Spin-orbit Coupling Interaction Research Articles

Theoretical investigations of the spin Hamiltonian parameters for the CoCl(PPh3)3 molecules

The perturbation formulas of the spin Hamiltonian parameters (zero-field splitting and g factor g// and g⊥) are established for a 3d8 ion in trigonally distorted tetrahedra for the first time. In the theoretical treatments, the contributions from the Jahn–Teller effect, the ligand orbital and spin–orbit coupling interactions and configuration interactions are taken into account from the cluster approach in a uniform way. The above formulas are applied to the studies of the spin Hamiltonian parameters for the three CoCl(PPh3)3 molecules, and the experimental electron paramagnetic resonance spectra of all the molecules are satisfactorily explained. The significant compressions of the ligand tetrahedra with mixed chlorine and PPh3 groups around Co+ are analysed for three distinct CoCl(PPh3)3 compounds, characterised by the Cl–Co–P bond angles θ larger than the tetrahedral angle of 109.47°. The local trigonal distortions are discussed in view of the Jahn–Teller effect.

Interaction-induced quantum anomalous Hall phase in (111) bilayer ofLaCoO3

In the present paper, the Gutzwiller density functional theory (LDA+G) has been applied to study the bilayer system of ${\mathrm{LaCoO}}_{3}$ grown along the $(111)$ direction on ${\mathrm{SrTiO}}_{3}$. The LDA calculations show that there are two nearly flat bands located at the top and bottom of ${e}_{g}$ bands of Co atoms with the Fermi level crossing the lower one. After including both the spin-orbit coupling and the Coulomb interaction in the LDA+G method, we find that the interplay between spin-orbit coupling and Coulomb interaction stabilizes a very robust ferromagnetic insulator phase with the nonzero Chern number indicating the possibility of realizing the quantum anomalous Hall effect in this system.

Non-Abelian parafermions in time-reversal-invariant interacting helical systems

The interplay between bulk spin-orbit coupling and electron-electron interactions produces umklapp scattering in the helical edge states of a two-dimensional topological insulator. If the chemical potential is at the Dirac point, umklapp scattering can open a gap in the edge state spectrum even if the system is time-reversal invariant. We determine the zero-energy bound states at the interfaces between a section of a helical liquid which is gapped out by the superconducting proximity effect and a section gapped out by umklapp scattering. We show that these interfaces pin charges which are multiples of $e/2$, giving rise to a Josephson current with $8\ensuremath{\pi}$ periodicity. Moreover, the bound states, which are protected by time-reversal symmetry, are fourfold degenerate and can be described as ${\mathbb{Z}}_{4}$ parafermions. We determine their braiding statistics and show how braiding can be implemented in topological insulator systems.

Theory studies of the local lattice distortions and the EPR parameters for Cu2+, Mn2+ and Fe3+ centres in ZnWO4

The local lattice distortions and the electron paramagnetic resonance (EPR) parameters (g factors, hyperfine structure constants and zero-field splittings) for Cu2+, Mn2+ and Fe3+ in ZnWO4 are theoretically studied based on the perturbation calculations for rhombically elongated octahedral 3d9 and 3d5 complexes. The impurity centres on Zn2+ sites undergo the local elongations of 0.01, 0.002 and 0.013 Å along the C2 axis and the planar bond angle variations of 8.1°, 8.0° and 8.6° for Cu2+, Mn2+ and Fe3+, respectively, due to the Jahn–Teller effect and size and charge mismatch. In contrast to the host Zn2+ site with obvious axial elongation (∼0.31 Å) and perpendicular (angular) rhombic distortion, all the impurity centres demonstrate more regular octahedral due to the above local lattice distortions. The copper centre exhibits significant Jahn–Teller reductions for the spin-orbit coupling and orbital angular momentum interactions, characterised by the Jahn–Teller reduction factor J (≈0.29 ≪ 1). The calculated EPR parameters agree well with the experimental results. The local structures of the impurity centres are analysed in view of the corresponding lattice distortions.

