Spin-orbit Coupling Interaction Research Articles

Polarized and unpolarized phases of spin-orbit-coupled Bose-Einstein condensates in optical lattice

We investigate the phase transition of the Bose-Einstein condensates with equal-weight Rashba and Dresselhaus spin-orbit coupling trapped in one-dimensional optical lattice. Based on the variational and two-mode approximation, the critical condition for phase transition between polarized and unpolarized Bloch wave phase is obtained analytically for the first time, which explicitly reveals rich competitive relationship among spin-orbit coupling, optical lattice and atomic interactions in determining the phase transition of the system. It is shown that the change of the energy minima and the phase transition point by the optical lattice depends on the atomic interactions and spin-orbit coupling. Our results provide a theoretical evidence for deep understanding of the competition mechanism between the optical lattice and spin-orbit coupling for the ground state phase transition of spin-orbit-coupled Bose-Einstein condensates in optical lattice.

Accurate theoretical study of potential energy curves, spectroscopic parameters, vibrational energy levels and spin-orbit coupling interaction on SiH<sup>+</sup>(X<sup>1</sup>Σ<sup>+</sup>) ion

<sec>The analytical potential energy function (APEF) of SiH<sup>+</sup>(X<sup>1</sup>Σ<sup>+</sup>) is fitted by Aguado-Paniagua function with 112 <i>ab initio</i> energy points, which are calculated by Molpro 2012 Package with the multi-reference configuration interaction including the Davidson correction method using AV<i>X</i> Z and AV<i>X</i> dZ (<i>X</i> = Q, 5, 6) basis sets. Moreover, the calculated <i>ab initio</i> energy points are subsequently extrapolated to complete basis set (CBS) limit to avoid the basis set superposition error. All the fitting parameters of APEFs for AV6Z, CBS(Q, 5), AV6dZ, CBS(Qd, 5d), SA-AV6dZ and SOC-AV6dZ methods are gathered. The potential energy curves (PEC) and the corresponding <i>ab initio</i> points are also shown. As can be seen, the PECs show excellent agreement with the <i>ab initio</i> points and a smooth behavior both in short range and long range, which ensures the high quality of fitting process for the current APEFs. </sec><sec> Based on these APEFs of different basis sets and methods including AVQZ, AV5Z, AV6Z, CBS(Q, 5), AVQdZ, AV5dZ, AV6dZ and CBS(Qd, 5d), the spectral constants <i>D</i><sub>e</sub>, <i>R</i><sub>e</sub>, <i>ω</i><sub>e</sub>, <i>B</i><sub>e</sub>, <i>α</i><sub>e</sub> and <i>ω</i><sub>e</sub><i>χ</i><sub>e</sub> are obtained. In addition, the effects of spin-orbit coupling interaction (SOC) on the system are also investigated. By comparing the spectral constants of SA-AV6dZ with the ones of SOC-AV6dZ, it is found that the effect of SOC on SiH<sup>+</sup>(X<sup>1</sup>Σ<sup>+</sup>) is small and can be ignored. We also compare the spectral constants in this work with the experimental values and other theoretical results. The results of this work accord well with the corresponding experimental and other theoretical results. It is worth noting that the deviation of dissociation energy between the theoretical calculations and experimental values is relatively large. Based on this conclusion, we suggest that the spectral constants including the dissociation energy for SiH<sup>+</sup>(X<sup>1</sup>Σ<sup>+</sup>) should be remeasured. </sec><sec> Based on the APEF of SOC-AV6dZ which should be more accurate than others in theory, the top 23 vibrational states (<i>j</i> = 0) of SiH<sup>+</sup>(X<sup>1</sup>Σ<sup>+</sup>) are calculated first by solving the radial Schrödinger equation. All the vibrational energy levels, classical turning points, rotation constants and six centrifugal distortion constants are also provided. The results of this work can provide significant references for the experimental and other theoretical work.</sec>

Ground energy level transition for two-body interacting Fermionic system with spin-orbit coupling and Zeeman interaction

