Spin-orbit States Research Articles

Quantum state-resolved molecular scattering of NO (2Π1/2) at the gas-[Cnmim][Tf2N] room temperature ionic liquid interface: Dependence on alkyl chain length, collision energy, and temperature

Room temperature ionic liquids (RTILs) represent a promising class of chemically tunable, low vapor pressure solvents with myriad kinetic applications that depend sensitively on the nature of gas-molecule interactions at the liquid surface. This paper reports on rovibronically inelastic dynamics at the gas-RTIL interface, colliding supersonically cooled hyperthermal molecular beams of NO (Π1/22, N = 0) from 1-alkyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide (or [Cnmim][Tf2N]) and probing the scattered NO molecules via laser induced fluorescence (LIF) from the A(2Σ) state. Specifically, inelastic energy transfer into NO rovibrational and electronic degrees of freedom is explored as a function of RTIL alkyl chain length (n), incident collision energy (Einc) and surface temperature (Ts). At low collision energies (Einc = 2.7(9) kcal/mol), the scattered NO molecules exhibit a rotational temperature (Trot) systematically colder than Ts for all chain lengths, which signals the presence of non-equilibrium dynamics in the desorption channel. At high collision energies (Einc = 20(2) kcal/mol), microscopic branching into trapping/desorption (TD) and impulsive scattering (IS) pathways is clearly evident, with the TD fraction (α) exhibiting a step-like increase between short (n = 2, 4) and long (n = 8, 12, 16) alkyl chains consistent with theoretical predictions. For all hydrocarbon chain lengths and RTIL temperature conditions, NO rotational excitation in the IS channel yields hyperthermal albeit Boltzmann-like distributions well described by a “temperature” (TIS = 900 -1200 K) that decreases systematically with increasing n. Non-adiabatic, collision induced hopping between ground and excited spin-orbit states is found to be independent of RTIL alkyl chain length and yet increase with collision energy. The scattering data confirm previous experimental reports of an enhanced presence of the alkyl tail at the gas-RTIL interface with increasing n, as well as provide support for theoretical predictions of an alkyl length dependent shift between chains oriented parallel vs. perpendicular to the surface normal.

Geometrical and electronic structure of the molybdenum and tungsten halides MX3 and MX4 (M = Mo, W; X = F, Cl): Jahn-Teller effect and spin-orbit coupling

The ground and lower-lying excited electronic states of MX3 and MX4 (M = Mo, W; X = F, Cl) molecules were systematically studied by the complete active space self-consistent field (CASSCF) and multiconfigurational quasi-degenerate second-order perturbation (XMCQDPT2) methods. Scalar-relativistic effects and spin-orbit coupling were taken into account employing the third-order Douglas-Kroll-Hess (DKH) Hamiltonian and full Breit-Pauli operator. The ground orbital state of MoF3 and MoCl3 complexes is quadruplet 4A2′ state in the equilibrium configuration with D3h symmetry. If the spin-orbit interaction is taken into account the calculations result in two 4E1/2 and 4E3/2 spin-orbit states with 11–14 cm−1 energy differences instead of one 4A2′ state. Spin-orbit interaction quenches the Jahn-Teller effect in 2E″ ground orbital state of WF3 complex in D3h configuration, and C2v configuration with (4E1/2 + 4E3/2) spin-mixed state corresponds to the minimum on the PES. The WCl3 complex reveals strong interaction of the spin-orbit states of different multiplicity. For WCl3 complex the configuration with D3h symmetry corresponds to the minimum on the PES for four lowest spin-mixed electronic states. The MoF4, MoCl4 and WCl4 complexes possess the tetrahedral equilibrium configuration with 3A2 orbital electronic state. If the spin-orbit interaction is taken into account the ground state changes to the threefold degenerated 3T2 spin-orbit state with weak Jahn-Teller effect. In the case of WF4 complex the strong Jahn-Teller effect has been discovered in the first excited 1E singlet electronic state of the tetrahedral structure, and D2d configuration with 1A1 electronic state possesses the lowest energy. The comparison with available experimental data has been performed. The tendencies in molecular parameters of complexes studied were analyzed.