Striped ferronematic ground states in a spin-orbit-coupledS=1Bose gas

We theoretically establish the mean-field phase diagram of a homogeneous spin-$1$, spin-orbit coupled Bose gas as a function of the spin-dependent interaction parameter, the Raman coupling strength and the quadratic Zeeman shift. We find that the interplay between spin-orbit coupling and spin-dependent interactions leads to the occurrence of ferromagnetic or ferronematic phases which also break translational symmetry. For weak Raman coupling, increasing attractive spin-dependent interactions (as in $^{87}$Rb or $^7$Li) induces a transition from a uniform to a stripe XY ferromagnet (with no nematic order). For repulsive spin-dependent interactions however (as in $^{23}$Na), we find a transition from an $XY$ spin spiral phase ($<S_{z} >= 0$ and uniform total density) with uniaxial nematic order, to a biaxial ferronematic, where the total density, spin vector and nematic director oscillate in real space. We investigate the stability of these phases against the quadratic Zeeman effect, which generally tends to favor uniform phases with either ferromagnetic or nematic order but not both. We discuss the relevance of our results to ongoing experiments on spin-orbit coupled, spinor Bose gases.

Studies on the Local Angular Distortion and Spin Hamiltonian Parameters for the Trigonal Co2+ Center in MgCl2

Abstract The local angular distortion and spin Hamiltonian parameters (g factors g||, g⊥ and the hyperfine structure constants) for the trigonal Co2+ center in MgCl2 are theoretically studied by diagonalizing the 6×6 energy matrix of ground 4T1 state for a trigonally distorted octahedral 3d7 cluster. Based on the cluster approach, the contributions from the admixtures of various J (= 1/2;3/2;5/2) states and the ligand orbital and spin-orbit coupling interactions are taken into account in a uniform way. The local impurity-ligand bond angle in the Co2+ center is found to be about 3.44° larger than the host metal-ligand bond angle in the pure crystal due to substitution of smaller Mg2+ by bigger Co2+, inducing a further compressed ligand octahedron. The calculated spin Hamiltonian parameters using the above local angular distortion are in good agreement with the experimental data. The present studies on the local structure and the spin Hamiltonian parameters for Co2+ in MgCl2 are tentatively extended to a more general case by comparing the relevant impurity behaviours for Co2+ in various trigonal environments.

Effects of5delectrons and spin-orbit interaction on the characteristics of bulk plasmons in lead

An ab initio study of the dynamical dielectric response of bulk lead is presented. The influence of the $5d$ semicore states on the characteristics of the bulk plasmon is analyzed by means of first-principles pseudopotential calculations. The effects of spin-orbit interactions and local-fields are also studied in detail. The inclusion of the $5d$ semicore states in the valence configuration completely changes the high-energy-transfer dielectric properties of bulk Pb. In particular, it lowers the computed bulk plasmon energy by about 3.5 eV, bringing its frequency to good agreement with experimental data. In general, the high-energy-transfer dielectric response of bulk Pb is found to be shaped mostly by the interplay between the interband transitions involving the semicore $5d$ states and the spin-orbit coupling interaction. Local-field effects are found to affect the relative spectral weight of the high-energy excitations, while leaving their dispersion mostly unaffected.

Polarization of a quasi-two-dimensional repulsive Fermi gas with Rashba spin-orbit coupling: A variational study

Motivated by the remarkable experimental control of synthetic gauge fields in ultracold atomic systems, we investigate the effect of an artificial Rashba spin-orbit coupling on the spin polarization of a two-dimensional repulsive Fermi gas. By using a variational many-body wave function, based on a suitable spinorial structure, we find that the polarization properties of the system are indeed controlled by the interplay between spin-orbit coupling and repulsive interaction. In particular, two main effects are found: (1) The Rashba coupling determines a gradual increase of the degree of polarization beyond the critical repulsive interaction strength, at variance with conventional two-dimensional Stoner instability. (2) The critical interaction strength, above which finite polarization is developed, shows a dependence on the Rashba coupling, i.e., it is enhanced in case the Rashba coupling exceeds a critical value. A simple analytic expression for the critical interaction strength is further derived in the context of our variational formulation, which allows for a straightforward and insightful analysis of the present problem.

