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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 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Spin-phonon dispersion in magnetic materials

Microscopic coupling between the electron spin and the lattice vibration is responsible for an array of exotic properties from morphic effects in simple non magnets to magnetodielectric coupling in multiferroic spinels and hematites. Traditionally, a single spin–phonon coupling constant is used to characterize how effectively the lattice can affect the spin, but it is hardly enough to capture novel electromagnetic behaviors to the full extent. Here, we introduce a concept of spin–phonon dispersion to project the spin moment change along the phonon crystal momentum direction, so the entire spin change can be mapped out. Different from the phonon dispersion, the spin–phonon dispersion has both positive and negative frequency branches even in the equilibrium ground state, which correspond to the spin enhancement and spin reduction, respectively. Our study of bcc Fe and hcp Co reveals that the spin force matrix, that is, the second-order spatial derivative of spin moment, is similar to the vibrational force matrix, but its diagonal elements are smaller than the off-diagonal ones. This leads to the distinctive spin–phonon dispersion. Furthermore, the concept of spin–phonon dispersion expands the traditional Elliott-Yafet theory in nonmagnetic materials to the entire Brillouin zone in magnetic materials, thus opening the door to excited states in systems such as CoF 2 and NiO, where a strong spin-lattice coupling is detected in the THz regime.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Dynamic Shaping of Grid Response of Multi-Machine Multi-Inverter Systems Through Grid-Forming IBRs: Preprint

We consider the problem of controlling the frequency response of weakly-coupled multi-machine multi-inverter low-inertia power systems via grid-forming inverter-based resources (IBRs). In contrast to existing methods, our approach relies on dividing the larger system into multiple strongly-coupled subsystems, without ignoring either the underlying network or approximating the subsystem response as an aggregate harmonic mean model. Rather, through a structured clustering and recursive dynamic shaping approach, the frequency response of the overall system to load perturbations is shaped appropriately. We demonstrate the proposed approach for a three-node triangular configuration and a small-scale radial network. Furthermore, for small-scale radial microgrids, we demonstrate the ability of IBRs to tune the effective transfer functions of synchronous machines. This enables us to relax the uniform turbine time-constant assumptions and widen the scope of existing synchronization results for proportionally heterogeneous machines.

frequency-shaping control↗
DOE OSTI2026

Comparative Evaluation of Spectral Methods for Robust Reactor Noise Estimation

Reactor noise analysis provides a noninvasive means to determine neutron kinetic parameters from stochastic fluctuations in detector signals. However, standard cross-power spectral density (CPSD) analyses can be sensitive to numerical processing choices, which may introduce processing-dependent systematic shifts in estimates of the prompt neutron decay constant (α) and limit reproducibility. This study uses a hybrid multitaper–Welch spectral estimator to analyze subcritical noise measurements from a fast-spectrum critical assembly. The decay constant α was extracted using three frequency-domain methods: the CPSD, the magnitude-squared coherence (MSC), and the generalized magnitude-squared coherence (GMSC). These coherence-based estimators normalize detector auto-spectral structure and are expected to reduce the sensitivity of fitted α values to processing parameters. A Sobol global sensitivity analysis identified which numerical inputs most strongly influence the fitted values of α. All estimators produced a linear dependence of α on inverse count rate, with delayed-critical extrapolations near 1.7 × 10 4 s −1 , in agreement within 8% of MCNP6.3 KOPTS benchmark calculations. Sensitivity results show that while the CPSD depends on both time-bin width and taper selection, the MSC and GMSC are dominated by time-bin width alone, indicating reduced parameter coupling and greater robustness to processing variability. These findings demonstrate the feasibility and practical value of coherence-based spectral estimators for extracting α from reactor noise and support their broader application to multi-detector and irregular datasets in subcritical system characterization.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2023

Magnetic coupling between Fe(NO) spin probe ligands through diamagnetic Ni II , Pd II and Pt II tetrathiolate bridges