Experimental realization of artificial gauge field has made it possible to simulate important models with electromagnetic field or spin-orbit interaction in condensed matter physics, which opens a new avenue to engineer novel quantum states and phenomena. The spin-orbit coupled system reveals many significant phenomena in condensed matter physics, such as quantum spin Hall effect, topological insulator and topological superconductor. The combined effect of Zeeman interaction and spin-orbit coupling leads to a nontrivial topological phase. The analytic solution of few-body system provides an in-depth insight into the physical phenomena, which has been studied extensively. Through the analytic study of two-body physics, we show new quantum phenomena for various gauge field parameters. We investigate the two-body interacting fermionic gas with spin-orbit coupling and Zeeman interaction in a ring trap. Through the plane wave expansion method, two-body fermionic system is solved analytically. In the absence of Zeeman interaction, the total momentum of the ground state is zero. With the increase of Zeeman interaction, an energy level crossing occurs between the lowest energy levels for different total momentum spaces and the ground state changes from zero total momentum space to non-zero total momentum space. Considering the Zeeman interaction, the total momentum of the ground state changes from zero to finite value. The single particle analysis shows that the ground energy level transition is induced by Zeeman energy level splitting. The momentum distributions of the ground state are given to provide an intuitive physical picture. This work can be further extended to the exploration of the heteroatom system, lattice system and higher spin system.

Valley- and spin-polarized broken-symmetry states of interacting electrons in gatedMoS2quantum dots

Understanding strongly interacting electrons enables the design of materials, nanostructures and devices. Developing this understanding relies on the ability to tune and control electron-electron interactions by, e.g., confining electrons to atomically thin layers of 2D crystals with reduced screening. The interplay of strong interactions on a hexagonal lattice with two nonequivalent valleys, topological moments, and the Ising-like spin-orbit interaction gives rise to a variety of phases of matter corresponding to valley and spin polarized broken symmetry states. In this work we describe a highly tunable strongly interacting system of electrons laterally confined to monolayer transition metal dichalcogenide MoS$_2$ by metalic gates. We predict the existence of valley and spin polarized broken symmetry states tunable by the parabolic confining potential using exact diagonalization techniques for up to $N=6$ electrons. We find that the ground state is formed by one of two phases, either both spin and valley polarized or valley unpolarised but spin intervalley antiferromagnetic, which compete as a function of electronic shell spacing. This finding can be traced back to the combined effect of Ising-like spin-orbit coupling and weak intervalley exchange interaction. These results provide an explanation for interaction-driven symmetry-breaking effects in valley systems and highlight the important role of electron-electron interactions for designing valleytronic devices.

First-Principles Study of Structural, Electronic and Thermoelectric Properties of Ni-Doped Bi2Se3

Direct conversion of waste heat to electrical energy could address present energy challenges. Bi2 Se3 is one of few thermoelectric materials known to operate at room temperature. Comprehensive analysis using density functional theory was conducted to explore the effect of nickel doping on structural, electronic, and thermoelectric properties of Bi2 Se3 . Local density approximation (LDA) was used with an addition of spin-orbit coupling (SOC) and van der Waals interaction scheme consideration. Analysis of the effect of SOC was elaborated. It was found that nickel has changed the crystal structure of Bi2 Se3 . Nickel has also changed band structure and density of state that alter the thermoelectric performance. The decreased band gap has decreased the thermopower. However, it gives advantages to the improvement of electrical conductivity. Higher electrical conductivity has risen thermal conductivity. Despite the decreased thermopower and increased thermal conductivity, the higher electrical conductivity has improved the overall thermoelectric performance of Bi2 Se3 when nickel is introduced.

Natural circular dichroism in the surface plasmon resonance and interband transition of noble metal nanocrystals induced by surface magnetism

Circular dichroism is typically used in the visible and ultraviolet wavelength range to study the structure of chiral substances which lacks inversion symmetry. When a magnetic dipole moment interferes the electric dipole transition, circular dichroism arises from achiral substances even in the absence of an applied magnetic field. Here, the experimental observation of natural circular dichroism in the surface plasmon resonances and interband transitions of spherical gold, silver, and copper nanocrystals in solution is presented. The anomalous circular dichroism is qualitatively explained by spin-orbit coupling and exchange interaction that occur through local magnetic moments from surface defects. The s-d and d-d exchange interactions occur between spins of adatoms and the conduction and d-band electrons. Dipolar and quadrupolar plasmon modes showed opposite sign of ellipticity (dipoles: −, quadrupoles: +), manifesting the conservation of orbital angular momentum and indicating the nature of an orbital excitation in the magnetoplasmon. The plasmon-mode dependent ellipticity was consistently observed at anisotropic nanocrystals including triangles, octahedra, decahedra, nanorods, and core-shell nanoparticles regardless of chirality and polarity of adsorbate molecules. Interband transitions in gold nanocrystals of small size showed a sign reversal to negative ellipticity, and thus the surface has magnetic moments of d-electrons opposite to the core.