Orbital Ferromagnetism in Interacting Few-Electron Dots with Strong Spin-Orbit Coupling

Investigations of quantum dots yield information about the properties of semiconductors on the smallest scales. Researchers show that quantum dots can exhibit an orbital ferromagnet phase due to the interplay of strong Rashba spin-orbit coupling and Coulomb interactions.

Half Metallic Ferrimagnetism in Hole-Doped Lanthanide Iridates

Electronic and magnetic properties of a material of double perovskite [Pr 2−x Sr x MgIrO 6] 2 had been studied by first-principles density functional approach. Under the cooperative effect of spin-orbit coupling (SOC) and Coulomb interactions of Ir-5d and Pr-4f electrons, our calculations reveal half metallic ferrimagnetism (HMFiM) with the total angular moment μ t o t = ±3μ B per unit cell for x = 0.5 and 1.5, desirable for spintronic applications. HMFiM is fully retained in presence of SOC due to the large exchange splitting between spin-up and spin-down bands at the Fermi level

Unexpected magnetization enhancement in hydrogen plasma treated ferromagnetic (Zn,Cu)O film

The effects of H+ incorporation on oxygen vacancies (HO+) on the giant ferromagnetic behavior (moment up to 3.26 μB/Cu) in ZnO:Cu polycrystalline films have been closely examined using different microstructural and magnetic characterization tools. Fine thermal stability (up to 450 °C) and low resistivity demonstrate a significant correlation between Cu 3d-states and HO+ donor defects in H plasma treated ZnO:Cu films, analogous to dual-donor (VO and Zni) defects mediated case. These HO+ donors can delocalize their electrons to the orbits of Cu atoms and contribute to a stronger spin-orbit coupling interaction. Suitable HO+ defect concentration and matched proportion between Cu2+ and Cu+ species ensure that orbital momentum shall not be quenched. Hence, unexpected moment enhancement, less than spin-orbit coupling upper limit (3.55 μB/Cu), can be also expected in this scenario. The manipulation from spin-only to spin-orbit coupling mode, using a facile thermally-mediated H plasma exposure way, will allow achieving spin transport based diluted magnetic semiconductor device.

Communication: Relativistic Fock-space coupled cluster study of small building blocks of larger uranium complexes.

We present a study of the electronic structure of the [UO2](+), [UO2](2 +), [UO2](3 +), NUO, [NUO](+), [NUO](2 +), [NUN](-), NUN, and [NUN](+) molecules with the intermediate Hamiltonian Fock-space coupled cluster method. The accuracy of mean-field approaches based on the eXact-2-Component Hamiltonian to incorporate spin-orbit coupling and Gaunt interactions are compared to results obtained with the Dirac-Coulomb Hamiltonian. Furthermore, we assess the reliability of calculations employing approximate density functionals in describing electronic spectra and quantities useful in rationalizing Uranium (VI) species reactivity (hardness, electronegativity, and electrophilicity).

Long-range interaction induced phases in Weyl semimetals

The interplay of spin orbit coupling and electron electron interaction condensing new phases of matter is an important new phenomena in solid state physics. In this paper we explore the nature of excitonic phases induced in Weyl semimetals by long range Coulomb repulsion. Its has been previously shown that short range repulsion leads to a ferromagnetic insulator while short range attraction results in a charge density wave state. Here we show the the charge density wave is the energetically favored state in the presence of long range repulsion.