Reaction of the nitrosylated-iron metallodithiolate ligand, paramagnetic (NO)Fe(N 2 S 2 ), with [M(CH 3 CN) n ][BF 4 ] 2 salts (M = Ni II , Pd II , and Pt II ; n = 4 or 6) affords di-radical tri-metallic complexes in a stairstep type arrangement ([FeMFe] 2+ , M = Ni, Pd, and Pt), with the central group 10 metal held in a MS 4 square plane. These isostructural compounds have nearly identical ν(NO) stretching values, isomer shifts, and electrochemical properties, but vary in their magnetic properties. Despite the intramolecular Fe∙∙∙Fe distances of ca. 6 Å, antiferromagnetic coupling is observed between {Fe(NO)} 7 units as established by magnetic susceptibility, EPR, and DFT studies. The superexchange interaction through the thiolate sulfur and central metal atoms is on the order of Ni II < Pd II $\ll$ Pt II with exchange coupling constants (J) of -3, -23, and -124 cm -1 , consistent with increased covalency of the M–S bonds (3d < 4d < 5d). This trend is reproduced by DFT calculations with molecular orbital analysis providing insight into the origin of the enhancement in the exchange interaction. Specifically, the magnitude of the exchange interaction correlates surprisingly well with the energy difference between the HOMO and HOMO-1 orbitals of the triplet states, which is reflected in the central metal's contribution to these orbitals. These results demonstrate the ability of sulfur-dense metallodithiolate ligands to engender strong magnetic communication by virtue of their enhanced covalency and polarizability.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Electric charging effects on insulating surfaces in cryogenic liquids

Here, this paper presents a new technique to study the adsorption and desorption of ions and electrons on insulating surfaces in the presence of strong electric fields in cryoliquids. The experimental design consists of a compact cryostat coupled with a sensitive electro-optical Kerr device to monitor the stability of the electric fields. The behavior of nitrogen and helium ions on a poly(methyl methacrylate) (PMMA) surface was compared to a PMMA surface coated with a mixture of deuterated polystyrene and deuterated polybutadiene. Ion accumulation and removal on these surfaces were unambiguously observed. Within the precision of the data, both surfaces behave similarly for the physisorbed ions. The setup was also used to measure the (quasi-)static dielectric constant of PMMA at T ≈ 70 K. The impact of the ion adsorption on the search for a neutron permanent electric dipole moment in a cryogenic environment, such as the nEDM@SNS experiment, is discussed.

Cryogenics↗
NASA NTRS1993

Can weak crust explain the correlation of geoid and topography on Venus?

The effect on geoid and topography of low viscosity crust overlying a steady-state convecting mantle is estimated under the assumption that the shear between crust and mantle does not alter the mantle flow. The weak crustal layer can change the sign of the geoid to topography ratio (admittance). The positive long wavelength admittance for Venus is consistent with a weak crust overlying a mantle with a viscosity that increases strongly with depth. The accepted interpretation of the strong positive correlation of geoid and topography on Venus, is that the convecting mantle of Venus has a constant viscosity with depth. Topography results from vertical normal stresses caused by mantle convection and highlands occur where mantle upwells. For topography to be supported by normal stress, the time scale for crustal flow must be long compared to the time scale for changes in the pattern of mantle flow. Because the high surface temperature of Venus may cause the crust to have a low viscosity, this assumption may be false. Topography should then be dominated by shear coupling between the crust and mantle. In the absence of a crustal layer, convection in a constant viscosity layer gives rise to a geoid anomaly that correlates positively with surface topography. When the viscosity in the layer increases with depth by several orders of magnitude, the surface topography and geoid anomaly become anti-correlated.

Buck, W. Roger↗
DOE OSTI2024

Photoinduced Magnetic Exchange-Jump Promotes Ground State Biradical Electron Spin Polarization

