Spin-orbit Coupling Interaction Research Articles

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.

Enhanced spin-orbit coupling and orbital moment in ferromagnets by electron correlations

In atomic physics, the Hund's rule states that the largest spin and orbital state is realized due to the interplay of spin-orbit coupling (SOC) and Coulomb interactions. Here, we show that in ferromagnetic solids the effective SOC and the orbital magnetic moment can be dramatically enhanced by a factor of $1/[1\ensuremath{-}(2{U}^{\ensuremath{'}}\ensuremath{-}U\ensuremath{-}{J}_{H}){\ensuremath{\rho}}_{0}]$, where $U$ and ${U}^{\ensuremath{'}}$ are the on-site Coulomb interaction within the same orbitals and between different orbitals, respectively, ${J}_{H}$ is the Hund's coupling, and ${\ensuremath{\rho}}_{0}$ is the average density of states. This factor is obtained by using the two-orbital as well as five-orbital Hubbard models with SOC. We also find that the spin polarization is more favorable than the orbital polarization, being consistent with experimental observations. The theory is also extended to study the spin fluctuations and long-range Coulomb interactions, and can be applied to understand the enhanced orbital magnetic moment and giant Faraday effect in ferromagnetic nanogranules in recent experiments. This present paper provides a fundamental basis for understanding the enhancements of SOC and orbital moment by Coulomb interactions in ferromagnets, which would have wide applications in spintronics.

Raman laser induced self-organization with topology in a dipolar condensate.

We investigate the ground states of a dipolar Bose-Einstein condensate (BEC) subject to Raman laser induced spin-orbit coupling with mean-field theory. Owing to the interplay between spin-orbit coupling and atom-atom interactions, the BEC presents remarkable self-organization behavior and thus hosts various exotic phases including vortex with discrete rotational symmetry, stripe with spin helix, and chiral lattices with C4 symmetry. The peculiar chiral self-organized array of square lattice, which spontaneously breaks both U(1) and rotational symmetries, is observed when the contact interaction is considerable in comparison with the spin-orbit coupling. Moreover, we show that the Raman-induced spin-orbit coupling plays a crucial role in forming rich topological spin textures of the chiral self-organized phases by introducing a channel for atoms to turn on spin flipping between two components. The self-organization phenomena predicted here feature topology owing to spin-orbit coupling. In addition, we find long-lived metastable self-organized arrays with C6 symmetry in the case of strong spin-orbit coupling. We also present a proposal to observe these predicted phases in ultracold atomic dipolar gases with laser-induced spin-orbit coupling, which may stimulate broad theoretical as well as experimental interest.

Evidence of the Anomalous Fluctuating Magnetic State by Pressure-Driven 4f Valence Change in EuNiGe3.

In rare-earth compounds with valence fluctuation, the proximity of the 4f level to the Fermi energy leads to instabilities of the charge configuration and the magnetic moment. Here, we provide direct experimental evidence for an induced magnetic polarization of the Eu3+ atomic shell with J = 0, due to intra-atomic exchange and spin-orbital coupling interactions with the Eu2+ atomic shell. By applying external pressure, a transition from antiferromagnetic to a fluctuating behavior in EuNiGe3 single crystals is probed. Magnetic polarization is observed for both valence states of Eu2+ and Eu3+ across the entire pressure range. The anomalous magnetism is discussed in terms of a homogeneous intermediate valence state where frustrated Dzyaloshinskii-Moriya couplings are enhanced by the onset of spin-orbital interaction and engender a chiral spin-liquid-like precursor.

Recent Progress of Organic Semiconductor Materials in Spintronics.