Correlation effects in (111) bilayers of perovskite transition-metal oxides

We investigate the correlation-induced Mott, magnetic, and topological phase transitions in artificial (111) bilayers of perovskite transition-metal oxides $\mathrm{La}\mathrm{Au}{\mathrm{O}}_{3}$ and $\mathrm{Sr}\mathrm{Ir}{\mathrm{O}}_{3}$ for which the previous density-functional theory calculations predicted topological insulating states. Using the dynamical-mean-field theory with realistic band structures and Coulomb interactions, $\mathrm{La}\mathrm{Au}{\mathrm{O}}_{3}$ bilayer is shown to be far away from a Mott insulating regime, and a topological-insulating state is robust. On the other hand, $\mathrm{Sr}\mathrm{Ir}{\mathrm{O}}_{3}$ bilayer is on the verge of an orbital-selective topological Mott transition and turns to a trivial insulator by an antiferromagnetic ordering. Oxide bilayers thus provide a novel class of topological materials for which the interplay between the spin-orbit coupling and electron-electron interactions is a fundamental ingredient.

Renormalization group study of interaction-driven quantum anomalous Hall and quantum spin Hall phases in quadratic band crossing systems

It is shown that topological insulating phases driven by interactions can be realized without the need for spin-orbit coupling or large intersite interaction in a two-dimensional system of spin-1/2 fermions with a single pair of parabolically touching bands. Using a weak-coupling, Wilsonian renormalization group procedure, we show that a quantum anomalous Hall phase is realized for Hubbard interaction, while a quantum spin Hall phase is favored for longer-ranged interactions.

Controlling hole spins in quantum dots and wells

We review recent theoretical results for hole spins influenced by spin-orbit coupling and Coulomb interaction in two-dimensional quantum wells as well as the decoherence of single hole spins in quantum dots due to hyperfine interaction with surrounding nuclear spins. After reviewing the different forms of spin-orbit coupling that are relevant for electrons and heavy holes in III-V semiconductor quantum wells, we illustrate the combined effect of spin-orbit coupling and Coulomb interactions for hole systems on spin-dependent quasiparticle group velocities. We further analyze spin-echo decay for a single hole spin in a nuclear-spin bath, demonstrating that this decoherence source can be controlled in these systems by entering a motional-averaging regime. Throughout this review, we emphasize physical effects that are unique to hole spins (rather than electrons) in nanoscale systems.

Effect of spin orbit coupling and HubbardUon the electronic structure of IrO2

We have studied in detail the electronic structure of IrO${}_{2}$ including spin orbit coupling (SOC) and electron-electron interaction, both within the generalized gradient approximation plus Hubbard $U$ (GGA+U) and GGA plus dynamical mean field theory (GGA+DMFT) approximations. Our calculations reveal that the Ir ${t}_{2g}$ states at the Fermi level largely retain the ${J}_{\mathrm{eff}}=\frac{1}{2}$ character, suggesting that this complex spin orbit entangled state may be robust even in metallic IrO${}_{2}$. We have calculated the phase diagram for the ground state of IrO${}_{2}$ as a function of $U$ and find a metal insulator transition that coincides with a magnetic phase change, where the effect of SOC is only to reduce the critical values of $U$ necessary for the transition. We also find that dynamic correlations, as given by the GGA+DMFT calculations, tend to suppress the spin-splitting, yielding a Pauli paramagnetic metal for moderate values of the Hubbard $U$. Our calculated optical spectra and photoemission spectra including SOC are in good agreement with experiment, demonstrating the importance of SOC in IrO${}_{2}$.

Creation of two-dimensional composite solitons in spin-orbit-coupled self-attractive Bose-Einstein condensates in free space.

