability, and chemical stability. This study characterizes a composite membrane (NC700) featuring PFSA-impregnated expanded polytetrafluoroethylene (ePTFE) reinforcement and cerium-based radical scavengers, benchmarked against unreinforced NR211. Complementary techniques, including electron microscopy, X-ray scattering, infrared spectroscopy, thermogravimetric analysis, and dynamic mechanical analysis, identify the structural and compositional strategies employed in NC700. Water sorption isotherms reveal lower water uptake for NC700 across all conditions, attributed to reinforcement and cerium incorporation. Reinforcement reduces in-plane swelling from 11% to 2.1% at 90% RH, confirming strong swelling anisotropy, while maintaining mechanical properties at elevated temperatures. While the ionic conductivity of NC700 is approximately 10% lower than that of NR211, the reduced thickness yields a 40% decrease in calculated area-specific resistance, suggesting the composite architecture can favorably shift the conductivity-stability trade-off. The composite structure also reduces gas permeability, indicating potential for improved separator function alongside favorable transport properties. Systematic deconvolution of reinforcement and additive contributions shows that conductivity losses from cerium incorporation are largely offset by gains from the lower equivalent-weight polymer, providing quantitative relationships that may guide composite membrane design for fuel cells and other electrochemical applications.

25 ENERGY STORAGE↗

DOE OSTI2026

Improving the Performance of NEML2 with Modern Graph Compilation Backends

NEML2 vectorizes constitutive-model evaluation for large-scale multiphysics simulation, using PyTorch as its tensor backend so that a batch of material-point updates runs on CPU or GPU through a single implementation. In the two prior reports in this series it was a C++-native library, deployed through TorchScript tracing and just-in-time (JIT) compilation; it has since been rewritten from the ground up into a Python-native library deployed through Ahead-of-Time Inductor (AOTInductor), a modern PyTorch graph-compilation backend. The rewrite is driven by a persistent tension, not a language preference: NEML2 composes constitutive models at runtime from a registry of small, independently-authored pieces, and that flexibility is difficult to reconcile with the compile-time knowledge an efficient GPU kernel needs. This report documents the rewrite and the investment that accompanied it: the AOTInductor export pipeline that turns a Python-authored model into a portable, Python-free compiled artifact loadable from pure C++; the eager and compiled runtimes and the new implicit solver layer built on them; a head-to-head benchmark of legacy JIT against AOTInductor; the physics-model catalog and its worked examples; the developer tooling; and the corresponding overhaul of MOOSE’s NEML2 integration that lets MOOSE consume it. A central objective is to examine whether modern PyTorch graph-compilation backends are effective for MOOSE GPU integration. The benchmark answers directly: AOTInductor outperforms legacy JIT on every GPU scenario measured, by 1.0–4.5×. Modern graph-compilation backends are effective for MOOSE GPU integration, and AOTInductor specifically – not compilation in the abstract – is why.

Hu, Gary (Tianchen) [Argonne National Laboratory (↗

DOE OSTI2026

Deep Learning and Photogrammetric Reconstruction for Automated Crack Detection and Dimensional Measurement in Mining Operations

