Various multi-spin magnetic exchange interactions (MEI) of chiral nature have been recently unveiled. Owing to their potential impact on the realisation of twisted spin-textures, their implication in spintronics or quantum computing is very promising. Here, I address the long-range behavior of multi-spin MEI on the basis of a multiple-scattering formalism implementable in Green functions based methods. I consider the impact of spin-orbit coupling (SOC) as described in the one- (1D) and two-dimensional (2D) Rashba model, from which the analytical forms of the four- and six-spin interactions are extracted and compared to the bilinear isotropic, anisotropic and Dzyaloshinskii-Moriya interactions (DMI). Similarly to the DMI between two sites $i$ and $j$, there is a four-spin chiral vector perpendicular to the bond connecting the two sites. The oscillatory behavior of the MEI and their decay as function of interatomic distances are analysed and quantified for the Rashba surfaces states characterizing Au surfaces. The interplay of beating effects and strength of SOC gives rise to a wide parameter space where chiral MEI are more prominent than the isotropic ones. The multi-spin interactions for a plaquette of $N$ magnetic moments decay like $\{q_F^{N-d} P^{\frac{1}{2}(d-1)}L\}^{-1}$ simplifying to $\{q_F^{N-d} R^{\left[1+\frac{N}{2}(d-1)\right]}N\}^{-1}$ for equidistant atoms, where $d$ is the dimension of the mediating electrons, $q_F$ the Fermi wave vector, $L$ the perimeter of the plaquette while $P$ is the product of interatomic distances. This recovers the behavior of the bilinear MEI, $\{q_F^{2-d} R^{d}\}^{-1}$, and shows that increasing the perimeter of the plaquette weakens the MEI. More important, the power-law pertaining to the distance-dependent 1D MEI is insensitive to the number of atoms in the plaquette in contrast to the linear dependence associated with the 2D MEI.
We study a microscopic derivation and the properties of the Dzyaloshinskii-Moriya interaction (DMI) between local magnetic moments in ferromagnet/heavy metal heterostructures. First, we derive DMI by Ruderman-Kittel-Kasuya-Yosida interaction through electrons in a heavy metal with Rashba spin orbit interaction (SOI). Next, we study the dependences of the DMI on the Rashba SOI, lattice constant, and chemical potential. We find that the DMI amplitude increases linearly when the Rashba SOI is small, has a maximum when the Rashba SOI is comparable to the hopping integral, and decreases when the Ra…
We propose that existence of local orbital angular momentum (OAM) on the surfaces of high-Z materials play a crucial role in the formation of Rashba-type surface band splitting. Local OAM state in a Bloch state produces asymmetric charge distribution (electric dipole). Presence of surface electric field aligns the electric dipole and results in chiral OAM states and the relevant Rashba- type splitting. Therefore, the band splitting originates from electric dipole interaction, not from the Zeeman splitting as proposed in the original Rashba picture. The characteristic spin chiral structure of R…
We present the Fermi-surface map of the spin-chiral bulk states for the non-centrosymmetric semiconductor BiTeI using de Haas-van Alphen and Shubnikov-de Haas oscillations. We identify two distinct Fermi surfaces with a unique spindle-torus-type topology and the non-trivial Berry phases, confirming the spin chirality with oppositely circulating spin-texture. Near the quantum limit at high magnetic fields, we find a substantial Zeeman effect with an effective g-factor of ~ 60 for the Rashba-split Fermi surfaces. These findings provide clear evidence of strong Rashba and Zeeman coupling in the b…
We investigate theoretically the Rashba spin-orbit interaction in InAs/GaSb quantum wells(QWs). We find that the Rashba spin-splitting (RSS) depends sensitively on the thickness of the InAs layer. The RSS exhibits nonlinear behavior for narrow InAs/GaSb QWs and the oscillating feature for wide InAs/GaSb QWs. The nonlinear and oscillating behaviors arise from the weakened and enhanced interband coupling. The RSS also show asymmetric features respect to the direction of the external electric field.
