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Spin-orbital correlations from complex orbital order in MgV 2 O 4
MgV 2 O 4 is a spinel based on magnetic V 3+ ions, which host both spin (𝑆 = 1) and orbital (𝑙 eff = 1) moments. Owing to the underlying pyrochlore coordination of the magnetic sites, the spins in MgV 2 O 4 only antiferromagnetically order once the frustrating interactions imposed by the 𝐹𝑑$\overline{3}$𝑚 lattice are broken through an orbitally-driven structural distortion at T 𝑆 ≃ 60 K. Consequently, a Néel transition occurs at T 𝑁 ≃ 40 K. Low-temperature spatial ordering of the electronic orbitals is fundamental to both the structural and magnetic properties; however, considerable discussion on whether it can be described by complex or real orbital ordering is ambiguous. We apply neutron spectroscopy to resolve the nature of the orbital ground state and characterize hysteretic spin-orbital correlations using x-ray and neutron diffraction. Neutron spectroscopy finds multiple excitation bands and we parametrize these in terms of a multilevel (or excitonic) theory based on the orbitally degenerate ground state. Meaningful for the orbital ground state, we report an “optical-like” mode at high energies that we attribute to a crystal-field-like excitation from the spin-orbital 𝑗 eff = 2 ground-state manifold to an excited 𝑗 eff =1 energy level. We parametrize the magnetic excitations in terms of a Hamiltonian with spin-orbit coupling and local crystalline electric field distortions resulting from deviations from perfect octahedra surrounding the V 3+ ions. We suggest that this provides compelling evidence for complex orbital order in MgV 2 O 4 . We then apply the consequences of this model to understand hysteretic effects in the magnetic diffuse scattering where we propose that MgV 2 O 4 displays a high-temperature orbital memory of the low-temperature spin order.
The balance of orbital overlap and orbital energy in the activation of methane by actinide cations: insights from inductively coupled plasma tandem mass spectrometry
The actinides present a unique challenge to chemical theory. The classical view of covalent bonding is driven by the extent of spatial overlap of valence orbitals. Modern theory has expanded assessments of covalency to include considerations of orbital energy degeneracy to assess orbital energy mixing between metal and ligand valence orbitals. Actinide–ligand (An–L) bonding has more recently been described as a balance between orbital overlap and orbital energy mixing, where 5f and L valence orbital overlap decreases while energy mixing between An 5f and L valence orbitals increases across the series. To test these existing views, we employed inductively coupled plasma tandem mass spectrometry to examine the kinetic energy dependences of reactions of actinide cations, Th + –Am + , with methane. Further, this is the first experimental report of the energy dependences of methane activation reactions involving the cations of Pa, Np, Pu, and Am and the first experimental determination of transuranic An + –D, An + –CD 2 , An + –CD 3 , and An + –CD bond dissociation energies. The correlation of the measured An + –CD 2 bond energies with E p (6d 2 ) indicates that An + 6d orbitals are the dominant contributors in the An + –CD 2 bonds. Close examination of the relative reactivities of An + offers additional support that the balance of classical and modern views of molecular bonding may lie between Np + and Pu + and that the increased reactivity of Th + –Np + may be attributed to the increased spatial extension of the 5f orbitals whereas covalent An + bond formation may be more driven by the decreasing energies of the 5f orbitals across the actinide series.
Unraveling substituent effects on frontier orbitals of conjugated molecules using an absolutely localized molecular orbital based analysis
It is common to introduce electron-donating or electron-withdrawing substituent groups into functional conjugated molecules (such as dyes) to tune their electronic structure properties (such as frontier orbital energy levels) and photophysical properties (such as absorption and emission wavelengths). However, there lacks a generally applicable tool that can unravel the underlying interactions between orbitals from a substrate molecule and those from its substituents in modern electronic structure calculations, despite the long history of qualitative molecular orbital theory. In this work, the absolutely localized molecular orbitals (ALMO) based analysis is extended to analyze the effects of substituent groups on the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) of a given system. This provides a bottom-up avenue towards quantification of effects from distinct physical origins (e.g. permanent electrostatics/Pauli repulsion, mutual polarization, inter-fragment orbital mixing). For the example case of prodan (a typical dye molecule), it is found that inter-fragment orbital mixing plays a key role in narrowing the HOMO–LUMO gap of the naphthalene core. Specifically, an out-of-phase mixing of high-lying occupied orbitals on the naphthalene core and the dimethylamino group leads to an elevated HOMO, whereas an in-phase combination of LUMOs on the naphthalene core and the propionyl group lowers the LUMO energy of the entire molecule. We expect this ALMO-based analysis to bridge the gap between concepts from qualitative orbital interaction analysis and quantitative electronic structure calculations.