Spintronics, a new discipline focusing on the spin-dependent transport process of electrons, has been developing rapidly. Spin valves are the most significant carriers of spintronics utilizing the spin freedom of electrons. It is expected to pierce "Moore's Law" and become the core component in processors of the next generation. Organic semiconductors advance in their adjustable band gap, weak spin-orbit coupling and hyperfine interaction, excellent film-forming property, having enormous promise for spin valves. Here, the principle of spin valves is introduced, and the history and progress in organic spin injection and transport materials are summarized. Then we analyze the influence of spinterface on device performance and introduce reliable methods of constructing organic spin valves. Finally, the challenges for spin valves are discussed, and the future is proposed. We aim to draw the attention of researchers to organic spin valves and promote further research in spintronics through this paper.

Origin and regulation of triaxial magnetic anisotropy in the ferromagnetic semiconductor CrSBr monolayer.

Magnetic anisotropy plays a vital role in stabilizing the long-range magnetic order of two-dimensional ferromagnetic systems. In this work, using the first-principles method, we systematically explored the triaxial magnetic anisotropic properties of a ferromagnetic semiconductor CrSBr monolayer, which is recently exfoliated from its bulk. Further analysis shows that the triaxial magnetic anisotropic properties originate from the coexistence of the magnetic dipole-dipole interaction (shape anisotropy) and the spin-orbit coupling interaction (magnetocrystalline anisotropy). Interestingly, the shape anisotropy, which has been neglected in most previous works, dominates over the magnetocrystalline anisotropy. Besides, the experimental Curie temperature of the CrSBr monolayer is well reproduced using Monte Carlo simulations. What is more, the easy magnetic axes and ferromagnetism in the CrSBr monolayer can be manipulated by strains and are relatively more susceptible to the uniaxial strain in the x direction. Our study not only explains the mechanism of triaxial magnetic anisotropy of the CrSBr monolayer, but also sheds light on how to tune the magnetic anisotropy and Curie temperature in ferromagnetic monolayers.

Tunable electrical properties and multiple-phases of ferromagnetic GdS2, GdSe2 and Janus GdSSe monolayers.

With the continuous miniaturization and integration of spintronic devices, the two-dimensional (2D) ferromagnet coupling of ferromagnetic and diverse electrical properties has become increasingly important. Herein, we report three ferromagnetic monolayers: GdS2, GdSe2 and Janus GdSSe. They are bipolar magnetic semiconductors and demonstrate ferroelasticity with a large reversible strain of 73.2%. Three monolayers all hold large magnetic moments of about 8μB f.u.-1 and large spin-flip energy gaps in both the conduction and valence bands, which are highly desirable for applications in bipolar field effect spin filters and spin valves. Our calculations have testified to the feasibility of the experimental achievement of the three monolayers and their stability. Additionally, intrinsic valley polarization occurs in the three monolayers owing to the cooperative interplay between spin-orbit coupling and magnetic exchange interaction. Moreover, we identified square lattices for GdS2 and GdSe2 monolayers. The new and stable square lattices of GdS2 and GdSe2 monolayers show robust ferromagnetism with high Curie temperatures of 648 and 312 K, respectively, and the characteristics of spin-gapless semiconductors. Overall, these findings render GdS2, GdSe2 and Janus GdSSe monolayers promising candidate materials for multifunctional spintronic devices at the nanoscale.

Electronic properties of graphene/CdX (X=S, Se, and Te) semiconductor heterostructure and a proposal of all-optical injection and detection of electron spins in graphene

Graphene was predicted to have a long spin relaxation time in the range of microseconds to milliseconds due to its weak spin-orbit coupling and hyperfine interaction. However, very short spin relaxation times were measured experimentally on the order of nanoseconds. Magnetic proximity effect from spin valves were considered strongly to influence the electronic and spin properties in graphene. Here, a graphene/nonmagnetic semiconductor CdX heterostructure is proposed to eliminate the magnetic effect and to fulfill optical injection of spin polarization. Based on the first-principles calculation within the density functional theory, we perform a systematic study on the structural, electronic properties and band structures of the heterostructures, and find that graphene on CdX (X = S, Se and Te) slabs preserves its linear Dirac band structure within the bandgap of CdX, and a built-in electric field occurs near the interface. The built-in electric field drives spin polarized electrons into graphene preferably. An optical detection scheme of spin relaxation time of graphene is proposed based on Faraday and Hanle effects. • A graphene/nonmagnetic semiconductor heterostructure constructed to eliminate strong magnetic effects on spin relaxation time of electrons in graphene. • First-principles calculations reveal Graphene on CdX (X = S, Se and Te) slabs preserves its linear Dirac band structure which locates within the bandgap of CdX. • A built-in electric field exists within interface, which favor spin polarized electrons transported into graphene. • A new scheme of all-optical injection and detection of electron spin is proposed to measure true long spin relaxation time of graphene.