The spin-degeneracy of Bloch bands in a crystal can be lifted when spin-orbit (SO) coupling is present and inversion symmetry is absent. In two-dimensional electron systems (2DES) spin-degeneracy is lifted by Rashba interaction terms - symmetry invariants that are scalar products of spin and orbital axial vectors. Rashba interactions are symmetry allowed whenever a 2DES is not invariant under reflections through the plane it occupies. In this paper, we use a tight-binding model informed by ab initio electronic structure calculations to develop a theory of Rashba splitting in the t2g bands of t…
Elementary electronic excitation is studied theoretically for a 2DEG in the presence of spin orbit (SO) interaction induced by Rashba effect. In such a system, coupled plasmon-phonon excitation can be achieved via intra- and inter-SO electronic transitions. As a result, six branches of the coupled plasmon-phonon oscillations can be observed. The interesting features of these excitation modes are analyzed.
Realizing topological magnetism and its electric control are intensive topics in the spintronics due to their promising applications in information storage and logic technologies. Here we unveil that both can be achieved in the two-dimensional (2D) magnetoelectric multiferroics. Using first-principles calculations, we show that strong Dzyaloshinskii-Moriya interaction (DMI), which is the key ingredient for the formation of exotic chiral magnetism, could be induced in 2D multiferroics with vertical electric polarization via Rashba effect. We verify that such significant DMI can promote sub-10 n…
In the giant Rashba semiconductor BiTeI electronic surface scattering with Lorentzian linewidth is observed that shows a strong dependence on surface termination and surface potential shifts. A comparison with the topological insulator Bi2Se3 evidences that surface confined quantum well states are the origin of these processes. We notice an enhanced quasiparticle dynamics of these states with scattering rates that are comparable to polaronic systems in the collision dominated regime. The Eg symmetry of the Lorentzian scattering contribution is different from the chiral (RL) symmetry of the cor…
Recently a new propagating mode of coupled charge and spin oscillations was predicted in a two dimensional electron gas with a sufficiently strong Rashba interaction. We show that Coulomb interactions qualitatively modifies the spectrum and increases the characteristic wavelength of this mode by orders of magnitude, but does not suppress it. An absorption experiment that can conclusively detect the presence or absence of such a propagating mode is proposed.
The newly discovered two-dimensional magnetic semiconductors such as CrI$_3$ have triggered a surge of interest stemming from their exotic spin-dependent properties and potential applications in spintronics and magneto-optoelectronics. Using first-principle density-functional-theory calculations, we investigate the properties of the spin-polarization texture in momentum space in the prototype 2D centrosymmetric ferromagnetic (FM) bilayer of CrI$_3$, with perpendicular magnetization. The FM bilayer displays a rich in-plane spin texture in its highest valence bands. We show the existence of two …
The spin-dependent density of states and the density of spin polarization of an InAs-based two-dimensional electron gas with the Rashba spin-orbit coupling under an intense terahertz laser field are investigated by utilizing the Floquet states to solve the time-dependent Schrödinger equation. It is found that both densities are strongly affected by the terahertz laser field. Especially a terahertz magnetic moment perpendicular to the external terahertz laser field in the electron gas is induced. This effect can be used to convert terahertz electric signals into terahertz magnetic ones efficien…
We investigate the influence on the density of states and the density of spin polarization for a two-dimensional hole gas with Rashba spin-orbit coupling under intense terahertz laser fields. Via Floquet theorem, we solve the time-dependent Schrödinger equation and calculate these densities. It is shown that a terahertz magnetic moment can be induced for low hole concentration. Different from the electron case, the induced magnetic moment is quite anisotropic due to the anisotropic spin-orbit coupling. Both the amplitude and the direction of the magnetic moment depend on the direction of the t…
We report the angular dependence of magnetoresistance in two-dimensional electron gas at LaAlO$_3$/SrTiO$_3$ interface. We find that this interfacial magnetoresistance exhibits a similar angular dependence to the spin Hall magnetoresistance observed in ferromagnet/heavy metal bilayers, which has been so far discussed in the framework of bulk spin Hall effect of heavy metal layer. The observed magnetoresistance is in qualitative agreement with theoretical model calculation including both Rashba spin-orbit coupling and exchange interaction. Our result suggests that magnetic interfaces subject to…