Giant Orbital Anisotropy with Strong Spin–Orbit Coupling Established at the Pseudomorphic Interface of the Co/Pd Superlattice
Orbital anisotropy at interfaces in magnetic heterostructures has been key to pioneering spin–orbit-related phenomena. However, modulating the interface’s electronic structure to make it abnormally asymmetric has been challenging because of lack of appropriate methods. Here, the authors report that low-energy proton irradiation achieves a strong level of inversion asymmetry and unusual strain at interfaces in [Co/Pd] superlattices through nondestructive, selective removal of oxygen from Co3O4/Pd superlattices during irradiation. Structural investigations corroborate that progressive reduction of Co3O4into Co establishes pseudomorphic growth with sharp interfaces and atypically large tensile stress. The normal component of orbital to spin magnetic moment at the interface is the largest among those observed in layered Co systems, which is associated with giant orbital anisotropy theoretically confirmed, and resulting very large interfacial magnetic anisotropy is observed. All results attribute not only to giant orbital anisotropy but to enhanced interfacial spin–orbit coupling owing to the pseudomorphic nature at the interface. They are strongly supported by the observation of reversal of polarity of temperature-dependent Anomalous Hall signal, a signature of Berry phase. This work suggests that establishing both giant orbital anisotropy and strong spin–orbit coupling at the interface is key to exploring spintronic devices with new functionalities.
Performance of an atomic mean-field spin–orbit approach within exact two-component theory for perturbative treatment of spin–orbit coupling
The paper reports development of an atomic mean-field (AMF) spin–orbit approach within the spin-free exact two-component theory in its one-electron variant (SFX2C-1e), a new relativistic quantum-chemical method for treating spin-orbit coupling in molecules. The effective one-electron spin–orbit integral matrix in the four-component representation is assembled as a direct sum of one-centre spin–orbit integral matrices with the mean-field two-electron contributions evaluated using atomic SFX2C-1e Hartree–Fock density matrices. It is then transformed into two-component representation using analytic SFX2C-1e energy derivative formulation. The resulting two-component spin–orbit integral matrix is by design suitable for use in perturbative calculations of spin–orbit coupling, treating SFX2C-1e wavefunctions as unperturbed states. The accuracy of the present AMF approach has been demonstrated using benchmark calculations of spin–orbit splittings for representative diatomic radicals at the equation-of-motion coupled-cluster singles and doubles level. In conclusion, to demonstrate the applicability and accuracy of the present perturbative spin–orbit scheme in calculations of challenging heavy-element containing systems, a thorough computational investigation of six low-lying electronic states of ThO+ is reported.
Identifying Photoinduced Dipolar Polarization and Orbit–Orbit Interaction between Excitons in Organic–Inorganic Hybrid Perovskites
Abstract Photoinduced polarization and orbit–orbit interaction are important issues in hybrid perovskites toward developing optoelectronic functionalities. This paper identifies that photoinduced polarization occurs in hybrid perovskites with mixed‐cation methylammonium (MA)/formamidinium (FA) (MA x FA (1− x ) PbI 3 ) by measuring bulk polarization at 1 MHz in a magnetic field. Interestingly, when the internal dipole moment is increased upon increasing the MA:FA ratio, the photoinduced dipolar polarization can be substantially enhanced, clarifying the controversial issue of whether photoexcitation can induce a dielectric polarization within dipolar polarization regime in hybrid perovskites. Furthermore, upon increasing photoinduced dipolar polarization, it is found that the intrinsic orbit–orbit interaction between excitons can be increased, revealed by monitoring photocurrent change (Δ J sc ) upon switching the photoexcitation between linear and circular polarizations. This presents that organic cations are directly involved in the orbit–orbit interaction within band structures. Clearly, the studies provide an insightful understanding of the dipole moment effects on photoinduced dipolar polarization and orbit–orbit interaction between excitons in hybrid perovskites toward controlling the optoelectronic properties.