Spin-orbit states of neutron wave packets

We propose a method to prepare an entangled spin-orbit state between the spin and the orbital angular momenta of a neutron wavepacket. This spin-orbit state is created by passing neutrons through the center of a quadrupole magnetic field, which provides a coupling between the spin and orbital degrees of freedom. A Ramsey fringe type measurement is suggested as a means of verifying the spin-orbit correlations.

Infrared spectroscopy of molecular ions in selected rotational and spin-orbit states.

First results are presented obtained with an experimental setup developed to record IR spectra of rotationally state-selected ions. The method we use is a state-selective version of a method developed by Schlemmer et al. [Int. J. Mass Spectrom. 185, 589 (1999); J. Chem. Phys. 117, 2068 (2002)] to record IR spectra of ions. Ions are produced in specific rotational levels using mass-analyzed-threshold-ionization spectroscopy. The state-selected ions generated by pulsed-field ionization of Rydberg states of high principal quantum number (n ≈ 200) are extracted toward an octupole ion guide containing a neutral target gas. Prior to entering the octupole, the ions are excited by an IR laser. The target gas is chosen so that only excited ions react to form product ions. These product ions are detected mass selectively as a function of the IR laser wavenumber. To illustrate this method, we present IR spectra of C2H2 (+) in selected rotational levels of the (2)Πu,3/2 and (2)Πu,1/2 spin-orbit components of the vibronic ground state.

Valence Band Splitting on Multilayer MoS2: Mixing of Spin-Orbit Coupling and Interlayer Coupling.

Understanding the origin of valence band splitting is important because it governs the unique spin and valley physics in few-layer MoS2. We explore the effects of spin-orbit coupling and interlayer coupling on few-layer MoS2 using first-principles methods. We find spin-orbit coupling has a major contribution to the valence band splitting at K in multilayer MoS2. In double-layer MoS2, the interlayer coupling leads to the widening of the gap between the already spin-orbit split states. This is also the case for the bands of the K-point in bulk MoS2. In triple-layer MoS2, the strength of interlayer coupling of the spin-up channel becomes different from that of spin-down at K. This combined with spin-orbit coupling results in the band splitting in two main valence bands at K. With the increase of pressure, this phenomenon becomes more obvious with a decrease of main energy gap in the splitting valence bands at the K valley.

Spin–orbit alignment for KELT-7b and HAT-P-56b via Doppler tomography with TRES

We present Doppler tomographic analyses for the spectroscopic transits of KELT-7b and HAT-P-56b, two hot-Jupiters orbiting rapidly rotating F-dwarf host stars. These include analyses of archival TRES observations for KELT-7b, and a new TRES transit observation of HAT-P-56b. We report spin-orbit aligned geometries for KELT-7b (2.7 +/- 0.6 deg) and HAT-P-56b (8 +/- 2 deg). The host stars KELT-7 and HAT-P-56 are among some of the most rapidly rotating planet-hosting stars known. We examine the tidal re-alignment model for the evolution of the spin-orbit angle in the context of the spin rates of these stars. We find no evidence that the rotation rates of KELT-7 and HAT-P-56 have been modified by star-planet tidal interactions, suggesting that the spin-orbit angle of systems around these hot stars may represent their primordial configuration. In fact, KELT-7 and HAT-P-56 are two of three systems in super-synchronous, spin-orbit aligned states, where the rotation periods of the host stars are faster than the orbital periods of the planets.

Atomic-scale control of magnetic anisotropy via novel spin–orbit coupling effect in La2/3Sr1/3MnO3/SrIrO3 superlattices

Magnetic anisotropy (MA) is one of the most important material properties for modern spintronic devices. Conventional manipulation of the intrinsic MA, i.e., magnetocrystalline anisotropy (MCA), typically depends upon crystal symmetry. Extrinsic control over the MA is usually achieved by introducing shape anisotropy or exchange bias from another magnetically ordered material. Here we demonstrate a pathway to manipulate MA of 3d transition-metal oxides (TMOs) by digitally inserting nonmagnetic 5d TMOs with pronounced spin-orbit coupling (SOC). High-quality superlattices comprising ferromagnetic La2/3Sr1/3MnO3 (LSMO) and paramagnetic SrIrO3 (SIO) are synthesized with the precise control of thickness at the atomic scale. Magnetic easy-axis reorientation is observed by controlling the dimensionality of SIO, mediated through the emergence of a novel spin-orbit state within the nominally paramagnetic SIO.