Magneto-optic effects of monolayer transition metal dichalcogenides induced by Rashba spin-orbit coupling

The nontrivial magnetoopitcal effects are predicted to arise at the visible frequency range for monolayer transition metal dichalcogenides upon the application of magnetic exchange interactions. However, their magnetoopitcal rotation angles at the terahertz frequency range are always low, which hinders their practical applications in the terahertz magnetoopitcal devices. In this letter, we theoretically demonstrate that the magnetoopitcal effects of monolayer transition metal dichalcogenides at the terahertz frequency range can be enhanced and controlled via introducing the Rashba spin orbit coupling, whose rotation angles are comparable with those of conventional bulky magnetic materials. Such an effect originates from the change of spin-up and spin-down bands in the band structures of monolayer transition metal dichalcogenides when the Rashba spin orbit coupling and magnetic exchange interaction coexist, which enables the spin-flip intraband optical transitions and thus generates the terahertz magnetoopitcal responses. Our results open up possibilities for the use of Rashba spin orbit coupling to generate as well as control the magnetoopitcal effects in two-dimensional layered materials.

The Application of Organic Semiconductor Materials in Spintronics.

π-Conjugated semiconductors, primarily composed of elements with low atomic number, are regarded as promising spin-transport materials due to the weak spin–orbit coupling interaction and hence long spin relaxation time. Moreover, a large number of additional functions of organic semiconductors (OSCs), such as the abundant photo-electric properties, flexibility, and tailorability, endow the organic spintronic devices more unique properties and functionalities. Particularly, the integration of the photo-electric functionality and excellent spin transport property of OSCs in a single spintronic device has even shown great potential for the realization of spin manipulation in OSCs. In this review, the application of OSCs in spintronic study will be succinctly discussed. As the most important and extensive application, the long-distance spin transport property of OSCs will be discussed first. Subsequently, several multifunctional spintronic devices based on OSCs will be summarized. After that, the organic-based magnets used for the electrodes of spintronic devices will be introduced. Finally, according to the latest progress, spin manipulation in OSCs via novel spintronic devices together with other prospects and challenges will be outlined.

Tunable valley polarization, magnetic anisotropy and dipole moment for layered Janus 2H–VSSe with intrinsic room temperature ferromagnetism

Effects of strain, interlayer coupling and electric field on the valley polarization, magnetocrystalline anisotropy and dipole moment of layered Janus 2H–VSSe are systematically investigated by first-principles calculations. A unique V 3 d1 electronic configuration and strong electron coupling interaction guarantee the stable in-plane ferromagnetic ground states with Tc of 512 K. By considering spin-orbit coupling (SOC) and exchange interaction based on the effective Hamiltonian k•p model, a large valley splitting of 94.8 meV is observed, which is mainly contributed by the spontaneous magnetic exchange field and not SOC effect. Under various bi-axis strains, Janus 2H–VSSe monolayer still maintains intrinsic in-plane ferromagnetism, but exhibits tunable valley polarization and magnetocrystalline anisotropy, which are associated with the in-plane dx2-y2/dxy orbitals of V atoms. Importantly, stacking patterns can influence the spatial inversion symmetry and further alter the valley polarization for the layered Janus 2H–VSSe. Applied external electric-field can effectively control intrinsic built-in electric-field by charge redistribution in the vertical direction, which can remarkably change the dipole moments and slightly adjust the valley polarization. The layered Janus 2H–VSSe possesses intrinsic ferromagnetism, robust valley-contrasting physics and outfield-dependent dipole moment, making them competitive materials for practical applications in spin-valleytronics, optoelectronics and piezoelectric sensor.

Quantum Anomalous Hall Effect in Magnetic Doped Topological Insulators and Ferromagnetic Spin-Gapless Semiconductors-A Perspective Review.

