Spin-orbit Coupling Interaction Research Articles

Paramagnetic Effects in NMR Spectroscopy of Transition-Metal Complexes: Principles and Chemical Concepts.

ConspectusMagnetic resonance techniques represent a fundamental class of spectroscopic methods used in physics, chemistry, biology, and medicine. Electron paramagnetic resonance (EPR) is an extremely powerful technique for characterizing systems with an open-shell electronic nature, whereas nuclear magnetic resonance (NMR) has traditionally been used to investigate diamagnetic (closed-shell) systems. However, these two techniques are tightly connected by the electron-nucleus hyperfine interaction operating in paramagnetic (open-shell) systems. Hyperfine interaction of the nuclear spin with unpaired electron(s) induces large temperature-dependent shifts of nuclear resonance frequencies that are designated as hyperfine NMR shifts (δHF).Three fundamental physical mechanisms shape the total hyperfine interaction: Fermi-contact, paramagnetic spin-orbit, and spin-dipolar. The corresponding hyperfine NMR contributions can be interpreted in terms of through-bond and through-space effects. In this Account, we provide an elemental theory behind the hyperfine interaction and NMR shifts and describe recent progress in understanding the structural and electronic principles underlying individual hyperfine terms.The Fermi-contact (FC) mechanism reflects the propagation of electron-spin density throughout the molecule and is proportional to the spin density at the nuclear position. As the imbalance in spin density can be thought of as originating at the paramagnetic metal center and being propagated to the observed nucleus via chemical bonds, FC is an excellent indicator of the bond character. The paramagnetic spin-orbit (PSO) mechanism originates in the orbital current density generated by the spin-orbit coupling interaction at the metal center. The PSO mechanism of the ligand NMR shift then reflects the transmission of the spin polarization through bonds, similar to the FC mechanism, but it also makes a substantial through-space contribution in long-range situations. In contrast, the spin-dipolar (SD) mechanism is relatively unimportant at short-range with significant spin polarization on the spectator atom. The PSO and SD mechanisms combine at long-range to form the so-called pseudocontact shift, traditionally used as a structural and dynamics probe in paramagnetic NMR (pNMR). Note that the PSO and SD terms both contribute to the isotropic NMR shift only at the relativistic spin-orbit level of theory.We demonstrate the advantages of calculating and analyzing the NMR shifts at relativistic two- and four-component levels of theory and present analytical tools and approaches based on perturbation theory. We show that paramagnetic NMR effects can be interpreted by spin-delocalization and spin-polarization mechanisms related to chemical bond concepts of electron conjugation in π-space and hyperconjugation in σ-space in the framework of the molecular orbital (MO) theory. Further, we discuss the effects of environment (supramolecular interactions, solvent, and crystal packing) and demonstrate applications of hyperfine shifts in determining the structure of paramagnetic Ru(III) compounds and their supramolecular host-guest complexes with macrocycles.In conclusion, we provide a short overview of possible pNMR applications in the analysis of spectra and electronic structure and perspectives in this field for a general chemical audience.

Peculiar magnetotransport properties in epitaxially stabilized orthorhombic Ru3+ perovskite LaRuO3 and NdRuO3

Complex oxides are interesting materials where multiple physical properties and functionalities can be realized by integrating different elements in a single compound. However, owing to the chemical instability, not all the combinations of elements can be materialized despite the intriguing potential expected from their magnetic and electronic properties. Here we demonstrate an epitaxial stabilization of orthorhombic Ru3+ perovskite oxides: LaRuO3 and NdRuO3, and their magnetotransport properties that reflect the difference between non-magnetic La3+ and magnetic Nd3+. Above all, an unconventional anomalous Hall effect accompanied by an inflection point in magnetoresistance is observed around 1.3 T below 1 K for NdRuO3, which we propose is possibly related to a non-coplanar spin texture on Nd3+ sublattice. These studies not only serve as a new testbed for the interplay between spin-orbit coupling and Coulomb interaction but also open a new avenue to explore topological emergent phenomena in well-studied perovskite oxides.

