Weak Spin-orbit Coupling Research Articles

Ground-state phases of a rotating spin-orbit–coupled Bose-Einstein condensate in an optical lattice

We study the ground-state phases of a two-dimensional rotating spin-orbit–coupled Bose-Einstein condensate loaded in a one-dimensional spin-dependent optical lattice. In the absence of rotation, the system undergoes a phase transition from the stripe phase to the supersolid phase gradually for weak spin-orbit coupling strength and directly for strong spin-orbit coupling strength as the depth of the optical lattice increases. With increasing the rotation strength, the stripe phase transforms to the ringlike state, and the domain number of the ringlike state increases when the Bose-Einstein condensate is in the weak depth of the optical lattice. The supersolid phase transforms to the phase with a single domain of a vortex line for small rotation strength, and alternating vortex lines along the x-direction appear for large rotation strength when the Bose-Einstein condensate is in the strong depth of the optical lattice. The spin textures of the ground-state phases are also discussed.

Spin-orbit coupling induced two-electron relaxation in silicon donor pairs

We unravel theoretically a key intrinsic relaxation mechanism among the low-lying singlet and triplet donor-pair states in silicon, an important element in the fast-developing field of spintronics and quantum computation. Despite the perceived weak spin-orbit coupling (SOC) in Si, we find that our discovered relaxation mechanism, combined with the electron-phonon and inter-donor interactions, dominantly drives the transitions in the two-electron states over a large range of donor coupling regime. The scaling of the relaxation rate with inter-donor exchange interaction $J$ goes from $J^5$ to $J^4$ at the low to high temperature limits. Our analytical study draws on the symmetry analysis over combined band, donor envelope and valley configurations. It uncovers naturally the dependence on the donor-alignment direction and triplet spin orientation, and especially on the dominant SOC source from donor impurities. While a magnetic field is not necessary for this relaxation, unlike in the single-donor spin relaxation, we discuss the crossover behavior with increasing Zeeman energy in order to facilitate comparison with experiments.

RKKY interaction in three-dimensional electron gases with linear spin-orbit coupling

We theoretically study the impacts of linear spin-orbit coupling (SOC) on the Ruderman-Kittel-Kasuya-Yosida interaction between magnetic impurities in two kinds of three-dimensional noncentrosymmetric systems. It has been found that linear SOCs lead to the Dzyaloshinskii-Moriya interaction and the Ising interaction, in addition to the conventional Heisenberg interaction. These interactions possess distinct range functions from three dimensional electron gases and Dirac/Weyl semimetals. In the weak SOC limit, the Heisenberg interaction dominates over the other two interactions in a moderately large region of parameters. Sufficiently strong Rashba SOC makes the Dzyaloshinskii-Moriya interaction or the Ising interaction dominate over the Heisenberg interaction in some regions. The change in topology of the Fermi surface leads to some quantitative changes in periods of oscillations of range functions. The anisotropy of Ruderman-Kittel-Kasuya-Yosida interaction in bismuth tellurohalides family BiTe$X$ ($X$ = Br, Cl, and I) originates from both the specific form of Rashba SOC and the anisotropic effective mass. Our work provides some insights into understanding observed spin textures and the application of these materials in spintronics.

Magnetic two-dimensional organic topological insulator: Au-1,3,5-triethynylbenzene framework.

Based on first-principles calculations, we demonstrate that the recently-synthesized 2D organometallic framework consisting of Au atoms and 1,3,5-triethynylbenzene (Au-TEB) is a magnetic 2D organic topological insulator (OTI). The charge transfer and covalent bonding character lead to ferromagnetism and half-metallicity in the framework, and the weak spin-orbit coupling (SOC) of C pz orbitals mediated by Au d orbitals opens modest bandgaps in the vicinity of the Fermi level. Moreover, using tight-binding model simulations, we further characterize the nonzero Chern number and edge states of Au-TEB to confirm its topological nontriviality that remains intact when the framework is supported on an insulating substrate, and applying an external strain can increase the magnitude of SOC gaps, leading to an enhanced topological nontriviality. Our results suggest that the Au-TEB organometallic framework is promising for the potential applications in quantum spintronics with the merits of low cost and easy synthesis.