Autoionization following nanoplasma formation in atomic and molecular clusters

Nanoplasmas resulting from the ionization of nano-scale particles by intense laser pulses are typically described by quasiclassical models, where electron emission is understood to take place via thermal processes. Recently, we discovered that, following the interaction of intense near-infrared (NIR) laser pulses with molecular oxygen clusters, electron emission from nanoplasmas can also occur from atomic bound states via autoionization [Schutte et al., Phys. Rev. Lett. 114, 123002 (2015)]. Here we extend these studies and demonstrate that the formation and decay of doubly-excited atoms and ions is a very common phenomenon in nanoplasmas. We report on the observation of autoionization involving spin-orbit excited states in molecular oxygen and carbon dioxide clusters as well as in atomic krypton and xenon clusters ionized by intense NIR pulses, for which we find clear bound-state signatures in the electron kinetic energy spectra. By applying terahertz (THz) streaking, we show that the observed autoionization processes take place on a picosecond to nanosecond timescale after the interaction of the NIR laser pulse with the clusters.

Chlorine atom formation dynamics in the dissociation of halogenated pyridines after photoexcitation at 235 nm: A resonance enhanced multiphoton ionization-time of flight (REMPI-TOF) study

The photodissociation dynamics of halogen substituted pyridines, namely, 3-chloropyridine (ClPy) and 3-chloro-2,4,5,6-tetrafluoropyridine (ClFPy), has been studied around 235nm by detecting chlorine atoms in their spin orbit states Cl(2P3/2) and Cl∗(2P1/2) using the REMPI-TOF technique. We have determined the translational energy distribution, the recoil anisotropy parameter, β, and the spin–orbit branching ratio, for chlorine atom elimination channels. The TOF profiles for Cl and Cl∗ are found to be independent of laser polarization suggesting a zero value for β, within the experimental uncertainties. For 3-chloropyridine, the average translational energies for Cl and Cl∗ elimination channels are determined to be 3.7±1.0 and 7.0±1.5kcal/mol, respectively. Similarly, for 3-chloro-2,4,5,6-tetrafluoropyridine, the average translational energies for Cl and Cl∗ elimination channels are determined to be 8.0±1.5 and 9.0±1.5kcal/mol, respectively. The theoretical calculation suggests that the fluorine substitution increases the possibility of cross over to the π–σ∗ state from the initially prepared π–π∗ state.

Origin of the Spin-Orbital Liquid State in a Nearly J=0 Iridate Ba_{3}ZnIr_{2}O_{9}.

We show using detailed magnetic and thermodynamic studies and theoretical calculations that the ground state of Ba_{3}ZnIr_{2}O_{9} is a realization of a novel spin-orbital liquid state. Our results reveal that Ba_{3}ZnIr_{2}O_{9} with Ir^{5+} (5d^{4}) ions and strong spin-orbit coupling (SOC) arrives very close to the elusive J=0 state but each Ir ion still possesses a weak moment. Abinitio density functional calculations indicate that this moment is developed due to superexchange, mediated by a strong intradimer hopping mechanism. While the Ir spins within the structural Ir_{2}O_{9} dimer are expected to form a spin-orbit singlet state (SOS) with no resultant moment, substantial frustration arising from interdimer exchange interactions induce quantum fluctuations in these possible SOS states favoring a spin-orbital liquid phase down to at least 100mK.

