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All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Spin-Coherent Transport under Strong Spin-Orbit Interaction (Final Technical Report)

The major goals of the project consisted of acquiring insight in spin-dependent quantum coherent electronic transport phenomena arising from spin-orbit interaction, via experiments on semiconductor heterostructures and thin film semimetals patterned into mesoscopic and nanoscale geometries. The solid-state physics findings contain insight potentially useful for the creation of new quantum states of matter, for spin operations in quantum information processing, for future spin electronics, and for other future functionalities of power-saving electronic devices. The subject was of fundamental interest, but was also of long-term applied interest for quantum devices, spintronics devices, and general electronic devices. The experiments were conducted by low-temperature electronic magnetotransport in nanoscale structures of length scales similar to the quantum phase- and spin-coherence lengths and the carrier mean-free paths in the materials. Emphasis was placed on quantum coherence and spin coherence, to understand coherent spin-dependent electronic processes, on transport of electrons with very long mean-free path (ballistic transport), on the transfer of electron spin to nuclear spin (dynamic nuclear spin polarization in bismuth), and on the study of materials with quantum states emerging from spin-orbit interaction and electron-electron interaction (bismuth iridates). In two-dimensional electron systems in quantum wells of the narrow-bandgap semiconductors InAs and InGaAs the objectives included the characterization of quantum states arising from the Aharonov-Casher quantum-mechanical phase as an electromagnetic dual of the Aharonov-Bohm phase. Objectives also included quantum electronic transport at the mesoscopic scale on the semimetal bismuth in thin film form, and particularly on its strongly spin-orbit coupled surface states. An almost-strain-free method was developed to grow high-quality bismuth thin films. Devices fabricated on these films were then used to study a novel nuclear spin torque, whereby the bismuth carrier spin was transferred to the bismuth nuclei by the agency of both spin-orbit interaction and hyperfine interaction. Aspects of ballistic transport were studied in GaAs/AlGaAs heterostructures of very high mobility, and a hitherto unsuspected similarity was discovered between ballistic transport and hydrodynamic transport, of potential use in future power-saving electronic devices.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2026

Hidden Spin-Valley Locking Stabilizes Nanosecond Spin Polarization in 2D Perovskites

Room-temperature spin control in semiconductors is fundamental to spin-optoelectronics. Although inversion symmetry breaking offers one path for spin control in semiconductors, strong spin dephasing at elevated temperatures remains a persistent limitation. Hidden spin polarization without global symmetry breaking provides another promising material design strategy, but robust spin stabilization from this effect has yet to be experimentally realized. Here we show spin stabilization at room temperature in two-dimensional hybrid organic-inorganic perovskites through hidden spin-valley locking. We use functional non-primary ammonium cations to induce symmetry-breaking distortions in the metal-halide layers, producing giant local spin splitting while preserving global inversion symmetry. Time-resolved circular dichroism measurements reveal optically generated spin-polarized carriers that persist for 686 ps in (AzOH)2PbI4 and 4.7 ns in the lead-free analogue (AzOH)2SnI4 at room temperature, without an external magnetic field. First-principles calculations suggest that these long lifetimes arise from hidden spin valleys, enhanced dielectric screening and reduced spin-orbit-induced scattering in the Sn-based compound. Our design paradigm unlocks inversion-symmetric semiconductors with ultralong spin lifetimes, broadening the materials options for light-driven spin control.