Photoinduced electron spin polarization (ESP) is reported in the electronic ground states of three Pt(II) complexes that are comprised of two S = ½ nitronyl nitroxide (NN) radicals attached through different length para-phenylethynyl bridges to the 3,6 positions of a catecholate (CAT, donor) and 4,4’-di-tert-butyl-2,2’-bipyridine (bpy, acceptor). Complexes 1-3 have from 17 to 41 bonds separating NN radicals, and display cw-EPR spectra consistent with |J NN-NN | >> |a N |, |J NN-NN | ≥ |a N |, and |J NN-NN | < |a N |, respectively, where J NN-NN is the magnetic exchange coupling between NN radicals in the electronic ground state, and a N is the isotropic 14 N hyperfine coupling constant. Light-induced transient EPR spectra characterized as enhanced ground-state absorption were observed for all three complexes using 532 nm pulsed laser excitation into the ligand-to-ligand charge transfer (LL’CT) band of the (CAT)Pt(bpy) chromophore. The magnitude of the observed ESP increases in the order 1 < 2 < 3 and is inversely correlated with the magnitude of ground-state J NN-NN . In addition to the experimental observation net absorptive polarization in 1-3, light excitation also produces multiplet polarization in 2. Since the weak dipolar coupling leads to strong spectral overlap of the absorptive and emissive components, the multiplet polarization is not observed in 1 and 3 and is very weak in 2. Here, the ability to spin polarize multiple radical spins with a single photon is anticipated to advance new photoinduced multi qubit/qudit ESP protocols for quantum information science applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1991

Static and dynamical Meissner force fields

The coupling between copper-based high temperature superconductors (HTS) and magnets is represented by a force field. Zero-field cooled experiments were performed with several forms of superconductors: 1) cold-pressed sintered cylindrical disks; 2) small particles fixed in epoxy polymers; and 3) small particles suspended in hydrocarbon waxes. Using magnets with axial field symmetries, direct spatial force measurements in the range of 0.1 to 10(exp 4) dynes were performed with an analytical balance and force constants were obtained from mechanical vibrational resonances. Force constants increase dramatically with decreasing spatial displacement. The force field displays a strong temperature dependence between 20 and 90 K and decreases exponentially with increasing distance of separation. Distinct slope changes suggest the presence of B-field and temperature-activated processes that define the forces. Hysteresis measurements indicated that the magnitude of force scales roughly with the volume fraction of HTS in composite structures. Thus, the net force resulting from the field interaction appears to arise from regions as small or smaller than the grain size and does not depend on contiguous electron transport over large areas. Results of these experiments are discussed.

Weinberger, B. R.↗
NASA NTRS2000

Langmuir Probe Measurements of Inductively Coupled CHF3/Ar and Ar/CHF3/O2 Plasmas

Plasma parameters, such as, electron number density (ne), electron temperature (Te), y electron energy distribution function (EEDF), mean electron energy (Ee), ion number density (ni), and plasma potential (Vp), have been measured by using Langmuir probe in low-pressure (10-50 mTorr) inductively coupled CHF3/Ar and CHF3/Ar/O2 plasmas generated in the GEC cell. The measurements were made at the center of the plasma, keeping the lower electrode grounded, for various CHF3/Ar and Ar/CHF3/O2 mixtures operating at 10-50 mTorr pressures and two input RF power levels, 200 and 300 W. EEDF data show a strong Druyvesteyn distribution with relatively lower number of low energy electrons as compared to a Maxwell distribution and a large electron population with energies higher than the plasma potential. The results further show that at low CHF3 concentrations (less than 50%) the electron number density remains nearly constant with increase in pressure. At higher CHF3 concentrations, however, it decreases with increase in pressure. Plasma potential and electron temperature increase with decrease in pressure and with increase in CHF3 concentration. An analysis of the above observations and mechanisms will be presented.

Sharma, S. P.↗
NASA NTRS2007

Does Aerosol Weaken or Strengthen the South Asian Monsoon?