Strong electron-hole symmetric Rashba spin-orbit coupling in graphene/monolayer transition metal dichalcogenide heterostructures

Despite its extremely weak intrinsic spin-orbit coupling (SOC), graphene has been shown to acquire considerable SOC by proximity coupling with exfoliated transition metal dichalcogenides (TMDs). Here we demonstrate strong induced Rashba SOC in graphene that is proximity coupled to a monolayer TMD film, MoS2 or WSe2, grown by chemical vapor deposition with drastically different Fermi level positions. Graphene/TMD heterostructures are fabricated with a pickup-transfer technique utilizing hexagonal boron nitride, which serves as a flat template to promote intimate contact and therefore a strong interfacial interaction between TMD and graphene as evidenced by quenching of the TMD photoluminescence. We observe strong induced graphene SOC that manifests itself in a pronounced weak anti-localization (WAL) effect in the graphene magnetoconductance. The spin relaxation rate extracted from the WAL analysis varies linearly with the momentum scattering time and is independent of the carrier type. This indicates a dominantly Dyakonov-Perel spin relaxation mechanism caused by the induced Rashba SOC. Our analysis yields a Rashba SOC energy of ~1.5 meV in graphene/WSe2 and ~0.9 meV in graphene/MoS2, respectively. The nearly electron-hole symmetric nature of the induced Rashba SOC provides a clue to possible underlying SOC mechanisms.

Electrical gate control of spin current in van der Waals heterostructures at room temperature

Two-dimensional (2D) crystals offer a unique platform due to their remarkable and contrasting spintronic properties, such as weak spin–orbit coupling (SOC) in graphene and strong SOC in molybdenum disulfide (MoS2). Here we combine graphene and MoS2 in a van der Waals heterostructure (vdWh) to demonstrate the electric gate control of the spin current and spin lifetime at room temperature. By performing non-local spin valve and Hanle measurements, we unambiguously prove the gate tunability of the spin current and spin lifetime in graphene/MoS2 vdWhs at 300 K. This unprecedented control over the spin parameters by orders of magnitude stems from the gate tuning of the Schottky barrier at the MoS2/graphene interface and MoS2 channel conductivity leading to spin dephasing in high-SOC material. Our findings demonstrate an all-electrical spintronic device at room temperature with the creation, transport and control of the spin in 2D materials heterostructures, which can be key building blocks in future device architectures.

Spin mediated enhanced negative magnetoresistance in Ni80Fe20 and p-silicon bilayer

In this work, we present an experimental study of spin mediated enhanced negative magnetoresistance in Ni80Fe20 (50nm)/p-Si (350nm) bilayer. The resistance measurement shows a reduction of ~2.5% for the bilayer specimen as compared to 1.3% for Ni80Fe20 (50nm) on oxide specimen for an out-of-plane applied magnetic field of 3T. In the Ni80Fe20-only film, the negative magnetoresistance behavior is attributed to anisotropic magnetoresistance. We propose that spin polarization due to spin-Hall effect is the underlying cause of the enhanced negative magnetoresistance observed in the bilayer. Silicon has weak spin orbit coupling so spin Hall magnetoresistance measurement is not feasible. We use V2ω and V3ω measurement as a function of magnetic field and angular rotation of magnetic field in direction normal to electric current to elucidate the spin-Hall effect. The angular rotation of magnetic field shows a sinusoidal behavior for both V2ω and V3ω, which is attributed to the spin phonon interactions resulting from the spin-Hall effect mediated spin polarization. We propose that the spin polarization leads to a decrease in hole-phonon scattering resulting in enhanced negative magnetoresistance.

Anomalous Hall effect in MnAl/W bilayers: Modification from strong spin Hall effect of W

We report systematic measurements of anomalous Hall effect (AHE) in MnAl/W bilayers modified by strong spin Hall effect (SHE) of the heavy metals, in which a single L10-MnAl epitaxial layer reveals obvious orbital two-channel Kondo (2CK) effect. The results are compared with the AHE in MnAl/Cu with weak spin orbit coupling. As increasing the thickness of W, the strong SHE has gradually suppressed the orbital 2CK effect and modified the AHE of MnAl. A scaling involving multiple competing scattering mechanisms has been used to distinguish different contributions to the modified AHE. The direct observation of spin-orbit torque induced magnetization switching confirms that the result is a combination of the AHE of MnAl and SHE of W.