14 SOLAR ENERGY↗
DOE OSTI2025

High-throughput spin-bath characterization of spin defects in semiconductors

Detailed knowledge of the local environments of spin defects in semiconductors, such as nitrogenvacancy (NV) centers in diamond or divacancies in silicon carbide, is crucial for optimizing control and entanglement protocols in quantum sensing and information applications. However, at present a direct experimental characterization of individual defect environments is not scalable, as conventional spin-bath measurements are time consuming and difficult to automate. Achieving high-throughput characterization requires short experiments to probe the spin bath. However, with fewer and noisier measurements, the inverse problem of recovering spin-bath properties from measured data becomes ill posed, with multiple spin baths having a high likelihood of yielding the same data. In this work, we present a set of computational tools to resolve the ill-posed inverse problem of recovering the atomic positions and hyperfine couplings of random nuclei surrounding spin defects from sparse, noisy experimental coherence data, which can be obtained in hours. Here, we use a trans-dimensional Bayesian approach that incorporates ab initio data to yield full posterior distributions over nuclear spin environments, enabling robust recovery from limited data. We also provide practical tools and guidelines to determine the limits of detectability for hyperfine couplings under specific dynamical decoupling sequences and sampling conditions. In addition, we demonstrate how the tools developed here, in combination with ab initio simulations of spin baths, can guide the design of efficient experimental protocols for application-specific high-throughput screening. To showcase the utility of our approach, we apply it to design fast dynamical decoupling experiments to characterize the spin baths often individual NV centers in diamond. While the primary focus is on accelerating spin-bath characterization of spin defects, this Bayesian approach also lays the foundation for digital-twin studies of spin defects, where a virtual model of the spin-defect system evolves in real time with ongoing experimental measurements. Together, the set of tools we designed and applied paves the way for scalable deployment of spin defects in semiconductors for quantum sensing and information applications.

Bayesian methods↗
DOE OSTI2022

Spin liquid to spin glass crossover in the random quantum Heisenberg magnet

We study quantum SU($M$) spins with all-to-all and random Heisenberg exchange interactions of root-mean-square strength $J$. The $M \rightarrow \infty$ model has a spin liquid ground state with the spinons obeying the equations of the Sachdev-Ye-Kitaev (SYK) model. Numerical studies of the SU(2) model with $S=1/2$ spins show spin glass order in the ground state, but also display SYK spin liquid behavior in the intermediate frequency spin spectrum. We employ a $1/M$ expansion to describe the crossover from fractionalized fermionic spinons to a confining spin glass state with weak spin glass order $q_{EA}$. The SYK spin liquid behavior persists down to a frequency $\omega_\ast \sim J q_{EA}$, and for $\omega < \omega_\ast$, the spectral density is linear in $\omega$, thus quenching the extensive zero temperature entropy of the spin liquid. Furthermore, the linear $\omega$ spectrum is qualitatively similar to that obtained earlier using bosonic spinons for large $q_{EA}$. We argue that the extensive SYK spin liquid entropy is transformed as $T \rightarrow 0$ to an extensive complexity of the spin glass state.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Global quantum phase diagram and non-Abelian chiral spin liquid in a spin- 3 2 square-lattice antiferromagnet

Since strong quantum fluctuations are essential for the emergence of quantum spin liquids, there have been extensive exploration and identification of spin liquid candidates in spin-$\frac{1}{2}$ systems, while such activities are rare in higher spin systems. Here we report an example of non-Abelian chiral spin liquid emerging in a spin-$\frac{3}{2}$ Heisenberg model on a square lattice. By tuning Heisenberg exchange interaction and scalar chirality interaction, we map out a quantum phase diagram enclosing three conventional magnetic orders and a chiral spin liquid based on density-matrix renormalization group studies. The nature of the spin liquid is identified as a long-sought bosonic version of the Read-Rezayi state that supports non-Abelian Fibonacci anyonic statistics, identified by the ground state entanglement spectrum. Significantly, we establish that the non-Abelian chiral spin liquid emerges through the enlarged local degrees of freedom and enhanced quantum fluctuations near the classical phase boundaries of competing magnetic orders. Finally, our numerical discovery of an exotic quantum spin liquid in a spin-$\frac{3}{2}$ system suggests a route for discovering fractionalized quantum phases in frustrated higher spin magnetic compounds.