Superconducting Tunneling Spectroscopy of Spin-Orbit Coupling and Orbital Depairing in Nb : SrTiO 3
We have examined here the intrinsic spin-orbit coupling and orbital depairing in thin films of Nb-doped ${\mathrm{SrTiO}}_{3}$ by superconducting tunneling spectroscopy. The orbital depairing is geometrically suppressed in the two-dimensional limit, enabling a quantitative evaluation of the Fermi level spin-orbit scattering using Maki's theory. The response of the superconducting gap under in-plane magnetic fields demonstrates short spin-orbit scattering times ${{\tau}}_{\mathrm{so}}{\le}1.1\text{ }\text{ }\mathrm{ps}$. Analysis of the orbital depairing indicates that the heavy electron band contributes significantly to pairing. These results suggest that the intrinsic spin-orbit scattering time in ${\mathrm{SrTiO}}_{3}$ is comparable to those associated with Rashba effects in ${\mathrm{SrTiO}}_{3}$ interfacial conducting layers and can be considered significant in all forms of superconductivity in ${\mathrm{SrTiO}}_{3}$.
Spin-orbit coupling driven orbital-selective doping effect in Sr 2 Ru 1 - x Ir x O 4
Orbital-selective phenomena in mutliorbital systems have received much attention due to their uniqueness as well as possible connections to other phenomena. As orbital-selectiveness is mostly related to the crystal structure, finding a new control parameter other than structure would be of significant importance. Here in this paper we report discovery of an orbital-selective doping effect in Sr 2 Ru 1 - x Ir x O 4 (SRIO). Our systematic electronic structure study of SRIO reveals an anomalous orbital-selective doping effect and concomitant Lifshitz transitions (LTs) in the γ band. With the help of a tight-binding calculation, we find that the orbital-selective doping effect is due to variation in the spin-orbit coupling (SOC) strength. Our findings not only elucidate the mechanism of LTs in the γ band in SRIO but may also open new avenues for novel SOC-controlled orbital-selective phenomena.
Predicting Cislunar Orbit Lifetimes from Initial Orbital Elements
The volume of space between Earth’s geosynchronous orbit out to the Moon’s sphere of influence, including the lunar Lagrange points, is crucial for the successful planning and execution of space missions, but not fully understood dynamically. This region is a part of cislunar space. Trajectories through cislunar space are influenced by the gravitational forces of the Sun, Earth, Moon, and other Solar System planets leading to typically unpredictable and chaotic trajectory behavior. It is therefore difficult to predict the stability of an trajectory through cislunar space from a set of initial conditions or orbital elements. We simulate one million cislunar orbits to train a self-organizing map (SOM) to cluster the trajectories and orbits into families based on how long they remain stable within the cislunar space. Using the trained SOM, we are able to predict the stable lifetime of a trajectory through cislunar space from a set of initial orbital elements to within an accuracy of 10% for 8% of simulated trajectories and within 50% for 43% of the simulated trajectories. Clustering in the SOM suggests that a variety of trajectory morphologies have similar lifetimes. Once trained, the SOM can predict the stable lifetime of a given cislunar trajectory within milliseconds. The methods developed in this work enable the rapid identification of stable cislunar orbits and trajectories that could be used for future space exploration. Moreover, the developed SOM method can generate orbital and trajectory lifetime estimates from minimal observational data, such as a single two line element, making it useful for early warning systems and large-scale sensor network operations.