Modulation of magnetic damping constant of Fe2Co films by heavy doping of rare-earth Yb

The effect of rare-earth element Yb doping on modulating the magnetic properties, especially the damping constant, is investigated in a series of amorphous (Fe2Co)(1−x)Ybx thin films by the time-resolved magneto-optical Kerr effect at room temperature. A linear decrease of the saturation magnetization and in-plane uniaxial anisotropy field with the increase of x was observed and explained by the diluted effect of non-magnetic Yb doping. The magnetic damping constant performs a remarkable increase with Yb concentration. X-ray photoelectron spectroscopy reveals partial oxidation of Yb, which has large orbital moment and the associated large spin–orbital coupling (SOC) strength and may be responsible for the increased damping constant in contrast with the expected weak SOC and associated low damping constant of metallic Yb doping.

Electrically driven spin qubit based on valley mixing.

The electrical control of single spin qubits based on semiconductor quantum dots is of great interest for scalable quantum computing since electric fields provide an alternative mechanism for qubit control compared with magnetic fields and can also be easier to produce. Here we outline the mechanism for a drastic enhancement in the electrically-driven spin rotation frequency for silicon quantum dot qubits in the presence of a step at a heterointerface. The enhancement is due to the strong coupling between the ground and excited states which occurs when the electron wave function overcomes the potential barrier induced by the interface step. We theoretically calculate single qubit gate times tπ of 170 ns for a quantum dot confined at a silicon/silicon-dioxide interface. The engineering of such steps could be used to achieve fast electrical rotation and entanglement of spin qubits despite the weak spin-orbit coupling in silicon.

Spin-orbit coupling in quasi-one-dimensional Wigner crystals

We study the effect of Rashba spin-orbit coupling (SOC) on the charge and spin degrees of freedom of a quasi-one-dimensional (quasi-1D) Wigner crystal. As electrons in a quasi-1D Wigner crystal can move in the transverse direction, SOC cannot be gauged away in contrast to the pure 1D case. We show that for weak SOC, a partial gap in the spectrum opens at certain ratios between density of electrons and the inverse Rashba length. We present how the low-energy branch of charge degrees of freedom deviates due to SOC from its usual linear dependence at small wave vectors. In the case of strong SOC, we show that spin sector of a Wigner crystal cannot be described by an isotropic antiferromagnetic Heisenberg Hamiltonian any more, and that instead the ground state of neighboring electrons is mostly a triplet state. We present a new spin sector Hamiltonian and discuss the spectrum of Wigner crystal in this limit.

Coherent spin dynamics in a helical arrangement of molecular dipoles

Experiments on electron transport through helical molecules have demonstrated the appearance of high spin selectivity, in spite of the rather weak spin-orbit coupling in organic compounds. Theoretical models usually rely on different mechanisms to explain these experiments, such as large spin-orbit coupling, quantum dephasing, the role of metallic contacts, or the interplay between a helicity-induced spin-orbit coupling and a strong dipole electric field. In this work we consider the coherent electron dynamics in the electric field created by the helical arrangement of dipoles of the molecule backbone, giving rise to an effective spin-orbit coupling. We calculate the spin projection onto the helical axis as a figure of merit for the assessment of the spin dynamics in a very long helical molecule. We prove that the spin projection reaches a steady state regime after a short transient. We compare its asymptotic value for different initial conditions, aiming to better understand the origin of the spin selectivity found in experiments.

Spin-polarized electron transport through helicene molecular junctions

Recently, the spin-selectivity effect of chiral molecules has been attracting extensive and growing interest among the scientific communities. Here, we propose a model Hamiltonian to study spin-dependent electron transport through helicene molecules which are connected by two semi-infinite graphene nanoribbons and try to elucidate a recent experiment of the spin-selectivity effect observed in the helicene molecules. The results indicate that the helicene molecules can present a significant spin-filtering effect in the case of extremely weak spin-orbit coupling, which is three orders of magnitude smaller than the hopping integral. The underlying physics is attributed to intrinsic chiral symmetry of the helicene molecules. When the chirality is switched from the right-handed species to the left-handed species, the spin polarization is reversed exactly. These results are consistent with a recent experiment [V. Kiran et al., Adv. Mater. 28, 1957 (2016)]. In addition, the spin-filtering effect of the helicene molecules is robust against molecular lengths, dephasing strengths, and space position disorder. This theoretical work may motivate further studies on chiral-induced spin selectivity in molecular systems.