We study the spin relaxation torque in nonmagnetic or ferromagnetic metals with nonuniform spin-orbit coupling within the Keldysh Green's function formalism. In non-magnet, the relaxation torque is shown to arise when the spin-orbit coupling is not uniform. In the absence of an external field, the spin current induced by the relaxation torque is proportional to the vector chirality of Rashba-type spin-orbit field (RSOF). In the presence of an external field, on the other hand, spin relaxation torque arises from the coupling of the external field and vector chirality of RSOF. Our result indicat…
Strong spin-orbit coupling in noncentrosymmetric materials and interfaces results in remarkable physical phenomena, such as nontrivial spin textures, which may exhibit Rashba, Dresselhaus, and other intricated configurations. This provides a promising basis for nonvolatile spintronic devices and further implications. Here, we simulate from first principles a two-dimensional electron gas in ultrathin platinum and palladium layers grown on ferroelectric PbTiO$_3$(001). The latter allows, in principle, to switch and control the spin-to-charge conversion by the polarization reversal. We show how t…
The possibility of utilizing the rich spin-dependent properties of graphene has attracted great attention in pursuit of spintronics advances. The promise of high-speed and low-energy consumption devices motivates a search for layered structures that stabilize chiral spin textures such as topologically protected skyrmions. Here we demonstrate that chiral spin textures are induced at graphene/ferromagnetic metal interfaces. This is unexpected because graphene is a weak spin-orbit coupling material and is generally not expected to induce sufficient Dzyaloshinskii-Moriya interaction to affect magn…
A nonequilibrium Green's functions approach to spin-Hall effect is developed in a diffusive two-dimensional electron system with Rashba spin-orbit interaction. In the presence of long-range impurities, the coupled quantum kinetic equations are solved analytically in the self-consistent Born approximation. It is shown that the intrinsic spin-Hall effect stems from the dc-field-induced perturbation of the density of states. In addition, there is an additional disorder-mediated process, which involves the transition of nonequilibrium electrons between two spin-orbit-coupled bands. It results in a…
Recently large Rashba-like spin splitting has been observed in certain bulk ferroelectrics. In contrast with the relativistic Rashba effect, the chiral spin texture and large spin-splitting of the electronic bands depend strongly on the character of the band and atomic spin-orbit coupling. We establish that this can be traced back to the so-called orbital Rashba effect, also in the bulk. This leads to an additional dependence on the orbital composition of the bands, which is crucial for a complete picture of the effect. Results from first-principles calculations on ferroelectic GeTe verify the…
We have investigated the complex two-dimensional electron system with unequal Rashba and Dresselhaus spin-orbit interactions in the presence of a perpendicular magnetic field. The spin polarizations are obtained in a wide range of magnetic fields. It is shown that such a system is hard to be magnetized. We also find that the resonant charge and spin Hall conductances occurs simultaneously at a certain magnetic field, at which two (nearly) degenerate Landau levels are filled partly. The resonant Hall effects are universal in this type of semiconductor materials, and could have potential applica…
We discuss problem of Rashba field in bulk GaN and in GaN/AlGaN two-dimensional electron gas, basing on results of X-band microwave resonance experiments. We point at large difference in spin-orbit coupling between bulk material and heterostructures. We observe coupled plasmon-cyclotron resonance from the two-dimensional electron gas, but no spin resonance, being consistent with large zero-field spin splitting due to the Rashba field reported in literature. In contrast, small anisotropy of g-factor of GaN effective mass donors indicates rather weak Rashba spin-orbit coupling in bulk material, …
We report a Rashba spin splitting of a two-dimensional electron gas in the topological insulator Bi$_2$Se$_3$ from angle-resolved photoemission spectroscopy. We further demonstrate its electrostatic control, and show that spin splittings can be achieved which are at least an order-of-magnitude larger than in other semiconductors. Together these results show promise for the miniaturization of spintronic devices to the nanoscale and their operation at room temperature.