Surface crack detection and dimensional measurement at active mining sites present significant safety and operational challenges. Manual inspection methods are labor-intensive, spatially incomplete, and expose personnel to hazardous environments, while existing automated approaches have been developed primarily for concrete civil infrastructure and have not been validated on the complex, variable surfaces characteristic of mining environments. This dissertation presents an automated pipeline that integrates deep learning semantic segmentation with Structure-from-Motion photogrammetry to detect surface cracks and measure their aperture, length, and vertical displacement from standard RGB imagery acquired during routine Uncrewed Aerial Vehicle (UAV) survey operations, without requiring additional sensor hardware or manual measurement. The pipeline combines a U-Net architecture with an EfficientNet-B0 encoder, pretrained on the SDNET2018 concrete crack dataset and fine-tuned on a mining-specific dataset spanning laboratory concrete specimens, coal refuse impoundment embankments, and post-blast limestone quarry benches. Photogrammetric reconstruction is performed using COLMAP Structure-from-Motion and Multi-View Stereo, with crack segmentation masks projected into the reconstructed point cloud to enable three-dimensional vertical displacement measurement through local plane fitting and bimodal surface detection. The pipeline was validated across 36 controlled laboratory specimens at three imaging distances and four vertical displacement levels, achieving aperture measurement RMSE of 0.047 cm and R² of 0.954, and vertical displacement RMSE of 0.140 cm and R² of 0.966, against independent caliper measurements. Field application at a coal refuse impoundment in southwestern Pennsylvania detected 71 crack components across the embankment crest, with a dominant longitudinal crack exhibiting aperture values reaching 28 cm and a 95th percentile vertical displacement of 35.53 cm, consistent in magnitude and spatial distribution with simultaneously acquired LiDAR-derived estimates. Application across four post-blast limestone quarry bench datasets in California successfully characterized blast-induced fracture networks at ground sampling distances ranging from 0.59 to 1.23 cm/pixel, with detected crack geometries physically consistent with observable surface conditions at each site. The results demonstrate that deep learning-based crack detection and photogrammetric measurement can be integrated into routine UAV inspection workflows at mining sites, providing repeatable, scalable, and quantitative crack characterization across surface types, crack scales, and displacement magnitudes not previously addressed in the literature. The pipeline requires no dedicated surveying equipment beyond the UAV platforms already deployed at mine sites for survey and monitoring purposes, supporting practical adoption within existing operational workflows.

Crack detection, Dimensional Measurement↗

DOE OSTI2026

Weak localization and universal conductance fluctuations in large-area twisted bilayer graphene

We study diffusive magnetotransport in highly 𝑝-doped large-area twisted bilayer graphene in 1∘, 7∘, 9∘, and 20∘ samples. All samples exhibit weak localization, from which we extract the phase coherence length and intervalley scattering lengths, and from that determine that dephasing is caused by electron-electron scattering and intervalley scattering is caused by point defects. We observe signatures of universal conductance fluctuations in the 9∘ sample, which has high mobility and is near the van Hove singularity. Further improvements in sample quality and applications to large-area moiré materials will open new avenues to observe quantum interference effects.

Talkington, Spenser [University of Pennsylvania]↗

DOE OSTI2026

Aragonite saturation horizon variability along North Pacific seamounts and implications for deep-sea coral reefs

The 2014 discovery of living deep-sea coral reefs along the Northwest Hawaiian Islands (NWHI) and lower Emperor Seamount Chain (ESC), despite the North Pacific’s shallow aragonite saturation horizon (ASH) and high CaCO3 dissolution rates, underscores the need to understand the local seawater chemistry that allows these reefs to persist. We investigated seawater carbonate chemistry using discrete samples along the NWHI and ESC from two cruises ~1 year apart (08/26/21 – 09/26/21, 09/09/22 – 10/24/22). Across the two cruises, ASH depth difference ranged from 15 to 77 m. Since the Pacific ASH shoals by 1–2 m yr?¹, this long-term trend cannot explain the magnitude of ASH change observed between cruises. Temperature-salinity plots similarly indicate no major shifts in intermediate water masses that could account for these changes. Instead, ASH depth variability was primarily governed by localized biogeochemical processes, namely changes in intermediate water respiration and CaCO3 dissolution. Indicators for dissolution (TA*) and respiration (AOU) suggest changes in ASH depth were driven by changes in dissolution at the northern- and southern-most sites, whereas respiration exerted stronger control at central sites. Combining 2021 and 2022 data with data from 2014 – 2019 (excluding 2018) revealed high interannual ASH variability, by as much as >200 m at one site. Deep-sea coral reefs across the NWHI and ESC currently reside close to the ASH depth and likely experience seasonal and interannual shifts between under- and supersaturation. As ocean acidification progresses however, persistent exposure to undersaturated seawater could further threaten these critical deep-sea ecosystems.