Toward intrinsic ultra-high-temperature ferromagnetism in a CrAuTe2/graphene heterosystem.

Exploring intrinsic two-dimensional (2D) ferromagnetic (FM) materials with high Curie temperatures (TC) and large magnetic anisotropy energies (MAE) is one of the effective solutions to develop materials for high-performance spintronic applications. Using density functional theory calculations and high-throughput computations, we predict an intrinsic bimetallic FM monolayer, CrAuTe2, which has a large MAE and high TC. The results show that the value of the MAE can reach about 1.5 meV per Cr, and Monte Carlo simulations show that the TC of monolayer CrAuTe2 is about 840 K. Further analysis indicates that the joint effects of spin-orbit coupling (SOC) interaction and magnetic dipole-dipole interaction result in high in-plane magnetic anisotropy. In addition, this monolayer has good dynamic, thermal, and mechanical stabilities, which were confirmed by ab initio molecular dynamics simulations, phonon spectra, and elastic constants, respectively. In order to propose a practical synthesis approach, we built a CrAuTe2/graphene van der Waals heterostructure, and found that the heterostructure does not affect the magnetic properties of monolayer CrAuTe2. These findings appear promising for the future applications in nano-spintronics.

Exchange-correlation effects on the structural, electronic, and optical properties of Sr2RuO4 using DFT calculations

We perform a first principle study on the electronic, structural, and optical properties of Sr2RuO4 by various functionals: LSDA, GGA, GGA-mBJ, PBE-D3, optB88-vdW, vdW-DF2 and HSE06 using the plane-wave method of density functional theory (DFT) in the presence of the spin-orbit coupling (SOC) and Coulomb interaction parameter, U. The dynamical stability and the thermal stability are calculated via phonon dispersions and ab initio molecular dynamics simulations, respectively. The band structure calculation and the orbital-resolved density of states of LSDA and the schemes of GGA reveal different ground state. For GGA-mBJ and the hybrid functional, there is an indirect gap in the band structure. In the case of vdW functionals, our findings are in agreement with GGA. We compute a variety of optical responses and compare them with existing experimental studies. The results of the dielectric function suggest that GGA-mBJ (LSDA and GGA) may better account for the experimental findings in the presence (absence) of SOC at the infrared spectral region (infrared and visible spectral regions). We observe that the optical responses are strongly influenced by SOC and intraband transitions. Among the optical spectra, we focus more on the electron energy loss spectrum, which depends on the excitations, the exchange-correlation effects, and the multiorbital nature of Sr2RuO4.

Control of the magnetic anisotropy and Curie temperature of monolayer 1T-CrTe2 for room temperature application

Magnetic units with large magnetic anisotropy energy (MAE) and high Curie temperature (Tc) are crucial for spintronic and quantum computing devices, which are a persisting demand for miniaturization of magnetic units. Using first-principles calculations and Monte Carlo simulation, it is found that monolayer 1T-CrTe2 exhibits strong perpendicular magnetic anisotropy with a MAE of approximately 5.29 meV and high Tc of ∼136 K. Interestingly, we find that the MAE and Tc of monolayer 1T-CrTe2 are tunable through electron/hole doping, strain, and heterostructure engineering. The magnetic easy-axis can be adjusted from out of plane to in plane, which is mainly attributed to the coupling between Te atomic orbitals (px, py). Second-order perturbation theory reveals that the spin–orbit coupling interaction between the occupied px and unoccupied py orbitals in opposite spin channel near Fermi level gives rise to negative contribution of MAE. Moreover, Tc can be enhanced to ∼230 K through super–superexchange mechanism of heterostructure due to the electron hopping between t2g/eg orbitals of Cr4+ ions and e1/a1 orbitals of Fe2+ ions. Importantly, we find that Tc can be boosted above room temperature by applying moderate strain (6%), ascribing to significant enhancement of MAE and exchange coupling constant. The present work indicates that monolayer 1T-CrTe2-based two-dimensional materials are very promising for room temperature application in magnetic storage and information processing.