Aerosols are known to have the ability to block off solar radiation reaching the earth surface, causing it to cool - the so-called solar dimming (SDM) effect. In the Asian monsoon region, the SDM effect by aerosol can produce differential cooling at the surface reducing the meridional thermal contrast between land and ocean, leading to a weakening of the monsoon (Ramanathan et al. 2005). On the other hand, absorbing aerosols such as black carbon and dust, when forced up against the steep slopes of the southern Tibetan Plateau can produce upper tropospheric heating, and induce convection-dynamic feedback leading to an advance of the rainy season over northern India and an enhancement of the South Asian monsoon through the "Elevated Heat Pump" (EHP) effect (Lau et al. 2006). In this paper, we present modeling results showing that in a coupled ocean-atmosphere-land system in which concentrations of greenhouse gases are kept constant, the response of the South Asian monsoon to dust and black carbon forcing is the net result of the two opposing effects of SDM and EHP. For the South Asian monsoon, if the increasing upper tropospheric thermal contrast between the Tibetan Plateau and region to the south spurred by the EHP overwhelms the reduction in surface temperature contrast due to SDM, the monsoon strengthens. Otherwise, the monsoon weakens. Preliminary observations are consistent with the above findings. We find that the two effects are strongly scale dependent. On interannual and shorter time scales, the EHP effect appears to dominate in the early summer season (May-June). On decadal or longer time scales, the SDM dominates for the mature monsoon (July-August). Better understanding the physical mechanisms underlying the SDM and the EHP effects, the local emission and transport of aerosols from surrounding deserts and arid-regions, and their interaction with monsoon water cycle dynamics are important in providing better prediction and assessment of climate change impacts on precipitation of the Asian monsoon land regions.

Lau, William K. M.↗
NASA NTRS2010

Does Aerosol Weaken or Strengthen the South Asian Monsoon?

Aerosols are known to have the ability to block off solar radiation reaching the earth surface, causing it to cool - the so-called solar dimming (SDM) effect. In the Asian monsoon region, the SDM effect by aerosol can produce differential cooling at the surface reducing the meridional thermal contrast between land and ocean, leading to a weakening of the monsoon. On the other hand, absorbing aerosols such as black carbon and dust, when forced up against the steep slopes of the southern Tibetan Plateau can produce upper tropospheric heating, and induce convection-dynamic feedback leading to an advance of the rainy season over northern India and an enhancement of the South Asian monsoon through the "Elevated Heat Pump" (EHP) effect. In this paper, we present modeling results showing that in a coupled ocean-atmosphere-land system in which concentrations of greenhouse gases are kept constant, the response of the South Asian monsoon to dust and black carbon forcing is the net result of the two opposing effects of SDM and EHP. For the South Asian monsoon, if the increasing upper tropospheric thermal contrast between the Tibetan Plateau and region to the south spurred by the EHP overwhelms the reduction in surface temperature contrast due to SDM, the monsoon strengthens. Otherwise, the monsoon weakens. Preliminary observations are consistent with the above findings. We find that the two effects are strongly scale dependent. On interannual and shorter time scales, the EHP effect appears to dominate in the early summer season (May-June). On decadal or longer time scales, the SDM dominates for the mature monsoon (July-August). Better understanding the physical mechanisms underlying the SDM and the EHP effects, the local emission and transport of aerosols from surrounding deserts and arid-regions, and their interaction with monsoon water cycle dynamics are important in providing better prediction and assessment of climate change impacts on precipitation of the Asian monsoon land regions.

Lau, William K.↗
DOE OSTI2026

The origin of metallic conductivity in Pt 3 O 4 : a first principles study

The platinum oxide Pt 3 O 4 exhibits metallic conductivity even though it contains square-planar PtO4 units, which in related oxides such as PtO are usually associated with insulating behavior. To identify the electronic origin of this anomalous metallicity, we performed a comprehensive first-principles study using the PBE and r 2 SCAN functionals together with Hubbard U corrections and spin-orbit coupling (SOC). Structural benchmarks show that r 2 SCAN with SOC and a moderate U value (<4 eV) reproduces the experimental lattice constants and formation enthalpy, whereas larger U values (~8 eV) destabilize the cubic structure. Across all functionals and U values considered in this work, Pt 3 O 4 remains metallic. Analyses of the projected density of states, band structures, charge-density isosurfaces, and bonding characteristics demonstrate that the dominant contribution to the metallic character originates from delocalized Pt–O–Pt hybridized antibonding states at the Fermi level. Direct Pt–Pt interactions are present but contribute less strongly to the conductivity. Bader charge analysis reveals only weak Pt charge disproportionation, consistent with mixed Pt II /Pt III character, and a small charge-transfer energy that prevents localization of the Pt 5d electrons even at elevated U. In contrast, PtO develops a Mott or charge-transfer gap under modest U despite having the same PtO 4 coordination environment. These findings demonstrate that persistent Pt–O–Pt covalency is the primary driver of metallicity in Pt 3 O 4 and support the view that this phase can remain conductive under oxygen reduction and oxygen evolution reaction conditions in fuel cell and electrolyzer environments.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Topological confinement in Skyrme holography