coral reefs↗

DOE OSTI2023

Host galaxies of ultra-strong Mg ii absorbers at z ∼ 0.7

ABSTRACT We report spectroscopic identification of the host galaxies of 18 ultra-strong Mg ii systems (USMg ii) at 0.6 ≤ z ≤ 0.8. We created the largest sample by merging these with 20 host galaxies from our previous survey within 0.4 ≤ z ≤ 0.6. Using this sample, we confirm that the measured impact parameters ($\rm 6.3\leqslant D[kpc] \leqslant 120$ with a median of 19 kpc) are much larger than expected, and the USMg ii host galaxies do not follow the canonical $\rm {\it W}_{2796}-{\it D}$ anticorrelation. We show that the presence and significance of this anticorrelation may depend on the sample selection. The $\rm {\it W}_{2796}-{\it D}$ anticorrelation seen for the general Mg ii absorbers show a mild evolution at low $\rm W_{2796}$ end over the redshift range 0.4 ≤ z ≤ 1.5 with an increase of the impact parameters. Compared to the host galaxies of normal Mg ii absorbers, USMg ii host galaxies are brighter and more massive for a given impact parameter. While the USMg ii systems preferentially pick star-forming galaxies, they exhibit slightly lower ongoing star-forming rates compared to main sequence galaxies with the same stellar mass, suggesting a transition from star-forming to quiescent states. For a limiting magnitude of mr < 23.6, at least 29 per cent of the USMg ii host galaxies are isolated, and the width of the Mg ii absorption in these cases may originate from gas flows (infall/outflow) in isolated haloes of massive star forming but not starbursting galaxies. We associate more than one galaxy with the absorber in $\ge 21~{{\ \rm per\ cent}}$ cases, where interactions may cause wide velocity spread.

Astronomy & Astrophysics↗

DOE OSTI2026

Catalytic disproportionation on carbon superstructures enables long-life, high-loading Li–S batteries

Electrocatalysis has been widely explored as an effective strategy to accelerate polysulfide (PS) conversion and suppress the shuttle effect in lithium–sulfur (Li–S) batteries. However, the underlying mechanisms remain elusive, and electrocatalytic reactions are inactive during cell resting. In this work, we reveal and quantitatively analyze a previously unrecognized sulfur reduction route (SRR) driven by catalytic disproportionation at the carbon cathode surface—fundamentally distinct from conventional electrocatalysis. Unlike conventional stepwise pathways, this SRR enables high-order polysulfides (Sₓ²⁻, x = 5–8) to directly convert into S₈ and Li₂S₂, bypassing low-order intermediates. This sulfur-reduction shortcut is systematically elucidated through high-performance liquid chromatography, revealing the intrinsic catalytic contribution of carbon frameworks and the dynamic evolution of PS species. We demonstrate that carbon superstructures (CSS-0.5), assembled from nanosheet subunits with abundant N/O functionalities and interconnected charge-migration channels, synergistically promote this catalytic process. Benefiting from these features, CSS-0.5 delivers superior electrochemical performance under practical conditions, enabling high sulfur loading (6.0 mg cm⁻²) pouch cells with 80.5% capacity retention over 210 cycles. This study provides the first quantitative evidence of electrocatalytic disproportionation in Li–S batteries, offering mechanistic insights and design principles for advanced sulfur cathodes.

25 ENERGY STORAGE↗

DOE OSTI2026

Joint scheduling of energy, fast and primary frequency response reserves in integrated transmission–distribution networks

Inverter-based distributed energy resources (DERs) connected to distribution networks (DNs) can provide fast frequency support, but their reserve deliverability depends on feeder constraints and differs from synchronous primary frequency response (PFR). Existing transmission–distribution coordination studies usually treat reserve generically or neglect feeder-level feasibility, while frequency-security scheduling studies rarely represent distribution feeders explicitly. This paper develops a bi-level day-ahead scheduling framework for integrated transmission–distribution networks that jointly clears energy, transmission-side PFR, and distribution-side fast frequency response (FFR) under exogenous hourly inertia and largest-loss inputs from an external unit commitment (UC) schedule. The transmission problem is modeled with DC-optimal power flow (OPF) and closed-form second-order cone (SOC) frequency-security constraints, whereas each DN is represented by a reserve-aware branch-flow AC-OPF so that scheduled fast reserves remain deliverable during activation. The bi-level problem is reformulated through Karush–Kuhn–Tucker (KKT) conditions into a mixed-integer SOC program, and a penalty term is used to tighten the distribution-network relaxation. In the reduced test system, lower exogenous inertia increased the required primary response from 179.64 MW to 191.08 MW, distribution-side fast response reduced total frequency-response procurement by up to 4.9%, and neglecting distribution constraints overstated the combined distribution-side energy and reserve award by up to 18%. In the expanded study, the largest case was solved in 2.02 s with a 0.00% optimality gap. Time-domain simulations kept the frequency nadir above 59.0 Hz in all tested hours. These results demonstrate the value of fast-response modeling and distribution-feasible reserve delivery in coordinated market clearing.