Effects of spin–orbit coupling on the electronic states and spectroscopic properties of diatomic SeS

The electronic states and spectroscopic properties of selenium monosulfide (78Se32S) have been studied using relativistic configuration interaction methodology that includes effective core potentials of the constituent atoms. Potential energy curves of several spin-excluded (Λ−S) electronic states have been constructed and spectroscopic constants of low-lying bound Λ−S states within 5.1 eV are reported in the first stage of the calculations. In the next stage, the spin–orbit interaction has been incorporated and its effects on the potential energy curves and spectroscopic properties of the species have been investigated in detail. After the inclusion of spin–orbit coupling, the is identified as the spin–orbit (Ω) ground state of the species. The transition moments of several important dipole-allowed and spin-forbidden transitions are calculated and the radiative lifetimes of the excited states involved in the respective transitions are computed. Electric dipole moments (μz) for some low-lying bound Λ−S states as well as a few low-lying spin–orbit states (Ω-states) are also calculated in the present study.

Dynamics of Cl(2Pj) formation in the photodissociation of halogenated thiadiazole at 235 nm: A resonance enhanced multiphoton ionization-time of flight (REMPI-TOF) study

Abstract In one colour experiment, the photodissociation dynamics of halogen substituted thiadiazole, namely, 3,4-dichloro-1,2,5-thiadiazole, has been studied in a supersonic molecular beam around 235 nm, which prepares the molecules in its π–π* state. The study is conducted using resonance enhanced multiphoton ionization (REMPI) time-of-flight (TOF) technique, by detecting the nascent state of the primary chlorine atoms in their spin orbit states Cl(2P3/2) and Cl*(2P1/2). We have determined the translational energy distribution, the recoil anisotropy parameter, β, and the spin–orbit branching ratio, for chlorine atom elimination channels. State-specific TOF profiles are converted into kinetic energy distributions, using a least squares fitting method, taking into account the fragment anisotropies, βi. The TOF profiles for Cl and Cl* are found to be independent of laser polarization, i.e., the β is well characterized by a value of ∼0.0, within the experimental uncertainties. The translational energy distributions is well explained with only one component for both Cl and Cl* atom elimination channel. The average translational energies for Cl and Cl* channel are 5.2 ± 1.5 and 7.9 ± 1.5 kcal/mol, respectively. The energy partitioning into the translational modes is interpreted with the help of various models, such as impulsive and statistical models. The experimental studies revealing the nature of translational energies distribution for Cl and Cl* and its average value along with the theoretical calculations employing Time-Dependent Density Functional Theory (TD-DFT) and ab initio molecular orbital (MO) theory suggest that the initially prepared π–π* state crosses over to a nearby σ* repulsive state along the C Cl bond, from where the dissociation takes place. The results also indicates the role of fast internal conversion to ground state from the initially prepared π–π* state, from where various dissociation channels occurs. During the course of experiments, the absorption spectrum was also obtained with its absolute absorption cross section.

Strongly frustrated triangular spin lattice emerging from triplet dimer formation in honeycomb Li2IrO3.

Iridium oxides with a honeycomb lattice have been identified as platforms for the much anticipated Kitaev topological spin liquid: the spin-orbit entangled states of Ir4+ in principle generate precisely the required type of anisotropic exchange. However, other magnetic couplings can drive the system away from the spin-liquid phase. With this in mind, here we disentangle the different magnetic interactions in Li2IrO3, a honeycomb iridate with two crystallographically inequivalent sets of adjacent Ir sites. Our ab initio many-body calculations show that, while both Heisenberg and Kitaev nearest-neighbour couplings are present, on one set of Ir–Ir bonds the former dominates, resulting in the formation of spin-triplet dimers. The triplet dimers frame a strongly frustrated triangular lattice and by exact cluster diagonalization we show that they remain protected in a wide region of the phase diagram.

Near-UV photodissociation dynamics of CH₂I₂.