Effect of Rashba spin-orbit coupling interaction on energy states of silicon disk-shaped quantum dot

Silicon quantum dots (QDs) are considered an excellent platform for spin qubits due to their weak spin-orbit interaction (SOI). Indeed, due to quantum confinement, novel spin properties arise from the SOI. In this work, we have studied the influence of the Rashba SOI and the confinement potential on the energy spectrum of an electron confined in a Silicon disk-shaped quantum dot, in the presence of an external magnetic field. The effects of the QD size, the confinement potential and the Rashba alpha coefficient on the energy levels are also studied. We used the effective mass approximation to determine the energy levels and their wave functions for different states. The results are presented as a function of the magnetic field in the presence and absence of SOI. We find that the energy levels of the electrons behave very differently depending on the magnetic field. The energy of all states changes with increasing magnetic field and each energy level splits into two and the energy difference between these two levels also increases with magnetic field, in the presence and absence of SOI. The energy levels are proportional to the Rashba alpha coefficient and inversely proportional to the radius of the QD.

Pairing of fermions under spin-orbit coupling in two dimensions

We present a theoretical approach to the problem of two-dimensional fermion pairing under spin-orbit (SO) coupling and Zeeman interaction with an external magnetic field. We introduce a generic pairing Hamiltonian operating in the Hilbert space spanning free pairs and bare two-body bound states. The SO coupling of Rashba or Dresselhaus type provides $p$-wave dressing of an $s$-wave spin-singlet bound state by continua in the triplet scattering channels. In the strong-coupling (Bose-Einstein condensate) limit of the many-body fermion system at zero temperature our theory maps onto the two-channel Fano-Anderson model of a spinless resonant $p$-wave superfluid.

Spontaneous Valley Polarization in a Ferromagnetic Fe(OH)2 Monolayer

At present, creating sizable spontaneous valley polarization is at the center of the study of valleytronics, which, however, is still a huge challenge. In this work, we determined that the ferromagnetic Fe(OH)2 monolayer of the hexagonal lattice is a highly appealing candidate for valleytronics by using first-principles calculations in conjunction with tight-binding model analysis. In light of the simultaneous inversion symmetry breaking and time-reversal symmetry breaking, we illustrated that the strong spin-orbit coupling and robust ferromagnetic exchange interaction cause a spontaneous valley polarization as large as 67 meV for Fe(OH)2, indicative of room-temperature application. In addition, the physics of valley-selective circular dichroism, spin/valley Hall effects, and topological phase transition were also discussed.

Role of spin currents on electron-electron interaction in the quantum spin Hall phase