Quantum anomalous Hall effect, with a trademark of dissipationless chiral edge states for electronics/spintronics transport applications, can be realized in materials with large spin-orbit coupling and strong intrinsic magnetization. After Haldane's seminal proposal, several models have been presented to control/enhance the spin-orbit coupling and intrinsic magnetic exchange interaction. After brief introduction of Haldane model for spineless fermions, following three fundamental quantum anomalous Hall models are discussed in this perspective review: i) low-energy effective four band model for magnetic-doped topological insulator (Bi,Sb)2 Te3 thin films, ii) four band tight-binding model for graphene with magnetic adatoms, and iii) two (three) band spinful tight-binding model for ferromagnetic spin-gapless semiconductors with honeycomb (kagome) lattice where ground state is intrinsically ferromagnetic. These models cover 2D Dirac materials hosting spinless, spinful, and spin-degenerate Dirac points where various mass terms open bandgap and lead to quantum anomalous Hall effect. With emphasis on the topological phase transition driven by ferromagnetic exchange interaction and its interplay with spin-orbit-coupling, various symmetry constraints on the nature of mass term and the materialization of these models are discussed. This study will shed light on the fundamental theoretical perspectives of quantum anomalous Hall materials.

Spin polarization in monolayer MoS2 in the presence of proximity-induced interactions

When monolayer (ML) MoS2 is placed on a substrate, the proximity-induced interactions such as the Rashba spin-orbit coupling (RSOC) and exchange interaction (EI) can be introduced. Thus, the electronic system can behave like a spintronic device. In this study, we present a theoretical study on how the presence of the RSCO and EI can lead to the band splitting, the lifting of the valley degeneracy and to the spin polarization in [Formula: see text]- and [Formula: see text]-type ML MoS2. We find that the maxima of the in-plane spin orientation in the conduction and valence bands in ML MoS2 depend on the Rashba parameter and the effective Zeeman field factor. At a fixed Rashba parameter, the minima of the split conduction band and the maxima of the split valence band along with the spin polarization in ML MoS2 can be tuned effectively by varying the effective Zeeman field factor. On the basis that the EI can be induced by placing the ML MoS2 on a ferromagnetic substrate or by magnetic doping in ML MoS2, we predict that the interesting spintronic effects can be observed in [Formula: see text]- and [Formula: see text]-type ML MoS2. This work can be helpful to gain an in-depth understanding of the basic physical properties of ML MoS2 for application in advanced electronic and optoelectronic devices.

Multiple odd-parity superconducting phases in bilayer transition metal dichalcogenides

We study unconventional superconductivity in a two-dimensional locally noncentrosymmetric triangular lattice. The model is relevant to bilayer transition metal dichalcogenides with $2{\mathrm{H}}_{b}$ stacking structure, for example. The superconducting instability is analyzed by solving the linearized Eliashberg equation within the random phase approximation. We show that ferromagnetic fluctuations are dominant owing to the existence of disconnected Fermi pockets near van Hove singularity, and hence odd-parity spin-triplet superconductivity is favored. In the absence of the spin-orbit coupling, we find that odd-parity $f$-wave superconducting state is stabilized in a wide range of carrier density and interlayer coupling. Furthermore, we investigate impacts of the layer-dependent staggered Rashba and Zeeman spin-orbit coupling on the superconductivity. Multiple odd-parity superconducting phase diagrams are obtained as a function of the spin-orbit coupling and Coulomb interaction. Especially, a topological chiral $p$-wave pairing state is stabilized in the presence of a moderate Zeeman spin-orbit coupling. Our results shed light on a possibility of odd-parity superconductivity in various ferromagnetic van der Waals materials.

Role of Multistate Intersections in Photochemistry.

It has been generally accepted that the intersection of potential energy surfaces can facilitate nonadiabatic transitions and plays a crucial role in photochemistry. Although most previous studies have focused on the conical intersection of two electronic states, multistate intersections are common in polyatomic molecules, and their key roles in photochemistry have been uncovered by electronic structure calculations and nonadiabatic dynamics simulations. In this Perspective, the algorithms for searching two- or three-state intersections are first examined with an emphasis on the latest development in a general algorithm for location of multistate intersections. Then, we focus on intersystem crossing (ISC) that occurs in the region of multistate intersection, paying more attention to how the state-specific spin-orbit coupling interaction influences nonadiabatic ISC processes. Finally, the interweaving of nonadiabatic dynamics simulation and electronic structure calculation has been recognized as a correct way to ascertain the vital roles of multistate intersections in photochemical reactions.