It is commonly known that two-dimensional mean-field models of optical and matter waves with cubic self-attraction cannot produce stable solitons in free space because of the occurrence of collapse in the same setting. By means of numerical analysis and variational approximation, we demonstrate that the two-component model of the Bose-Einstein condensate with the spin-orbit Rashba coupling and cubic attractive interactions gives rise to solitary-vortex complexes of two types: semivortices (SVs, with a vortex in one component and a fundamental soliton in the other), and mixed modes (MMs, with topological charges 0 and ±1 mixed in both components). These two-dimensional composite modes can be created using the trapping harmonic-oscillator (HO) potential, but remain stable in free space, if the trap is gradually removed. The SVs and MMs realize the ground state of the system, provided that the self-attraction in the two components is, respectively, stronger or weaker than the cross attraction between them. The SVs and MMs which are not the ground states are subject to a drift instability. In free space (in the absence of the HO trap), modes of both types degenerate into unstable Townes solitons when their norms attain the respective critical values, while there is no lower existence threshold for the stable modes. Moving free-space stable solitons are also found in the present non-Galilean-invariant system, up to a critical velocity. Collisions between two moving solitons lead to their merger into a single one.

Six heterometallic coordination polymers containing cobalt(II): Syntheses, crystal structures and magnetic properties

Six new coordination polymers, [Co(NiL)(aipt)] (1), [Co2(ML)(hipt)2(CH3OH)(H2O)]·CH3OH (M=Cu (2), Ni (3)), [Co2(C2O4)2(CuL)2] (4), [Co4(NiL)4(ipt)4(H2O)2] (5) and [Co(CuL)(tpt)] (6) (H2L=2,3-dioxo-5,6,14,15-dibenzo-1,4,8,12-tetraazacyclo-pentadeca-7,13-dien; H2aipt=5-aminoisophthalic acid; H2hipt=5-hydroxyisophthalic acid; H2ipt=isophthalic acid; H2tpt=terephthalic acid), have been synthesized by a solvothermal method and characterized by single-crystal X-ray diffraction. Complexes 1, 4 and 5 exhibit different infinite chain structures formed by CoNi (1), Co2Cu2 (4), Co4Ni4 (5) units, respectively, via oxamide and diverse carboxylate bridges, while complexes 2, 3 and 6 exhibit different two-dimensional network structures formed by Co2M or Co2M2 units via oxamide and 5-hydroxyisophthalate or terephthalate bridges. The results of magnetic determination show weak antiferromagnetic interactions in 1–3 and 5–6, and the spin–orbit coupling interaction of Co(II) is a primary factor in the magnetic behaviors.

A Mechanistic Study of Photoinduced Electron Transfer from Triplet Erythrosin to Various Quinones Using Time Resolved Absorption and ESR-CIDEP Measurements

Abstract Photoinduced electron transfer reactions from the triplet erythrosin (Ery2−) dianion to various quinones (1,4-benzoquinone, 2,5-di-t-butyl-1,4-benzoquinone, duroquinone, 2,5-dichloro-1,4-benzoquinone, chloranil, bromanil, 2,3-dichloro-5,6-dicyano-1,4-benzoquinone and 9,10-anthraquinone) and other organic acceptors like 7,7,8,8-tetracyanoquinodimethane, 2,3,5,6-tetrafluoro-7,7,8,8-tetracyanoquinodimethane and with tetracyano-1,4-benzoquinone (cyanil), one of the strongest oxidizing agent reported in literature (E ○ = 0.90 V vs. SCE), were studied by laser flash photolysis in acetonitrile/water mixtures at room temperature. Quenching rate constants are obtained from Stern-Volmer plots. The measured bimolecular quenching rate constants are close to the diffusion controlled rates. Excitation of a contact radical-pair or a triplet exciplex as an intermediate in the photoinduced electron transfer reaction in a slightly polar solvent (1-propanol) is confirmed by the observation of the net absorptive chemically induced dynamic electron polarization (CIDEP) spectra. The unusual net–absorptive CIDEP spectrum is explained by spin-orbit coupling interactions due to presence of four iodine atoms in the structure of erythrosin (heavy atom effect). The dependence of the electron transfer rate constants, k et, on the driving force, ΔG et is slightly parabolic and indicates the Marcus Inverted Region.