2-dimensional systems↗
DOE OSTI2023

Giant interfacial spin Hall angle from Rashba-Edelstein effect revealed by the spin Hall Hanle process

The Rashba-Edelstein effect (REE), which generates interfacial spin polarization and subsequent spin current, is a compelling spin-charge conversion mechanism for spintronic applications, since it’s not limited by the elemental spin-orbit couplings. In this work we demonstrate REE at Pt/ferroelectric interfaces by showing a positive correlation between polarization and effective spin Hall angle in the recently elucidated spin Hall Hanle effects (SHHE), in which a Larmor precession of spin polarization in a diffusion process from the interface manifest as magnetoresistance and Hall effect. We show that REE leads to a large enhancement of the effective spin Hall angle of ferroelectric interface Pt/h-LuFeO 3 compared with that of Pt/Al 2 O 3 , without obvious differences in the spin relaxation time. Modeling using SHHEs involving REE as an additional source of interfacial polarization suggests that REE can lead to an interfacial spin Hall angle (0.4 ± 0.1) in Pt/h-LuFeO 3 that is one order of magnitude larger than the bulk value of Pt. Our results demonstrate that a ferroelectric interface can produce large spin-charge conversion and that SHHEs are a sensitive tool for characterizing interfacial spin-transport properties.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Floquet Spin Splitting and Spin Generation in Antiferromagnets

In antiferromagnetic spintronics, accessing the spin degrees of freedom is essential for generating spin currents and manipulating magnetic order, which generally requires lifting spin degeneracy. This is typically achieved through relativistic spin-orbit coupling or nonrelativistic spin splitting in altermagnets. Here, we propose an alternative approach: a dynamical spin splitting induced by an optical field in antiferromagnets. By coupling the driven system to a thermal bath, we demonstrate the emergence of steady-state pure spin currents as well as linear-response longitudinal and transverse spin currents. Crucially, thermal bath engineering enables a nonrelativistic Edelstein effect—the generation of a net spin accumulation—without relying on spin-orbit coupling. Furthermore, our results provide a broadly applicable and experimentally tunable route to control spins in antiferromagnets, offering new opportunities for spin generation and manipulation in antiferromagnetic spintronics.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Degeneracy Removal of Spin Bands in Collinear Antiferromagnets with Non–Interconvertible Spin–Structure Motif Pair

Energy bands in antiferromagnets are supposed to be spin degenerate in the absence of spin–orbit coupling (SOC). Recent studies have identified formal symmetry conditions for antiferromagnetic crystals in which this degeneracy can be lifted, spin splitting, even in the vanishing SOC (i.e., non-relativistic) limit. Materials having such symmetries could enable spin-split antiferromagnetic spintronics without the burden of using heavy-atom compounds. However, the symmetry conditions that involve spin and magnetic symmetry are not always effective as practical material selection filters. Furthermore, these symmetry conditions do not readily disclose trends in the magnitude and momentum dependence of the spin-splitting energy. Here, it is shown that the formal symmetry conditions enabling spin-split antiferromagnets can be interpreted in terms of local motif pairs, such as octahedra or tetrahedra, each carrying opposite magnetic moments. Here, collinear antiferromagnets with such a spin-structure motif pair, whose components interconvert by neither translation nor spatial inversion, will show spin splitting. Such a real-space motif-based approach enables an easy way to identify and design materials (illustrated in real example materials) having spin splitting without the need for SOC, and offers insights into the momentum dependence and magnitude of the spin splitting.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Neutron scattering study of fluctuating and static spin correlations in the anisotropic spin glass Fe 2 Ti O 5

The anisotropic spin-glass transition, in which spin freezing is observed only along the c axis in pseudobrookite Fe 2 TiO 5 , has long been perplexing because the Fe 3+ moments (d 5 ) are expected to be isotropic. Recently, neutron diffraction demonstrated that surfboard-shaped antiferromagnetic nanoregions coalesce above the glass transition temperature T g ≈55K, and a model was proposed in which the freezing of the surfboard magnetization fluctuations leads to the anisotropic spin-glass state. Given this model, we have carried out high-resolution inelastic neutron scattering measurements of the spin-spin correlations to understand the temperature dependence of the intrasurfboard spin dynamics on neutron (picosecond) timescales. Here, in this paper, we report on the temperature-dependence of the spin fluctuations measured from single-crystal Fe 2 TiO 5 . Strong quasi-elastic magnetic scattering, arising from intrasurfboard correlations, is observed well above T g . The spin fluctuations possess a steep energy–wave vector relation and are indicative of strong exchange interactions, consistent with the large Curie-Weiss temperature. As the temperature approaches T g from above, a shift in spectral weight from inelastic to elastic scattering is observed. At various temperatures between 4 and 300 K, a characteristic relaxation rate of the fluctuations is determined. Despite the freezing of most of the spin correlations, an inelastic contribution remains even at base temperature, signifying the presence of fluctuating intrasurfboard spin correlations to at least T/T g ≈0.1 , consistent with an energy landscape that is a hybrid between conventional and geometrically frustrated spin glasses.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Correlating Mechanical Sensitivity with Spin Transition in the Explosive Spin Crossover Complex [Fe(Htrz) 3 ] n [ClO 4 ] 2 n