Room-temperature ferromagnetism in two-dimensional Mn2B

Two-dimensional magnets with long-range magnetic order are desired for their potential applications in spintronics. Here, we propose an intrinsic two-dimensional ferromagnetism in Mn2B MBene. It is shown that Mn2B is in a metallic and ferromagnetic ground state based on first-principles calculations. The magnetic anisotropy is derived mainly from both the spin-orbit coupling (SOC) and dipole-dipole interactions. Normally, the dipole-dipole interaction is significantly smaller and is often overshadowed by the SOC. Nevertheless, the dipole-dipole interaction has superseded the SOC interaction, assuming a pivotal role in shaping Mn2B's magnetic anisotropy. Eventually, the net magnetic anisotropy energy of Mn2B is −80.7 μeV per unit cell (−1.69 × 10−4 J/m2) with in-plane magnetization, due to the larger magnetic shape anisotropy. Moreover, the critical temperature is estimated to be 548 K based on the Monte Carlo simulation of Heisenberg model, which is much higher than room temperature. Our findings indicate that Mn2B is potentially useful in spintronic devices.

Dzyaloshinskii–Moriya Interaction of Cr2O2ClI Janus Monolayer: A First‐Principles Calculation

The Dzyaloshinskii–Moriya interactions (DMIs) of Cr2O2ClI Janus monolayer are investigated using the first‐principles calculations. There are three DMI mechanisms (namely, the Half–Fert–Levy mechanism, the Fert–Levy mechanism, and the Rashba mechanism) in Cr2O2ClI Janus monolayer. The Half–Fert–Levy mechanism, by which the I atoms enhance the spin orbit coupling interaction on the type‐I Cr atoms but have no such effect on the type‐II Cr atoms, contributes to the y‐component of the DMI vector between two nearest‐neighbor Cr atoms. Originating from the strong spin orbit coupling interaction of the I atoms, the Fert–Levy mechanism results in a significant DMI vector via the Cr–I–Cr exchange path between two type‐I next‐nearest‐neighbor Cr atoms. Induced by the intrinsic electric field of the Janus structure, the Rashba mechanism results in nonzero in‐plane components of the DMI vectors. This work provides the first‐principles calculations of the DMIs of Cr2O2ClI Janus monolayer and reveals insight into the physics behind the calculated DMIs, which promote the understanding of the complicated DMIs due to multiple mechanisms in 2D magnetic Janus monolayers.

Size effects on polaron formation in lead chloride perovskite thin films

Lead halide perovskites (LHP) are of interest for light-emitting applications due to the tunability of their bandgap across the visible and near-infrared spectrum (IR) coupled with efficient photoluminescence quantum yields (PLQY). It is widely speculated that photoexcited electrons and holes spatially separate into large negative (electron) and positive (hole) polarons. Polarons are expected to be optically active. With the observed optoelectronic signatures expecting to show potential excited states within the polaronic potential well. From the polaron excited-state we predict that large polarons should be capable of spontaneous emission, photoluminescence, in the mid-IR to far-IR regime based on the concept of inverse occupations within the polaron potential well. Here we use density functional theory (DFT), including spin–orbit coupling interactions, for calculations on a two-dimensional Dion-Jacobson (DJ) lead chloride perovskite atomistic model of various sizes as a host material for either negative or positive polarons to examine the effects of size on polaron formation. This work provides computational evidence that polaron formation through selective charge injection does not show the same level of localisation for positive and negative polarons.