Noh, Seung-Gil↗

DOE OSTI2026

Dimensional Reduction for Sampled Priors and Application to Photometric Redshift Distributions

A typical Bayesian inference on the values of some parameters of interest q from some data D involves running a Markov Chain (MC) to sample from the posterior $p$($q$,$n$|$D$) $\propto$ $\mathcal{L}$($D$|$q$,$n$)$p$(q)$p$($n$), where n are some nuisance parameters with a separable prior. In some cases, the nuisance parameters are high-dimensional, and their prior p(n) is itself defined only by a set of samples that have been drawn from some other MC. The MC for the posterior will typically require evaluation of p(n) at arbitrary values of n, i.e., one needs to provide a density estimator over the full n space from the provided samples. But the high dimensionality of n hinders both the density estimation and the efficiency of the MC for the posterior. We describe a solution to this problem: a linear compression of the n space into a much lower-dimensional space u, which projects away directions in n space that cannot appreciably alter $\mathcal{L}$. The algorithm for doing so is a slight modification to principal components analysis, and is less restrictive on p(n) than other proposed solutions to this issue. We demonstrate this “mode projection” technique using the analysis of 2-point correlation functions of weak lensing fields and galaxy density in the Dark Energy Survey, where n is a binned representation of the redshift distribution n(z) of the galaxies.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2026

Biochar–polymer composites for 3D printing: a review

Biochar, a bio-based co-product of biofuel production via thermochemical conversion, holds potential as a filler for polymer composites to reduce costs, improve thermomechanical properties, and aid in environmental remediation. 3D-printed biochar composites have received growing interest over the past few years but have experienced difficulties such as poor layer adhesion and nozzle clogging. Currently, no literature review examines 3D-printed biochar composites and related biochar properties in-depth. This work summarizes and discusses recent studies on 3D-printed polymer and biochar composites and examines their mechanical, thermal, and additional properties that result from each study. Technical challenges in printability, such as nozzle clogging from particle size and biochar aggregation, are also discussed. Furthermore, this work discusses the variability of biochar properties resulting from the pyrolysis conditions and feedstock choice in relation to potential 3D printing outcomes. In particular, several studies reported that high lignin feedstocks could be candidates for 3D printing. The post-processing approaches of the biochar via physical and chemical methods are also introduced. Ball milling appears to hold the most promise for physical treatments due to its tunability of particle size, surface area, and functional groups, while chemical treatments with acids or alkalis are used to tailor biochar porosity and wettability. Overall, it was determined that future research needs to be done relating biochar production and post-processing methods to resulting 3D printing parameters as the number of studies is limited.

Day, Rachel [Auburn University, Auburn, AL]↗

DOE OSTI2024

Derivation of low-energy Hamiltonians for heavy-fermion materials

Here, by utilizing a multiorbital periodic Anderson model with parameters obtained from ab initio band structure calculations, combined with degenerate perturbation theory, we derive effective Kondo-Heisenberg and spin Hamiltonians that capture the interaction among the effective magnetic moments. This derivation encompasses fluctuations via both nonmagnetic 4⁢𝑓 0 and magnetic 4⁢𝑓 2 virtual states, and its accuracy is confirmed through comparison with experimental data obtained from CeIn 3 . The significant agreement observed between experimental results and theoretical predictions underscores the potential of deriving minimal models from first-principles calculations for achieving a quantitative description of 4⁢𝑓 materials. Moreover, our microscopic derivation unveils the underlying origin of anisotropy in the exchange interaction between Kramers doublets, shedding light on the conditions under which this anisotropy may be weak compared to the isotropic contribution.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