Spin crossover complexes are known to undergo bond length, volume, and enthalpy changes during spin transition. In an explosive spin crossover complex, these changes could affect the mechanical and initiation sensitivity of the explosive and lead to the development of a new class of sensitivity switchable materials. To explore this relationship, the well-known spin crossover compound [Fe(Htrz) 3 ] n [ClO 4 ] 2n (1) was re-evaluated for its explosive properties, and its mechanical impact sensitivity was correlated to spin transition. A variable temperature impact test was developed and used to evaluate the impact sensitivity of 1 in the low spin (LS, S = 0), thermally accessed high spin (HS, S = 2), and mixed LS and HS states. For comparison, the structurally similar Ni compound, [Ni(Htrz) 3 ] n [ClO 4 ] 2n (2), which does not undergo a spin transition at accessible temperatures, was synthesized and characterized, and its explosive properties and variable temperature impact sensitivity measured. These results reveal a correlation between impact sensitivity and spin transition, where 1 exhibits lower impact sensitivity in the LS state and increases in sensitivity upon transition to the HS state. Here, density functional theory was used to predict structural changes that occur upon spin transition that correlate to the change in sensitivity. This demonstrates, for the first time, an explosive spin crossover compound (ExSCO) that exhibits switchable impact sensitivity with a fully reversible internal switching mechanism.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Predicting Phonon-Induced Spin Decoherence from First Principles: Colossal Spin Renormalization in Condensed Matter

Developing a microscopic understanding of spin decoherence is essential to advancing quantum technologies. Electron spin decoherence due to atomic vibrations (phonons) plays a special role as it sets an intrinsic limit to the performance of spin-based quantum devices. Two main sources of phonon-induced spin decoherence—the Elliott-Yafet and Dyakonov-Perel mechanisms—have distinct physical origins and theoretical treatments. Here, we show calculations that unify their modeling and enable accurate predictions of spin relaxation and precession in semiconductors. We compute the phonon-dressed vertex of the spin-spin correlation function with a treatment analogous to the calculation of the anomalous electron magnetic moment in QED. We find that the vertex correction provides a giant renormalization of the electron spin dynamics in solids, greater by many orders of magnitude than the corresponding correction from photons in vacuum. Finally, our Letter demonstrates a general approach for quantitative analysis of spin decoherence in materials, advancing the quest for spin-based quantum technologies.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Spin Decoherence in VOPc@graphene Nanoribbon Complexes

Carbon nanoribbons or nanographene qubit arrays can facilitate quantum-to-quantum transduction between light, charge, and spin, making them an excellent testbed for fundamental science in quantum coherent systems and for the construction of higher-level qubit circuits. Here, in this work, we study spin decoherence due to coupling with a surrounding nuclear spin bath of an electronic molecular spin of a vanadyl phthalocyanine (VOPc) molecule integrated onto an armchair-edged graphene nanoribbon (GNR). Density functional theory (DFT) is used to obtain ground-state atomic configurations. Decay of spin coherence in Hahn echo experiments is then simulated using the cluster correlation expansion method with a spin Hamiltonian involving hyperfine and electric field gradient tensors calculated from DFT. We find that the decoherence time T 2 is anisotropic with respect to magnetic field orientation and determined only by the hydrogen nuclear spins on both VOPc and GNR. Large electron spin echo envelope modulation (ESEEM) due to nitrogen and vanadium nuclear spins is present at specific field ranges and can be completely suppressed by tuning the magnetic field. The relation between these field ranges and the hyperfine interactions is analyzed. The effects of interactions with the nuclear quadrupole moments are also studied, validating the applicability and limitations of the spin Hamiltonian when they are disregarded.