Experimental evaluation of the stabilization of the COT orbitals by 4f orbitals in COT 2 Ce using a Hubbard model
Significant orbital mixing is rare in lanthanide complexes because of the limited radial extent of the 4f orbitals, which results in a generally small stabilization due to 4f orbital interactions. Nevertheless, even a small amount of additional stabilization could enhance lanthanide separations. One lanthanide complex in which orbital mixing has been extensively studied both experimentally and computationally is cerocene, COT 2 Ce, where COT is cyclooctatetraene. This compound has a singlet ground state with a low-lying, triplet excited state. Previous fluorescence studies on trimethylsilyl-substituted cerocenes indicate the triplet state is 0.4 eV higher in energy than the singlet state. In addition, computational studies predict that the triplet is 0.3 to 1 eV higher in energy than the singlet. The synthesis of highly pure COT 2 Ce by Walter and Andersen allowed its physical properties to be accurately measured. Using these measurements, we evaluate the stabilization of the 4f orbitals using two, independent approaches. A Hubbard model is used to evaluate the stabilization of the ground state due to orbital mixing. This stabilization, which is also the singlet–triplet gap, is –0.29 eV using this model. Furthermore, this gap was also from the temperature independent paramagnetism of COT 2 Ce, which yielded a value of –0.32 eV.
Intrinsic orbital moment and prediction of a large orbital Hall effect in two-dimensional transition metal dichalcogenides
Carrying information using generation and detection of the orbital current, instead of the spin current, is an emerging field of research, where the orbital Hall effect (OHE) is an important ingredient. We show that the 2D transition metal dichalcogenides (TMDCs) such as MoX2, a currently popular class of materials of considerable interest, may in fact be excellent systems to observe the OHE. This is due to the broken inversion symmetry and the specific nature of the electron states at the K, K$^\prime$ valley points, that lead to robust momentum-dependent orbital moments, which flow in different directions due to the opposite Berry curvatures under an applied electric field. This is in complete contrast to the inversion-symmetric systems studied so far, where the (weak) orbital moment is induced only after the application of the external electric field. In addition, the spin-orbit coupling leads to the spin Hall effect, which we find to be quite small in the TMDCs, making these materials particularly suitable for direct observation of the OHE, with potential application in orbitronics.
Two-orbital degeneracy lifted local precursor to a metal-insulator transition in MgTi2O4
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Natural transition orbitals for complex two-component excited state calculations
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Spin and Orbital Effects on Asymmetric Exchange Interaction in Polar Magnets: M(IO 3 ) 2 (M = Cu and Mn)
We report magnetic polar materials feature an astonishing range of physical properties, such as magnetoelectric coupling, chiral spin textures, and related new spin topology physics. This is primarily attributable to their lack of space inversion symmetry in conjunction with unpaired electrons, potentially facilitating an asymmetric Dzyaloshinskii–Moriya (DM) exchange interaction supported by spin–orbital and electron–lattice coupling. However, engineering the appropriate ensemble of coupled degrees of freedom necessary for enhanced DM exchange has remained elusive for polar magnets. Here, we study how spin and orbital components influence the capability of promoting the magnetic interaction by studying two magnetic polar materials, α-Cu(IO 3 ) 2 ( 2 D) and Mn(IO 3 ) 2 ( 6 S), and connecting their electronic and magnetic properties with their structures. The chemically controlled low-temperature synthesis of these complexes resulted in pure polycrystalline samples, providing a viable pathway to prepare bulk forms of transition-metal iodates. Rietveld refinements of the powder synchrotron X-ray diffraction data reveal that these materials exhibit different crystal structures but crystallize in the same polar and chiral P2 1 space group, giving rise to an electric polarization along the b-axis direction. The presence and absence of an evident phase transition to a possible topologically distinct state observed in α-Cu(IO 3 ) 2 and Mn(IO 3 ) 2 , respectively, imply the important role of spin–orbit coupling. Neutron diffraction experiments reveal helpful insights into the magnetic ground state of these materials. While the long-wavelength incommensurability of α-Cu(IO 3 ) 2 is in harmony with sizable asymmetric DM interaction and low dimensionality of the electronic structure, the commensurate stripe AFM ground state of Mn(IO 3 ) 2 is attributed to negligible DM exchange and isotropic orbital overlapping. The work demonstrates connections between combined spin and orbital effects, magnetic coupling dimensionality, and DM exchange, providing a worthwhile approach for tuning asymmetric interaction, which promotes evolution of topologically distinct spin phases.