The near-UV photodissociation dynamics of CH2I2 has been investigated using a combination of velocity-map (slice) ion imaging and ab initio calculations characterizing the excited states. Ground state I((2)P3/2) and spin-orbit excited I*((2)P1/2) atoms were probed using 2 + 1 resonance-enhanced multiphoton ionization (REMPI) or with single-photon VUV ionization. Two-color ion images were recorded at pump wavelengths of 355 nm, 266 nm and 248 nm, and one-color ion images at the REMPI wavelengths of ∼304 nm and ∼280 nm. Analysis of the ion images shows that, regardless of iodine spin-orbit state, ∼20% of the available energy is partitioned into translation E(T) at all excitation wavelengths indicating that the CH2I co-fragment is formed highly internally excited. The translational energy distributions comprise a slow, "statistical" component that peaks near zero and faster components that peak away from zero. The slow component makes an increasingly large contribution to the distribution as the excitation wavelength is decreased. The C-I bond dissociation energy of D0 = 2.155 ± 0.008 eV is obtained from the trend in the E(T) release of the faster components with increasing excitation energy. The I and I* ion images are anisotropic, indicating prompt dissociation, and are characterized by β parameters that become increasingly positive with increasing E(T). The decrease in β at lower translational energies can be attributed to deviation from axial recoil. MRCI calculations including spin-orbit coupling have been performed to identify the overlapping features in the absorption spectrum and characterize one-dimensional cuts through the electronically excited potential energy surfaces. The excited states are of significantly mixed singlet and triplet character. At longer wavelengths, excitation directly accesses repulsive states primarily of B1 symmetry, consistent with the observed 〈β〉, while shorter wavelengths accesses bound states, also of B1 symmetry that are crossed by repulsive states.

Evidence for strongf−dhybridization in the intermetallic ferromagnetCePdIn2

We have investigated the contribution of Ce $4f$ states to the electronic structure of the intermetallic ferromagnet ${\mathrm{CePdIn}}_{2}$ by means of x-ray absorption spectroscopy and resonant and nonresonant photoemission spectroscopy. The line shape of the Ce ${M}_{5,4}$ absorption edge reveals the localized nature of the $4f$ states, and is consistent with a predominantly 3+ ionic state for Ce ions. Fitting of the Ce $3d$ core level gives a Ce $4f$ occupation number at room temperature of 0.92, which is in good agreement with the Ce effective magnetic moment of $2.20{\ensuremath{\mu}}_{B}$ (corresponding to $\ensuremath{\sim}87%$ of the free-electron moment) as calculated from the inverse magnetic susceptibility. Moreover, the hybridization strength between $4f$ and conduction electrons is found to be $\ensuremath{\sim}180$ meV, revealing that ${\mathrm{CePdIn}}_{2}$ is a strongly hybridized system. This is consistent with the results from the analysis of the resonant valence band photoemission measurements at both the ${N}_{5,4}$ and the ${M}_{5}$ edges, showing that the Ce $4f$ states are composed of the features predicted by the single-impurity Anderson model, i.e., a broad $4{f}^{0}$ peak centered at 1.9 eV and two $4{f}^{1}$ spin-orbit states much closer to the Fermi level. The same spectra also show that the Ce $4f$ resonant spectral weight extends over a wide binding energy range, overlapping with that presumably occupied by the Pd $4d$ ligand states. This energy overlap is interpreted as a signature of the strong hybridization governing the system, which could possibly favor the emergence of long-range ferromagnetism through the indirect exchange between localized $4f$ states mediated by highly dispersive $d$ electrons.

Optical Control of Donor Spin Qubits in Silicon.

We show how to achieve optical, spin-selective transitions from the ground state to excited orbital states of group-V donors (P, As, Sb, Bi) in silicon. We consider two approaches based on either resonant, far-infrared (IR) transitions of the neutral donor or resonant, near-IR excitonic transitions. For far-IR light, we calculate the dipole matrix elements between the valley-orbit and spin-orbit split states for all the goup-V donors using effective mass theory. We then calculate the maximum rate and amount of electron-nuclear spin-polarization achievable through optical pumping with circularly polarized light. We find this approach is most promising for Bi donors due to their large spin-orbit and valley-orbit interactions. Using near-IR light, spin-selective excitation is possible for all the donors by driving a two-photon Λ-transition from the ground state to higher orbitals with even parity. We show that externally applied electric fields or strain allow similar, spin-selective Λ-transition to odd-parity excited states. We anticipate these results will be useful for future spectroscopic investigations of donors, quantum control and state preparation of donor spin qubits, and for developing a coherent interface between donor spin qubits and single photons.