Abstract We study phase transitions in five-dimensional Einstein gravity with a negative cosmological constant, coupled to a Skyrme matter field. These transitions are topological generalizations of the Hawking–Page transition between thermal anti de Sitter (AdS) spacetime and an AdS black hole. Phases are characterized by a topological number associated with the Skyrme field configuration. Depending on that topological number and on the Skyrme coupling strength, there occur transitions between those phases at two, one, or no value(s) of the temperature. Through the holographic (AdS/CFT) correspondence, these solutions are dual to topologically non-trivial states in a conformal field theory with an SU (2)-symmetry, which support either confined or deconfined (quasi-)particles at strong coupling. We compare to similar known phase transitions, and discuss potential applications to confinement in topological phases of condensed matter and the quark–gluon plasma.

Astronomy & Astrophysics↗
DOE OSTI2022

Dynamical exponent of a quantum critical itinerant ferromagnet: A Monte Carlo study

Here we consider the effect of the coupling between two-dimensional (2D) quantum rotors near an XY ferromagnetic quantum critical point and spins of itinerant fermions. We analyze how this coupling affects the dynamics of rotors and the self-energy of fermions. A common belief is that near a q = 0 ferromagnetic transition, fermions induce an Ω/q Landau damping of rotors (i.e., the dynamical critical exponent is z = 3) and Landau overdamped rotors give rise to non-Fermi liquid fermionic self-energy Σ∝ω 2/3 . This behavior has been confirmed in previous quantum Monte Carlo (QMC) studies. Here we show that for the XY case the behavior is different. We report the results of large-scale quantum Monte Carlo simulations, which show that at small frequencies z = 2 and Σ∝ω 1/2 . We argue that the new behavior is associated with the fact that a fermionic spin is by itself not a conserved quantity due to spin-spin coupling to rotors, and a combination of self-energy and vertex corrections replaces 1/q in the Landau damping by a constant. We discuss the implication of these results to experiments.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Anisotropic magnetocaloric effect and critical behavior in CrSbSe3

In this work, we report anisotropic magnetocaloric effect and critical behavior in a quasi-one-dimensional ferromagnetic CrSbSe 3 single crystal. The maximum magnetic entropy change - Δ S M max is 2.16 J kg - 1 K - 1 for the easy a axis (2.03 J kg - 1 K - 1 for the hard b axis) and the relative cooling power RCP is 163.1 J kg - 1 for the easy a axis (142.1 J kg - 1 for the hard b axis) near T c with a magnetic field change of 50 kOe. The magnetocrystalline anisotropy constant K u is estimated to be 148.5 kJ m - 3 at 10 K, decreasing to 39.4 kJ m - 3 at 70 K. The rescaled Δ S M ( T , H ) curves along all three axes collapse onto a universal curve, respectively, confirming the second-order ferromagnetic transition. Further critical behavior analysis around T c ~ 70 K gives that the critical exponents β = 0.26 ( 1 ) , γ = 1.32 ( 2 ) , and δ = 6.17 ( 9 ) for H ∥ a , while β = 0.28 ( 2 ) , γ = 1.02 ( 1 ) , and δ = 4.14 ( 16 ) for H ∥ b . The determined critical exponents suggest that the anisotropic magnetic coupling in CrSbSe 3 is strongly dependent on orientations of the applied magnetic field.