Rational design of dibenzo[a,c]phenazine-derived isomeric thermally activated delayed fluorescence luminophores for efficient orange-red organic light-emitting diodes

It is an immense challenge to develop efficient long-wavelength (orange-to-red) thermally activated delayed fluorescence (TADF) materials due to the increasing nonradiative decay rates following the energy-gap law. Herein, two pairs of asymmetric isomers; DPyPzTPA and TPAPzDPy, and PyPzDTPA and DTPAPzPy based on electron-deficient moieties dibenzo[a,c]phenazine (Pz) and pyridine (Py) combined with electron-donor units of triphenylamine (TPA) were designed and synthesized. Their photophysical properties could be finely modulated by changing the position and number of Py groups as well as TPA fragments onto Pz cores. DPyPzTPA and DTPAPzPy possess much more rigidity and thus less geometry relaxation and non-radiative decay between ground states and excited states than those of PyPzDTPA and TPAPzDPy. Intriguingly, DPyPzTPA exhibits the highest relative photoluminescence quantum yield (ΦPL) and the fastest reverse intersystem crossing (rISC) rate among them owing to relatively stronger rigidity and spin-orbit coupling (SOC) interactions between the lowest singlet (S1) and energetically close-lying excited triplet state and therefore, the device showed the highest maximum external quantum efficiency (EQEmax) of 16.6% (60.9 lm/W, 53.3 cd/A) with Commission Internationale de I'Eclairage (CIE) coordinates of (0.43, 0.55), peak wavelength 556 nm. In stark contrast, due to its lower rigidity and extremely weak delayed fluorescence (DF) characteristic and thus the much lower ΦPL, TPAPzDPy-based devices are only half as efficient (30.8 lm/W, 27.5 cd/A, 8.3% EQE) despite the isomers possessing equal singlet-triplet energy gaps (ΔEST) of 0.43 eV. On the other hand, the device based on DTPAPzPy also demonstrated a strongly enhanced performance (59.1 lm/W, 52.7 cd/A, 16.1% EQE) than its isomer PyPzDTPA-based device (39.5 lm/W, 35.2 cd/A, 10.3% EQE). This work explicitly implicates that the asymmetric and isomeric molecular design is a potential strategy for promoting the development of highly efficient long-wavelength TADF materials.

Electronic phase transition, perpendicular magnetic anisotropy and high Curie temperature in Janus FeClF

How to enhance the spin polarization, the Curie temperature and the perpendicular magnetic anisotropy (PMA) is crucial for the applications of 2D magnets in spintronic devices. In this work, based on the experimental FeCl2 flakes and the predicted in-plane magnetic anisotropy (IMA) and lower Curie temperature of FeCl2 monolayer, we use first-principles and Monte Carlo simulation to explore the strain and carrier-doping effects on the electronic and magnetic properties of Janus FeClF monolayer. The structure is stable within −10% to 2% biaxial strain. Janus FeClF monolayer can experience transitions from a half-semiconductor to a spin gapless semiconductor (SGS) around the −6% compressive strain, and from the IMA to the PMA at the −7% compressive strain. The super-exchange Fe–F/Cl–Fe interaction induces the ferromagnetic coupling, and the Curie temperature can be considerably enhanced from 56 K to 281 K at the −10% compressive strain. The half-metallicity can be achieved whether under electron doping or hole doping. The Fe-d orbitals and the spin–orbit coupling interaction between occupied and unoccupied intraorbital states are responsible for the electronic phase transition and the magnetic anisotropy, respectively. Remarkably, the compressive −10% strain and the 0.02 e doping collectively increase the Curie temperature to near room temperature (286 K). The high spin polarization (exhibiting SGS and half-metal), the PMA and the near-room-temperature ferromagnetism induced by strain and doping make Janus FeClF a promising candidate for 2D spintronic applications, which will stimulate experimental and theoretical broad studies on this class of Janus monolayers FeXY (X,Y = F, Cl, Br, and X ≠ Y).