The spin current density functional theory (SCDFT) is the generalization of the standard DFT to treat a fermionic system embedded in the effective external field produced by the spin-orbit coupling interaction. Even in the absence of a spin polarization, the SCDFT requires the electron-electron potential to depend on the spin currents ${\mathbf{J}}^{x}, {\mathbf{J}}^{y}$, and ${\mathbf{J}}^{z}$, which only recently was made possible for practical relativistic quantum-mechanical simulations, through the inclusion of a fraction of nonlocal Fock exchange into local-density or generalized-gradient density functional approximations [J. K. Desmarais, J.-P. Flament, and A. Erba, Phys. Rev. B 102, 235118 (2020)]. Here, we apply the SCDFT to the quantum spin Hall phase and show how it improves (even qualitatively) the description of its electronic features relative to the DFT. We study the Bi (001) 2D bilayer and its band insulator to topological insulator phase transition (via $s+{p}_{z}\ensuremath{\leftrightarrow}{p}_{x}+i{p}_{y}$ band inversion) as a function of mechanical strain. We show that the explicit account of spin currents in the electron-electron potential of the SCDFT is key to the appearance of a Dirac cone at the $\mathrm{\ensuremath{\Gamma}}$ point in the valence band structure at the onset of the topological phase transition. Finally, the valence band structure of this system is rationalized using a simple first-order $\mathbf{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{p}$ quasidegenerate perturbation theory model.

Magnetic anisotropy energies and metal-insulator transitions in monolayers of α−RuCl3 and OsCl3 on graphene

Transition metal thriclorides, with $4d$ or $5d$ electrons, are materials at the forefront of recent studies about the interplay of spin-orbit coupling and strong Coulomb interactions. Within our first-principles calculations (DFT+$U$+SOC) we study the effects of graphene on the electronic and magnetic properties of the monolayers of $\alpha$-RuCl$_3$ and OsCl$_3$. Despite the spatially inhomogeneous $n$-type doping induced by graphene, we show that the occupancy of the upper Hubbard bands of MLs of \rucl and OsCl$_3$ can be tuned through external electric fields, and allows the control of (i) metal-insulator transitions, and (ii) the magnetic easy-axis and anisotropy energies. Our findings point towards the tunning of electronic and magnetic properties of transition metal thriclorides monolayers by using graphene and external electronic fields.

Ru-Doping-Induced Spin Frustration and Enhancement of the Room-Temperature Anomalous Hall Effect in La2/3 Sr1/3 MnO3 Films.

In transition-metal-oxide heterostructures, the anomalous Hall effect (AHE) is a powerful tool for detecting the magnetic state and revealing intriguing interfacial magnetic orderings. However, achieving a larger AHE at room temperature in oxide heterostructures is still challenging due to the dilemma of mutually strong spin-orbit coupling and magnetic exchange interactions. Here, Ru-doping-enhanced AHE in La2/3 Sr1/3 Mn1-x Rux O3 epitaxial films is exploited. As the B-site Ru doping level increases up to 20%, the anomalous Hall resistivity at room temperature can be enhanced from nΩ cm to µΩcm scale. Ru doping leads to strong competition between the ferromagnetic double-exchange interaction and the antiferromagnetic superexchange interaction. The resultant spin frustration and spin-glass state facilitate a strong skew-scattering process, thus significantly enhancing the extrinsic AHE. The findings can pave a feasible approach for boosting the controllability and reliability of oxide-based spintronic devices.

Collective Spin Modes in Fermi Liquids with Spin–Orbit Coupling

A combination of spin-orbit coupling and electron-electron interaction gives rise to a new type of collective spin modes, which correspond to oscillations of magnetization even in the absence of the external magnetic field. We review recent progress in theoretical understanding and experimental observation of such modes, focusing on three examples of real-life systems: a two-dimensional electron gas with Rashba and/or Dresselhaus spin-orbit coupling, graphene with proximity-induced spin-orbit coupling, and the Dirac state on the surface of a three-dimensional topological insulator. This paper is dedicated to the 95th birthday of Professor Emmanuel I. Rashba.

Topological defects of dipolar bose-einstein condensates with dresselhaus spin-orbit coupling in an anharmonic trap

We consider the topological defects and spin structures of binary Bose-Einstein condensates (BECs) with Dresselhaus spin-orbit coupling (D-SOC) and dipole-dipole interaction (DDI) in an anharmonic trap. The combined effects of D-SOC, DDI and anharmonic trap on the ground-state phases of the system are analyzed. Our results show various structural phase transitions can be achieved by adjusting the magnitudes of the D-SOC and DDI. Meantime, a ground-state phase diagram is given as a function of the D-SOC and DDI strengths. In addition, we find that tuning the D-SOC and the DDI can derive novel rich topological configurations, including ghost vortex, half-quantum vortex, skyrmion pair, vertical skyrmion string and horizontal skyrmion string.