2-dimensional systems↗
DOE OSTI2022

Gifts from anomalies: Exact results for Landau phase transitions in metals

Non-Fermi liquid phenomena arise naturally near critical points of Landau ordering transitions in metallic systems, where strong fluctuations of a bosonic order parameter destroy coherent quasiparticles. Despite progress in developing controlled perturbative techniques, much of the low energy physics of such metallic quantum critical points remains poorly understood. We demonstrate that exact, non-perburbative results can be obtained for both optical transport and static susceptibilities in “Hertz-Millis” theories of Fermi surfaces coupled to critical bosons. Such models possess a large emergent symmetry and anomaly structure, which we leverage to fix these quantities. In particular, we show that in the infrared limit, the boson self energy at zero wave vector, \mathbf{q}=0 𝐪 = 0 , is a constant independent of frequency, and the real part of the optical conductivity, \sigma(\omega) σ ( ω ) , is purely a delta function Drude peak with no other corrections. Therefore, further frequency dependence in the boson self energy or optical conductivity can only come from irrelevant operators in a clean system. Exact relations between Fermi liquid parameters as the critical point is approached from the disordered phase are also obtained. The absence of a universal, power law frequency dependence in the boson self energy contrasts with previous perturbative calculations, and we explain the origin of this difference.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

Machine Learning an Ab-Initio Based Bond-Order Potential for Bismuthene

Bismuthene is a heavy 2D material whose strong spin–orbit coupling and recently observed single-element ferroelectricity have intensified interest in its structural, vibrational, and transport properties. Accurate modeling of these behaviors requires a short-range interatomic potential that can reproduce the underlying bonding physics at a fraction of the computational cost of first-principles methods. However, such a potential is currently unavailable. Here, in this work, we construct a Tersoff bond-order potential for β-bismuthene using a reinforcement-learning framework that integrates a continuous Monte Carlo Tree Search with a simplex-based local optimizer. The optimized parameter sets reproduce first-principles lattice constants, cohesive energy, the equation of state, elastic constants, and phonon dispersion. We validate the models by performing thermal-conductivity calculations and uniaxial fracture simulations our findings confirm the reliability of the resulting models across multiple thermomechanical regimes. Comparison of the three best solutions reveals how differences in pairwise interactions, angular terms, and bond-order behavior govern phonon features and mechanical responses. We demonstrate an interpretable and computationally efficient potential for bismuthene and demonstrate a general reinforcement-learning strategy for developing bond-order models in emerging 2D materials.

deformation↗
DOE OSTI2021

Strong Ferromagnetic Exchange Coupling and Single-Molecule Magnetism in MoS 4 3– -Bridged Dilanthanide Complexes

We report the synthesis and characterization of the trinuclear 4d-4f compounds [Co(C 5 Me 5 ) 2 ][(C 5 Me 5 ) 2 Ln(μ-S) 2 Mo(μ-S) 2 Ln(C 5 Me 5 ) 2 ], 1-Ln (Ln = Y, Gd, Tb, Dy), containing the highly polarizable MoS 4 3 - bridging unit. UV-Vis-NIR diffuse reflectance spectra and DFT calculations of 1-Ln reveal a low-energy metal-to-metal charge transfer transition assigned to charge transfer from the singly occupied 4d z 2 orbital of Mo V to the empty 5d orbitals of the lanthanides (4d in the case of 1-Y ), mediated by sulfur-based 3p orbitals. Electron paramagnetic resonance spectra collected for 1-Y in a tetrahydrofuran solution show large 89 Y hyperfine coupling constants of A ⊥ = 23 MHz and A || = 26 MHz, indicating the presence of significant yttrium-localized unpaired electron density. Magnetic susceptibility data support similar electron delocalization and ferromagnetic Ln-Mo exchange for 1-Gd , 1-Tb , and 1-Dy . This ferromagnetic exchange gives rise to an S = 15/2 ground state for 1-Gd and one of the largest magnetic exchange constants involving Gd III observed to date, with J Gd-Mo = +16.1(2) cm -1 . Additional characterization of 1-Tb and 1-Dy by ac magnetic susceptibility measurements reveals that both compounds exhibit slow magnetic relaxation. Although a Raman magnetic relaxation process is dominant for both 1-Tb and 1-Dy , an extracted thermal relaxation barrier of U eff = 68 cm -1 for 1-Dy is the largest yet reported for a complex containing a paramagnetic 4d metal center. Furthermore, these results provide a potentially generalizable route to enhanced n d-4f magnetic exchange, revealing opportunities for the design of new n d-4f single-molecule magnets and bulk magnetic materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