Hamiltonians↗
DOE OSTI2025

Extraction of the non-spin- and spin-transfer isovector responses via the 12 C ⁡( 10 Be, 10 B + 𝛾)⁢ 12 B reaction

The isovector response in 12 B was investigated via the 12 C ⁡( 10 Be, 10 B + 𝛾)⁢ 12 B* reaction at 100⁢𝐴MeV. By utilizing the 𝛾-decay properties of the 1.74 MeV 0 + and 0.718 MeV 1 + states in 10 B, the separate extraction of the non-spin-transfer (Δ⁢𝑆 = 0) and spin-transfer (Δ⁢𝑆 = 1) isovector responses up to an excitation energy of 50 MeV in 12 B in a single measurement is demonstrated. The experimental setup employed the S800 spectrometer to detect and analyze the 10 B ejectiles and the Gamma-Ray Energy Tracking In-beam Nuclear Array (GRETINA) for obtaining the Doppler-reconstructed spectrum for 𝛾 rays emitted in flight by 10 B. A 12 C foil was placed at the pivot point of the spectrograph. Here, the 12 B reaction product was not detected. Contributions from transitions associated with the transfer of different units of angular momentum in the non-spin- and spin-transfer responses were analyzed using a multipole decomposition analysis. The extracted non-spin-dipole (Δ⁢𝑆 = 0, Δ⁢𝐿 = 1) and spin-dipole (Δ⁢𝑆 = 1, Δ⁢𝐿 = 1) responses were found to be consistent with available data from other charge-exchange probes, validating the non-spin- and spin-transfer filters used. While statistical uncertainties and experimental resolutions were relatively large due to the modest intensity of the 10 Be secondary beam, the results show that, with the much higher intensities that will be available at new rare-isotope beam facilities, the ( 10 Be, 10 B + 𝛾) reaction and its Δ⁢𝑇 𝑧 = −1 partner, the ( 10 C, 10 B + 𝛾) reaction, are powerful tools for elucidating the isovector non-spin- and spin-transfer responses in nuclei.

Charge-exchange reactions↗
DOE OSTI2020

Effective spin-mixing conductance of topological-insulator/ferromagnet and heavy-metal/ferromagnet spin-orbit-coupled interfaces: A first-principles Floquet-nonequilibrium Green function approach

The spin-mixing conductance (SMC) is a key quantity determining efficiency of spin transport across interfaces. Thus, knowledge of its precise value is required for accurate measurement of parameters quantifying numerous effects in spintronics, such as spin-orbit torque, spin Hall magnetoresistance, spin Hall effect, and spin pumping. However, the standard expression for SMC, provided by the scattering theory in terms of the reflection probability amplitudes, is inapplicable when strong spin-orbit coupling (SOC) is present directly at the interface. This is the precisely the case of topological-insulator/ferromagnet and heavy-metal/ferromagnet interfaces of great contemporary interest. We introduce an approach where first-principles Hamiltonian of these interfaces, obtained from noncollinear density functional theory (ncDFT) calculations, is combined with charge-conserving Floquet-nonequilibrium-Green-function formalism to compute directly the pumped spin current $I^{S_z}_L$ into semi-infinite left lead of two-terminal heterostructures Cu/X/Co/Cu or Y/Co/Cu—where X = Bi 2 Se 3 and Y = Pt or W—due to microwave-driven steadily precessing magnetization of the Co layer. This allows us to extract an effective SMC as a prefactor in $I^{S_z}_L$ versus precession cone angle θ dependence, as long as it remains the same, $I^{S_z}$ ∝ sin 2 θ , as in the case where SOC is absent. By comparing calculations where SOC in switched off versus switched on in ncDFT calculations, we find that SOC consistently reduces the pumped spin current and therefore the effective SMC.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Measurement of the proton spin structure at long distances