Magnetoelectric polarizability and optical activity: Spin and frequency dependence

We extend a microscopic theory of polarization and magnetization to include the spin degree of freedom of the electrons, introducing a general spin-orbit coupling and Zeeman interaction term in the Hamiltonian. At finite frequencies and including spin, the magnetoelectric polarizability tensor is replaced by two separate tensors, one that relates the polarization P to the magnetic field B and a separate tensor that relates the magnetization M to the electric field E. When combined with other relevant response tensors a third-rank tensor that relates the induced current density to gradients in the electric field can be introduced; it is gauge invariant, in a form suitable for numerical calculations, and describes optical activity---including spin effects---even in materials that may lack time-reversal symmetry.

Out-of-plane ferromagnetism in two-dimensional 1T−RhO2

Using the combined theoretical approaches, the structural, electronic, and magnetic properties of the two-dimensional (2D) $1T$ phase of monolayer ${\mathrm{RhO}}_{2}$ were studied. Density-functional theory plus $U$ calculation indicate that $1T\text{\ensuremath{-}}{\mathrm{RhO}}_{2}$ favors a ferromagnetic metallic phase with an out-of-plane magnetization, and it can be achieved by exfoliation from the layered bulk oxides containing monolayer $1T\text{\ensuremath{-}}{\mathrm{RhO}}_{2}$. Monte Carlo simulation shows that the ferromagnetic phase is stable below the Curie temperature of 73.9 K based on the Heisenberg Hamiltonian model. Magnetic anisotropy energy and its cause were further investigated to understand the microscopic origin of the 2D magnetization. Our results indicate that spin-orbit coupling interaction between Rh $4d$ stabilizes perpendicular magnetic anisotropy, resulting in the out-of-plane magnetization, over in-plane magnetic anisotropy. In addition, mechanical tensile strain can strengthen perpendicular magnetic anisotropy by increasing positive contribution of the interaction to the magnetic anisotropy energy.

Tunning magnetism and anisotropy by ferroelectric polarization in 2D van der Waals multiferroic heterostructures

Since the successful exfoliation of two-dimensional (2D) magnetic CrI3 film, an increasing interest of research is the 2D analog of fascinating physical property of 3D material, of which the most attractive for both fundamental research and practical applications is the achieving effective magnetoelectric coupling and manipulation in 2D van der Waals (vdW) multiferroic heterostructure (HS). Herein, we report the discovery of ferroelectrically tunable orbital reconstruction in α-RuCl3/CuInP2S6 2D vdW HSs, enabling the remarkable transitions of magnetic ordering from proximate quantum spin-liquid state to ferromagnetic as well as the easy magnetization axis tuning from in-plane to out-of-plane direction. In addition, Monte Carlo simulation verified that, α-RuCl3 would transform into a perpendicular ferromagnetic material with Curie temperature of 89 K when the ferroelectric polarization points to α-RuCl3. Furthermore, by analyzing the density of states and the d-orbital-resolved magnetocrystalline anisotropy energy (MAE) of Ru atoms based on the second-order perturbation theory we elucidate that the contribution to MAE from the spin-orbit coupling interaction between d orbitals of Ru atoms show a transition from positive to negative, and ultimately dominating the MAE variation from easy-plane to easy-axis magnetization upon the reversible FE polarization. Therefore, the CuInP2S6 nonvolatile ferroelectric switching enables the nonvolatile electrical control of magnetic ordering and anisotropy. This work paves the way for exploring high-efficiency nanodevices and nonvolatile information storage based on the multiferroic 2D vdW HSs.