Observation of flat band, Dirac nodal lines and topological surface states in Kagome superconductor CsTi3Bi5

Kagome lattices of various transition metals are versatile platforms for achieving anomalous Hall effects, unconventional charge-density wave orders and quantum spin liquid phenomena due to the strong correlations, spin-orbit coupling and/or magnetic interactions involved in such a lattice. Here, we use laser-based angle-resolved photoemission spectroscopy in combination with density functional theory calculations to investigate the electronic structure of the newly discovered kagome superconductor CsTi3Bi5, which is isostructural to the AV3Sb5 (A = K, Rb or Cs) kagome superconductor family and possesses a two-dimensional kagome network of titanium. We directly observe a striking flat band derived from the local destructive interference of Bloch wave functions within the kagome lattice. In agreement with calculations, we identify type-II and type-III Dirac nodal lines and their momentum distribution in CsTi3Bi5 from the measured electronic structures. In addition, around the Brillouin zone centre, {{mathbb{Z}}}_{2} nontrivial topological surface states are also observed due to band inversion mediated by strong spin-orbit coupling.

Time Translation Symmetry Breaking in an Isolated Spin-Orbit-Coupled Fluid of Light.

We study the interplay between intrinsic spin-orbit coupling and nonlinear photon-photon interactions in a nonparaxial, elliptically polarized fluid of light propagating in a bulk Kerr medium. We find that in situations where the nonlinear interactions induce birefringence, i.e., a polarization-dependent nonlinear refractive index, their interplay with spin-orbit coupling results in an interference between the two polarization components of the fluid traveling at different wave vectors, which entails the breaking of translation symmetry along the propagation direction. This phenomenon leads to a Floquet band structure in the Bogoliubov spectrum of the fluid, and to characteristic oscillations of its intensity correlations. We characterize these oscillations in detail and point out their exponential growth at large propagation distances, revealing the presence of parametric resonances.

Theoretical studies on the g-factors and the local structure of W5+ ions in tungsten phosphate glasses

In this work, we adopt the three-order perturbation formulae for g-factors (g//, g^) of d1 ions in the octahedral environment to calculate the g-factors of W5+ ions in tungsten phosphate glasses containing lithium (P2O5-Li2WO4-Li2O). In the light of the high valence state of the studied W5+ centers and hence the strong covalency of the studied octahedral [WO6]7- cluster, we consider the contributions to g-factors from the ligand orbital and spin-orbit (SO) coupling interactions based on the cluster approach. The required tetragonal crystal-field parameters are calculated from the local structure of W5+ ions based on the superposition model. According to the theoretical calculations, we find that the octahedral [WO6]7- clusters possess the tetragonally compressed distortion with a shorter W-O bond length (≈1.54 Å) and a longer one (≈2.26 Å) along C4 axis and four normal W-O bond length (≈1.94 Å) in the perpendicular plane, which infers that the W5+ ions are in the form of tungstyl ions (i.e., WO3-). Based on the local structural data, the theoretical values of g// and g^ agree well with the experimental values.

Two-dimensional 4f magnetic EuSn2X2 (X = P, As) monolayers: A first-principles study

Two-dimensional (2D) ferromagnetic semiconductors (FMSs) hold exciting and promising potential for application in spintronic devices at the nanoscale. Currently, most 2D FMSs are based on 3d electrons; 4f electrons can provide nontrivial magnetism but have been much less studied to date. This paper presents a theoretical study, via first-principles calculations, of EuSn2X2 (X = P, As) monolayers based on rare-earth cations with f-electrons. The results show that EuSn2X2 monolayers possess a large magnetization (7 μB/Eu), a controllable magnetic anisotropy energy, and a unique d-electron-mediated f–f exchange mechanism. Both types of EuSn2X2 (X = P, As) monolayers are FMSs with indirect bandgaps of 1.00 and 0.99 eV, respectively, based on the Heyd–Scuseria–Ernzerhof (HSE06) method, which can be transform to direct bandgap semiconductors under biaxial strain. Interestingly, under the latter, spin–orbit coupling interaction gradually replaces the dipole–dipole interaction in the dominant position of magnetic anisotropy, resulting in the magnetic easy axis changing from in-plane to the more desirable out-of-plane. Considering their excellent dynamic, thermal, and mechanical stabilities and small cleavage energy, these EuSn2X2 monolayers can be exfoliated from their synthesized bulk. Our study not only helps to understand the properties of 2D 4f rare-earth magnets but also signposts a route toward improving the performance of EuSn2X2 monolayers in nano-electronic devices.