Color tuning of Bi2+ luminescence in barium borates

The luminescence of Bi2+ has its origin in p–p transitions between different spin–orbit states in the 6s26p1 electronic configuration. The divalent state is highly unusual for Bi and because of the low stability of Bi2+, research on the intraconfigurational p–p transitions of Bi2+ is limited. Narrow-band emission has been observed in the orange/red spectral region, which makes Bi2+ luminescence interesting for application in white light LEDs. In this paper we investigate the luminescence of Bi2+ in a variety of borate host lattices with the aim to tune the emission wavelength and to investigate the influence of the host on the luminescence properties. Bi2+ was doped into Sr1−xBaxB4O7, α-BaB2O4, α-BaB4O7, Ba2B10O17 and BaB8O13. Luminescence was observed for Bi2+ in all hosts, except α-BaB2O4, indicating that Bi2+ cannot be stabilized in this host. In the other borates the emission wavelength varies between 586nm (in BaB8O13) and 671nm (in α-BaB4O7). The shift in emission wavelength is explained by a variation in crystal field splitting and spin–orbit coupling. The luminescence lifetime of the p–p emission is in the μs range, varying between 6 and 13μs, reflecting the parity forbidden character of the p–p transition. Narrow-band red emission at 612nm (FWHM=35nm) is observed for Ba2B10O17:Bi2+. These luminescence characteristics of Bi2+ are favorable for application in w-LEDs, but an important drawback is that only low concentrations (in the ppm range) can be stabilized in the divalent state.

On-site electron correlations in Bi2Se3 topological insulator

We explore the role of local, multi-orbital electron correlations in Bi2Se3 topological insulator. Based on local-density-approximation plus dynamical-mean-field-theory (LDA + DMFT) we derive a Kondo-Mott electronic transition, predicting maximally non-metallicity in three-dimensional Bi-chalcogenide topological insulators. Our results within the spin-orbit Kondo state show good agreement with scanning tunneling spectroscopy taken on pure and Cu-doped Bi2Se3 samples and effective mass enhancement of Dirac electrons for Cu x Bi2Se3, confirming the hypothesis of electron correlations in three-dimensional p-band topological insulators.

Magnetoresistance in the Spin-Orbit Kondo State of Elemental Bismuth.

Materials with strong spin-orbit coupling, which competes with other particle-particle interactions and external perturbations, offer a promising route to explore novel phases of quantum matter. Using LDA + DMFT we reveal the complex interplay between local, multi-orbital Coulomb and spin-orbit interaction in elemental bismuth. Our theory quantifies the role played by collective dynamical fluctuations in the spin-orbit Kondo state. The correlated electronic structure we derive is promising in the sense that it leads to results that might explain why moderate magnetic fields can generate Dirac valleys and directional-selective magnetoresistance responses within spin-orbit Kondo metals.

Theoretical investigation of NpC, NpC2 and NpC4 molecules

The electronic structure and geometrical parameters of ground and low-lying excited states of neptunium mono-, di- and tetracarbides were investigated by relativistic CASSCF/CASPT2 multireference calculations with an all-electron basis set as well as with density functional theory (B3LYP) in conjunction with relativistic pseudopotentials. The CASPT2 calculations were extended with complete active space state interaction calculations in order to include spin–orbit coupling and calculate the absorption electronic spectra. In case of the actinide monocarbides, vibrational frequencies were calculated both for the lowest-energy spin-free and spin–orbit states. For the di- and tetracarbides infrared and Raman spectral characteristics were obtained using DFT calculations. For NpC2, two structures were investigated: the symmetric triangular (Np-C2) structure including an acetylide moiety which was found to be the ground state and the symmetric linear (CNpC) structure. In case of NpC4, fourteen different structures were investigated. The ground state was found to be a planar fan-like structure where neptunium is connected to a bent C 4 moiety. The found structures agree well with the previous results on other actinide carbides (Th, U, Pu, Am). The bonding characteristics of the low-energy structures were analysed on the basis of valence molecular orbitals.