Effect of structural and magnetic disorder on the 3d−5d exchange interactions in La2−xCaxCoIrO6

The delicate balance between spin-orbit coupling, Coulomb repulsion and crystalline electric field interactions observed in Ir-based oxides is usually manifested as exotic magnetic behavior. Here we investigate the evolution of the exchange coupling between Co and Ir for partial La substitution by Ca in La$_{2}$CoIrO$_6$. A great advantage of the use of Ca$^{2+}$ as replacement for La$^{3+}$ is the similarity of its ionic radii. Thus, the observed magnetic changes can more easily be associated to electronic variations. A thorough investigation of the structural, electronic and magnetic properties of the La$_{2-x}$Ca$_{x}$CoIrO$_6$ system was carried out by means of synchrotron x-ray powder diffraction, muon spin rotation and relaxation ($\mu$SR), AC and DC magnetization, XAS, XMCD, Raman spectroscopy, electrical resistivity and dielectric permittivity. Our XAS results show that up to 25% of Ca substitution at the La site results in the emergence of Co$^{3+}$, possibly in high spin state, while the introduction of larger amount of Ca leads to the increase of Ir valence. The competing magnetic interactions resulting from the mixed valences lead to a coexistence of a magnetically ordered and an emerging spin glass (SG) state for the doped samples. Our $\mu$SR results indicate that for La$_{2}$CoIrO$_6$ a nearly constant fraction of a paramagnetic (PM) phase persists down to low temperature, possibly related to the presence of a small amount of Ir$^{3+}$ and to the anti-site disorder at Co/Ir sites. For the doped compounds the PM phase freezes below 30 K, but there is still some dynamics associated with the SG. The dielectric data obtained for the parent compound and the one with 25% of Ca-doping indicate a possible magnetodielectric effect, which is discussed in terms of the electron hopping between the TM ions, the anti-site disorder and the distorted crystalline structure.

Theoretical studies of the g factors and local structures of the Ni3+ centers in Na2Zn(SO4)2·4H2O and K2Zn(SO4)2·6H2O crystals

The local structures and the g factors gi (i = x, y, z) for Ni3+ centers in Na2 Zn(SO4 )2 ·4H2 O (DPPH) and K2 Zn(SO4 )2 ·6H2 O (PHZS) crystals are theoretically studied by using the perturbation formulas of the g factors for a 3d7 ion with low spin (S = 1/2) in orthorhombically compressed octahedra. In these formulas, the contributions to g factors from both the spin-orbit coupling interactions of the central ion and ligands are taken into account, and the required crystal-field parameters are estimated from the superposition model and the local geometry of the systems. Based on the calculations, the Ni-O bonds are found to suffer the axial compression δz (or Δz) of about 0.111 Å (or 0.036 Å) along the z-axis for Ni3+ centers in DPPH (or PHZS) crystals. Meanwhile, the Ni-O bonds may experience additional planar bond length variation δx (≈0.015 Å) along x- and y-axes for the orthorhombic Ni3+ center in DPPH. The theoretical g factors agree well with the experimental data. The obtained local structural parameters for both Ni3+ centers are discussed.

Effect of Coulomb interactions on optoelectronic properties of Eu doped lanthanide stannates pyrochlore: DFT ​+ ​U investigations

In optoelectronics, the perovskite structures in layered form, also called pyrochlore have been demonstrated to be very largely favorable to the insertion of lanthanides ions, which led them to create new phosphor emitting in a broad spectral range going from visible to near infrared. The pyrochlore oxides such as La2Sn2O7 have attained much interest due to their electronic and optical properties. In the present work, we used first-principle calculations to compute the electronic band structure and related optical properties for pure La2Sn2O7 and La2Sn2O7 doped with europium. Spin orbit coupling (SOC) and electron-electron interaction, both within the generalized gradient approximation plus Hubbard parameter U (SOC ​+ ​GGA ​+ ​U) approximations have been used within the framework of density functional theory (DFT). It was found that La2Sn2O7 compound exhibits a direct band gap semiconductor with 2.7 ​eV. Doping of europium further decreases the band gap of pyrochlore of material up to 1.8 ​eV. Optical properties revealed that both compounds are potential materials for optoelectronic device fabrication.