Local hybridized states of adsorbed atomic Sn on WS2 substrate

We study the growth of Sn and the local electronic properties of Sn grown WS2 surfaces by in-situ scanning tunneling microscopy (STM), scanning tunneling spectroscopy, and first principles density functional theory calculations. Our investigations suggest substitutional doping of Sn at the S sites, with Sn atoms occupying a slightly elevated position of 80 pm on the WS2 surface. These results agree well with our STM observations on room temperature growth of atomic Sn, indicating commensurate or nearly commensurate adsorption at the top S sites with a buckling height of 40 ± 10 pm. Pristine WS2 without any S vacancies on the surface exhibits a bandgap of 1.39 eV, while ingap local density of states comprised of W d and S p orbitals are detected when S vacancies are considered. Upon adsorption of Sn atoms, we find the signature of modulated hybridized ingap electronic states of Sn p and W d orbitals with a spin orbit coupling interaction up to 38 meV at the K point of the Brillouin zone. These results throw important light on the future fabrication of Janus like SnWS vertical heterojunctions with atomic level doping accuracy, which will have enormous device applications.

Tuning the spin texture of graphene with size-specific Cu n clusters: a first-principles study

The size dependent interaction of Cu n (n = 1‒5) clusters with pristine and defective (C-vacancy) graphene is studied by employing density functional theory. The computed binding energies are in the range of ∼0.5 eV for pristine graphene and ∼3.5 eV for defective graphene, indicating a much stronger interaction in the later system. The induced spin–orbit coupling interaction, due to the proximity of the Cu n cluster, is studied with non-collinear spin-polarized simulations. The clusters cause a spin splitting in the order of few meV. The resultant low energy bands spin textures are also computed, and a spin–valley coupling in the case of even atom clusters on pristine graphene is predicted, leading to the emergence of a spin lifetime anisotropy. For defective graphene, a complete out-of-plane spin texture and a large spin splitting of 40–100 meV is obtained for Cu n (n = 1, 2, 3, 5) clusters due to local magnetic moment. On the other hand, for Cu4/defective graphene, having no net magnetic moment, the spin–valley coupling prevails close to the band edges.

First-principles study on the magnetic anisotropy of the CoFe/ MgAl2O4 heterostructures

Practical applications of novel spintronic devices require heterostructures with high magnetic anisotropy (MA). Here, the MA of the CoFe/MgAl2O4 heterostructures was studied by using first-principles calculations. It was found that all the CoFe/MgAl2O4 models exhibit perpendicular magnetic anisotropy (PMA) and that the Co/MgAl2O4 interface is generally more favorable than the Fe/MgAl2O4 interface for inducing large PMA. Importantly, the CoFe/MgAl2O4 heterostructure with the Co/MgAl2O4 interface shows an interfacial PMA density of up to ∼ 0.91 mJ/m2. Moreover, the PMA of the CoFe/MgAl2O4 heterostructure is greatly enhanced compared to the corresponding bare CoFe film. Through density of state analysis combined with the layer- and orbital-hybridization-resolved MA contributions, it is found that the positive contribution from spin-orbit coupling interaction between opposite spin dz2 and dyz orbitals of the interfacial Co for CoFe/MgAl2O4 heterostructure is significantly higher than that of the surface Co for the bare CoFe film, which can well explain the enhancement of the PMA. Our calculated results extend the application of perpendicular magnetic tunnel junctions based on MgAl2O4.