Measuring the spin structure of protons and neutrons tests our understanding of how they arise from quarks and gluons, the fundamental building blocks of nuclear matter. At long distances, the coupling constant of the strong interaction becomes large, requiring non-perturbative methods to calculate quantum chromodynamics processes, such as lattice gauge theory or effective field theories. In this work, we report proton spin structure measurements from scattering a polarized electron beam off polarized protons. The spin-dependent cross-sections were measured at large distances, corresponding to the region of low momentum transfer squared between 0.012 and 1.0GeV 2 . This kinematic range provides unique tests of chiral effective field theory predictions. Our results show that a complete description of the nucleon spin remains elusive, and call for further theoretical works, for example, in lattice quantum chromodynamics. Finally, our data extrapolated to the photon point agree with the Gerasimov–Drell–Hearn sum rule, a fundamental prediction of quantum field theory that relates the anomalous magnetic moment of the proton to its integrated spin-dependent cross-sections.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Pattern of global spin alignment of ϕ and K*0 mesons in heavy-ion collisions

The strong force, as one of the four fundamental forces at work in the universe, governs interactions of quarks and gluons, and binds together the atomic nucleus. Notwithstanding decades of progress since Yukawa first developed a description of the force between nucleons in terms of meson exchange 1 , a full understanding of the strong interaction remains a major challenge in modern science. One remaining difficulty arises from the non-perturbative nature of the strong force, which leads to the phenomenon of quark confinement at distance scales on the order of the size of the proton. Here we show that in relativistic heavy-ion collisions, where quarks and gluons are set free over an extended volume, two species of produced vector (spin-1) mesons, namely φ and K∗0 , emerge with a surprising pattern of global spin alignment. In particular, the global spin alignment for φ is unexpectedly large, while that for K∗0 is consistent with zero. The observed spin-alignment pattern and magnitude for the φ cannot be explained by conventional mechanisms, while a model with strong force fields2, 3 accommodates the current data. This is the first time that the strong force field is experimentally supported as a key mechanism that leads to global spin alignment. We extract a quantity proportional to the intensity of the field of the strong force. Within the framework of the Standard Model, where the strong force is typically described in the quark and gluon language of Quantum Chromodynamics, the field being considered here is an effective proxy description. This is a qualitatively new class of measurement, which opens a new avenue for studying the behaviour of strong force fields via their imprint on spin alignment.

Abdallah, M. S.↗
DOE OSTI2024

Chemical Design of Spin Frustration to Realize Topological Spin Glasses

Patterning spins to generate collective behavior is at the core of condensed matter physics. Physicists develop techniques, including the fabrication of magnetic nanostructures and precision layering of materials specifically to engender frustrated lattices. As chemists, we can access such exotic materials through targeted chemical synthesis and create new lattice types by chemical design. Here, in this study, we introduce a new approach to induce magnetic frustration on a modified honeycomb lattice through a competition of alternating antiferromagnetic (AFM) and ferromagnetic (FM) nearest-neighbor interactions. By subtly modulating these two types of interactions through facile synthetic modifications, we created two systems: (1) a topological spin glass and (2) a frustrated spin-canted magnet with low-temperature exchange bias. To design this unconventional magnetic lattice, we used a metal–organic framework (MOF) platform, Ni 3 (pymca) 3 X 3 (NipymcaX where pymca = pyrimidine-2-carboxylato and X = Cl, Br). We isolated two MOFs, NipymcaCl and NipymcaBr, featuring canted Ni 2+ -based moments. Despite this similarity, differences in the single-ion anisotropies of the Ni 2+ spins result in distinct magnetic properties for each material. NipymcaCl is a topological spin glass, while NipymcaBr is a rare frustrated magnet with low-temperature exchange bias. Density functional theory calculations and Monte Carlo simulations on the NipymcaX lattice support the presence of magnetic frustration as a result of alternating AFM and FM interactions. Our calculations enabled us to determine the ground-state spin configuration and the distribution of spin–spin correlations relative to paradigmatic kagomé and triangular lattices. This modified honeycomb lattice is similar to the electronic Kekulé-O phase in graphene and provides a highly tunable platform to realize unconventional spin physics.

Exchange bias↗
DOE OSTI2020

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.

74 ATOMIC AND MOLECULAR PHYSICS↗