Real-Space Imaging of a Single-Molecule Monoradical Reaction.

Organic radicals consisting of light elements exhibit a low spin-orbit coupling and weak hyperfine interactions with a long spin coherence length, which are crucial for future applications in molecular spintronics. However, the synthesis and characterization of these organic radicals have been a formidable challenge due to their chemical instability arising from unpaired electrons. Here, we report a direct imaging of the surface chemical transformation of an organic monoradical synthesized via the monodehydrogenation of a chemically designed precursor. Bond-resolved scanning tunneling microscopy unambiguously resolves various products formed through a complex structural dissociation and rearrangement of organic monoradicals. Density functional theory calculations reveal detailed reaction pathways from the monoradical to different cyclized products. Our study provides unprecedented insights into complex surface reaction mechanisms of organic radical reactions at the single molecule level, which may guide the design of stable organic radicals for future quantum technology applications.

Unconventional free charge in the correlated semimetal Nd2Ir2O7

Nd2Ir2O7 is a correlated semimetal with the pyrochlore structure, in which competing spin-orbit coupling and electron-electron interactions are believed to induce a time-reversal symmetry broken Weyl semimetal phase characterized by pairs of topologically protected Dirac points at the Fermi energy. However, the emergent properties in these materials are far from clear, and exotic new states of matter have been conjectured. Here we demonstrate optically that at low temperatures the free carrier spectral weight is proportional to T^2 where T is the temperature, as expected for massless Dirac electrons. However, we do {\em not} observe the corresponding T^3 term in the specific heat. That the system is not in a Fermi liquid state is further corroborated by the "Planckian" T-linear temperature dependence of the momentum relaxation rate and the progressive opening of a correlation-induced gap at low temperatures. These observations can not be reconciled within the framework of band theory of electron-like quasiparticles and point toward the effective decoupling of the charge transport from the single particle sector.

Influence of a magnetic field on Rashba spin–orbit interaction in an anisotropic quantum dot

The influence of a magnetic field on the Rashba spin–orbit interaction in an anisotropic quantum dot is theoretically studied, and the expression of the ground state energy of a magnetopolaron is obtained with the Pekar variational method. The ground state energy of the magnetopolaron splits into two branches due to the Rashba effect, and the splitting appears saturated phenomenon with increasing the transverse and longitudinal effective confinement lengths. Because the contribution of the magnetic field cyclotron resonance frequency to the Rashba spin–orbit splitting is a positive value, the energy spacing becomes larger as the magnetic field cyclotron resonance frequency increases. Due to the spin–orbit coupling interaction, the energy splits at zero magnetic field. The total energy is reduced due to the presence of phonons. Therefore, the polaron state is more stable than the bare electron state, and the polaron energy splitting is more stable.

Spin orbit coupling effects on the non-collinear magnetism of structurally relaxed Fe/Cu (001) thin films: First principles calculations

The effect of the spin–orbit coupling interaction and atomic relaxation, on the ground state non-collinear magnetism of deposited Fe thin films, on a Cu (001) surface, is studied by using first principles density functional theory calculations. The total energy values and spin and orbital magnetic local moments are calculated for a Fe film of N = 6 atomic layers deposited on a 12 layer thick Cu film playing the role of substrate. As a first step, we allow the thin film and surface layers to atomically relax. We found important contractions of about 20% between the first and second, the third and fourth, and firth and sixth Fe layers. Then, we obtain collinear and non-collinear magnetic arrangements which agree with the main experimental resultssatte that show a non-collinear configuration at low temperatures (around 40 K). The magnetic properties of the first four Fe layers are well reproduced. The agreement is better than the results obtained ignoring the spin–orbit coupling and the structure relaxation. Although both calculations predict non-collinear configurations with energy values slightly above that of a collinear ground state. In some cases, the energy differences between two collinear (or non-collinear) solutions with different spin orientation axis is only under the value of one meV. The calculated orbital local moment arrangements are clearly similar to the spin magnetic local moment ones and show a correct dependence on the dimensionality aspects of the system when changing the spin axis quantization direction.