Nonequivalent Spin Exchanges of the Hexagonal Spin Lattice Affecting the Low-Temperature Magnetic Properties of RInO 3 (R = Gd, Tb, Dy): Importance of Spin–Orbit Coupling for Spin Exchanges between Rare-Earth Cations with Nonzero Orbital Moments
Here, rare-earth indium oxides RInO 3 (R = Gd, Tb, Dy) consist of spin-frustrated hexagonal spin lattices made up of rare-earth ions R 3+ , where R 3+ = Gd 3+ (f 7 , L = 0), Tb 3+ (f 8 , L = 3), and Dy 3+ (f 9 , L = 5). We carried out DFT calculations for RInO 3 , including on-site repulsion U with/without spin–orbit coupling (SOC), to explore if their low-temperature magnetic properties are related to the two nonequivalent nearest-neighbor (NN) spin exchanges of their hexagonal spin lattices. Our DFT + U + SOC calculations predict that the orbital moments of the Tb 3+ and Dy 3+ ions are smaller than their free-ion values by ~2μ B while the Tb 3+ spins have an inplane magnetic anisotropy, in agreement with the experiments. This suggests that the f orbitals of each R 3+ (R = Tb, Dy) ion are engaged, though weakly, in bonding with the surrounding ligand atoms. The magnetic properties of GdInO 3 with the zero orbital moment are adequately described by the spin exchanges extracted by DFT + U calculations. In describing the magnetic properties of TbInO 3 and DyInO 3 with nonzero orbital moments, however, the spin exchanges extracted by DFT + U + SOC calculations are necessary.
Comment on “Additional Insights Between Fermi-Löwdin Orbital SIC and the Localization Equation Constraints in SIC-DFT”
In a recent Letter, Aquino and Wong (AW) analyze the connection between the Fermi-Löwdin orbital self-interaction correction (FLO-SIC) and the traditional Perdew– Zunger self-interaction correction (PZ-SIC) methods. In this work, the authors present a derivation of the conditions required to minimize the SIC density functional theory (DFT) total energy in FLO-SIC. These involve the gradient of the energy with respect to parameters known as Fermi-orbital descriptors (FODs) (called orbital “centroids” in ref 1) that are used together with the total charge density to determine the Fermi- Löwdin orbitals (FLOs). AW state that the conditions, the vanishing of the FOD gradient components, “resemble” the localization equations (LE), the minimum energy conditions in traditional PZ-SIC. The LE involve the equality of certain off-diagonal matrix elements of different orbital-dependent Hamiltonians. While AW are careful to say that their equations do not prove the mathematical equivalence of the two methods, the discussion in the text and the graphical table of contents figure suggest that vanishing FOD gradients imply satisfaction of the LE and vice versa, and hence that the methods are equivalent. We believe this ambiguity clouds an important issue, rather than clarifying it.
ORBIT-2 Dataset for Scaling Exascale Vision Foundation Models for Weather and Climate Downscaling
This dataset release corresponds to the work conducted in ORBIT-2: Scaling Exascale Vision Foundation Models for Weather and Climate Downscaling, where large-scale AI methods were applied to improve climate and weather resolution. The collection integrates four widely used, publicly available datasets: ERA5, PRISM, DAYMET, and IMERG. To prepare the data for ORBIT-2 model training and evaluation, we applied a preprocessing pipeline that generates paired low-resolution and high-resolution samples, enabling supervised downscaling experiments. The transformation from coarse to fine scales was performed using bilinear regridding, consistent with the procedures described in WeatherBench2, a community benchmark for weather and climate AI models. This dataset supports the development and evaluation of foundation models designed for weather and climate downscaling at exascale. Additional details on methodology and applications can be found in Wang et al., ORBIT-2 (arXiv:2505.04802, 2025).