Mechanistic Insight and Intersystem Crossing Dynamics of the C(3P) + H2CO/D2CO Reaction

The reaction of atomic carbon, C(3P), with H2CO has been investigated using the direct dynamics trajectory surface hopping (DDTSH) method with Tully's fewest switches algorithm. The lowest lying ground triplet and single states are considered for the dynamics study at a reagent collision energy of 8.0 kcal/mol. From the trajectory calculations, we observed that CH2 + CO and H + HCCO are the two major product channels for the title reaction. The insertion mechanism of the C(3P) + H2CO reaction is rather complex and is followed by three distinct intermediates with no entrance channel barrier to the reaction on the B3LYP/6-31G(d,p) potential energy surfaces. The triplet insertion complexes are formed by three different approaches; "Sideways", "End-on" and "Head-on" attack of the triplet carbon atom toward H2CO molecule. Our dynamics calculations predict a new product channel (H + HCCO(X 2A'')) with a contribution of ∼46% of the overall products formation via ketocarbene intermediate through "Head-on" approach. Despite the weak spin-orbit coupling (SOC) interactions, intersystem crossing (ISC) via a ketocarbene intermediate has a small but significant contribution, about 2.3%, for the CH2 + CO channel. To understand the kinetic isotope effects on the reaction dynamics, we have extended our study for the C(3P) + D2CO reaction. It is seen that isotopic substitution of both the H atoms has a small reduction in the extent of ISC dynamics for the carbene formation. Our results, certainly, reveal the importance of the ketocarbene intermediate and the H + HCCO products channel as one of the major product formation channels in the title reaction, which was not reported earlier.

Spin-induced valley polarization in heterobilayer Janus transition-metal dichalcogenides

Inspired by potential application prospects of spintronics and valleytronics, a novel heterobilayer Janus structure is designed by replacing the chalcogenide atomic layers in the original bilayer MoS2. Based on first-principles calculations, it is found that the SMoS/SeMoS structure exhibits a direct band-gap semiconductor and a typical type-II band alignment with longer carrier lifetime. The transition metal (TM) atom represented by V/Cr/Mn can be stably adsorbed on the heterobilayer Janus SMoS/SeMoS sheet and effectively introduce magnetic moments (m). The calculation results demonstrate that the most stable adsorption site of the TM atom is CX(A), and the TM (V/Cr/Mn) adatom modified SMoS/SeMoS system is converted into metal (V-) or half-metal (Cr/Mn-), respectively. Under the coupling of different indirect exchange interactions, the structure exhibits stable intrinsic anti-ferromagnetic interactions for V-SMoS/SeMoS and ferromagnetic ground state for Cr/Mn-SMoS/SeMoS, respectively, and the magnetic transition temperature (T c) reaches a high temperature or even room temperature. Moreover, the robust out-of-plane magnetocrystalline anisotropy energy ensures stable long-range magnetic order. Specifically, the combination of spin injection and strong spin–orbit coupling interaction effectively breaks the time-reversal symmetry, which leads to valley polarization of the system. Based on this, the biaxial strain can effectively regulate the electronic structure, magnetic properties and valley polarization of TM-SMoS/SeMoS nanosheets with double breaking of spatial-inversion and time-reversal symmetry.

Spin Currents Induced in Open-Shell Molecules by Static and Uniform Magnetic and Electric Fields in the Presence of a Spin-Orbit Coupling Interaction and Conservation Law.

The derivation of the total induced current density vector field, in the presence of static and uniform magnetic and electric fields, is illustrated in a more clear and formally correct language together with a discussion on the charge-current conservation law not presented before for the spin-orbit coupling contribution. The theory here exposed turns out to be in fully agreement with the theory of Special Relativity and it is applicable to open-shell molecules in the presence of a nonvanishing spin orbit coupling. The discussion here exposed turns out to be accurately valid for a strictly central field due to the chosen approximation of the spin-orbit coupling Hamiltonian, but it is appropriate to deal correctly with molecular systems. The ab initio calculation of spin current densities has been implemented at both unrestricted Hartree-Fock and unrestricted DFT levels of theory. Some maps of spin currents on molecules of interest, i.e., the CH3 radical and the superoctazethrene molecule are also illustrated.