The Kubo formula is used to calculate the spin-Hall conductivity in a spin-polarized two-dimensional electron system with Rashba-type spin-orbit interaction. As in the case of the unpolarized electron system, spin Hall conductivity is entirely determined by states at the Fermi level, a property that persists in the presence of magnetic impurities. In the clean limit, the spin-Hall conductivity decreases monotonically with the Zeeman splitting, a result of the ordering effect on the electron spins produced by the magnetic field. In the presence of magnetic impurities, the spin-dependent scatter…
Tight-binding models for the recently observed surface electronic bands of SrTiO3 and KTaO3 are analyzed with a view to bringing out the relevance of momentum-space chiral angular momentum structures of both orbital and spin origins. Depending on the strength of electric field associated with inversion symmetry breaking at the surface, the orbital and the accompanying spin angular momentum structures reveal complex linear and cubic dependencies in the momentum k (linear and cubic Rashba effects, respectively) in a band-specific manner. Analytical expressions for the cubic orbital and spin Rash…
In spintronic devices, the two main approaches to actively control the electrons' spin degree of freedom involve either static magnetic or electric fields. An alternative avenue relies on the application of optical fields to generate spin currents, which promises to bolster spin-device performance allowing for significantly faster and more efficient spin logic. To date, research has mainly focused on the optical injection of spin currents through the photogalvanic effect, and little is known about the direct optical control of the intrinsic spin splitting. Here, to explore the all-optical mani…
We propose that the hybridization between two sets of Rashba bands can lead to an unconventional topology where the two Fermi circles from different bands own in-plane helical spin textures with the same chiralities, and possess group velocities with the same directions. Under the weak spin injection, the two Fermi circles both give the positive contributions to the spin-to-charge conversion and thus induce the giant inverse Rashba-Edelstein Effect with large conversion efficiency, which is very different from the conventional Rashba-Edelstein Effect. More importantly, through the first-princi…
Two-dimensional (2D) hybrid organic-inorganic perovskites (HOIPs) are introducing new directions in the 2D materials landscape. The coexistence of ferroelectricity and spin-orbit interactions play a key role in their optoelectronic properties. We perform a detailed study on a recently synthesized ferroelectric 2D-HOIP, (AMP)PbI$_4$ (AMP = 4-aminomethyl-piperidinium). The calculated polarization and Rashba parameter are in excellent agreement with experimental values. We report a striking new effect, i.e., an extraordinarily large Rashba anisotropy that is tunable by ferroelectric polarization:…
In antiferromagnetic (AFM) thin films, broken inversion symmetry or coupling to adjacent heavy metals can induce Dzyaloshinskii-Moriya (DM) interactions. Knowledge of the DM parameters is essential for understanding and designing exotic spin structures, such as hedgehog Skyrmions and chiral Néel walls, which are attractive for use in novel information storage technologies. We introduce a framework for computing the DM interaction in two-dimensional Rashba antiferromagnets. Unlike in Rashba ferromagnets, the DM interaction is not suppressed even at low temperatures. The material parameters cont…
The spin Hall effect is investigated in a high mobility two dimensional electron system with the spin-orbital coupling of both the Rashba and the Dresselhaus types. A spin current perpendicular to the electric field is generated by either the Rashba or the Dresselhaus coupling. The spin Hall conductance is independent of the stength of the coupling, but its sign is determined by the relative ratio of the two couplings. The direction of spin current is controllable by tuning the magnitude of the surface electric field perpendicular to the two dimensional plane via adjusting the Rashba coupling.…
Spin currents in a two dimensional electron gas with Rashba-type spin orbit coupling are derived from a spin connection. Using a functional integral method, we recover the result derived by Sinova {\em et al.}$[ \mathrm{Phys.Rev. Lett. 92, 126603 (2004)}]$ for a uniform electric field and in the absence of impurities. We extend this result to inhomogeneous electric and magnetic fields. We find that non-uniform magnetic fields can give rise to spin currents that are independent of the Rashba coupling and hence are less susceptible to impurities than in the case of uniform electric fields.