Electron spin dynamics in cubic GaN

Electron spin relaxation in bulk cubic GaN is investigated by time-resolved magneto-optical spectroscopy over a wide range of temperatures, external magnetic fields, and doping densities. Very long spin relaxation times in the nanosecond range are found even up to room temperature, making cubic GaN a highly interesting material for spintronics. These results on a system with relatively weak spin-orbit coupling differ significantly from previous results for bulk III-V semiconductors such as GaAs. There are several possible reasons for the observed discrepancy, including the role of charged dislocations and a phase mixture of cubic GaN with inclusions of hexagonal GaN. Spin relaxation in such disordered materials is still poorly understood, and so this work should stimulate further research on this relevant topic.

Topological node-line semimetal in compressed black phosphorus

Based on first-principles calculations and tight-binding model analysis, we propose that black phosphorus (BP) can host a three-dimensional topological node-line semimetal state under pressure when spin-orbit coupling (SOC) is ignored. A closed topological node line exists in the first Brillouin zone (BZ) near the Fermi energy, which is protected by the coexistence of time-reversal and spatial inversion symmetry with band inversion driven by pressure. Drumhead-like surface states have been obtained on the beard (100) surface. Due to the weak intrinsic SOC of phosphorus atom, a band gap less than 10 meV is opened along the node line in the presence of SOC and the surface states are almost unaffected by SOC.

Charge and spin diffusion on the metallic side of the metal-insulator transition: A self-consistent approach

We develop a self-consistent theory describing the spin and spatial electron diffusion in the impurity band of doped semiconductors under the effect of a weak spin-orbit coupling. The resulting low-temperature spin-relaxation time and diffusion coefficient are calculated within different schemes of the self-consistent framework. The simplest of these schemes qualitatively reproduces previous phenomenological developments, while more elaborate calculations provide corrections that approach the values obtained in numerical simulations. The results are universal for zinc-blende semiconductors with electron conductance in the impurity band, and thus they are able to account for the measured spin-relaxation times of materials with very different physical parameters. From a general point of view, our theory opens a new perspective for describing the hopping dynamics in random quantum networks.

Spiral magnetic order and topological superconductivity in a chain of magnetic adatoms on a two-dimensional superconductor

We study the magnetic and electronic phases of a 1D magnetic adatom chain on a 2D superconductor. In particular, we confirm the existence of a `self-organized' 1D topologically non-trivial superconducting phase within the set of subgap Yu-Shiba-Rusinov (YSR) states formed along the magnetic chain. This phase is stabilized by incommensurate spiral correlations within the magnetic chain that arise from the competition between short-range ferromagnetic and long-range antiferromagnetic electron-induced exchange interactions, similar to a recent study for a 3D superconductor [M. Schecter et al. Phys. Rev. B 93, 140503(R) 2016]. The exchange interaction along diagonal directions are also considered and found to display behavior similar to a 1D substrate when close to half filling. We show that the topological phase diagram is robust against local superconducting order parameter suppression and weak substrate spin-orbit coupling. Lastly, we study the effect of a direct ferromagnetic exchange coupling between the adatoms, and find the region of spiral order in the phase diagram to be significantly enlarged in a wide range of the direct exchange coupling.

Spin-torque generator engineered by natural oxidation of Cu.

The spin Hall effect is a spin–orbit coupling phenomenon, which enables electric generation and detection of spin currents. This relativistic effect provides a way for realizing efficient spintronic devices based on electric manipulation of magnetization through spin torque. However, it has been believed that heavy metals are indispensable for the spin–torque generation. Here we show that the spin Hall effect in Cu, a light metal with weak spin–orbit coupling, is significantly enhanced through natural oxidation. We demonstrate that the spin–torque generation efficiency of a Cu/Ni81Fe19 bilayer is enhanced by over two orders of magnitude by tuning the surface oxidation, reaching the efficiency of Pt/ferromagnetic metal bilayers. This finding illustrates a crucial role of oxidation in the spin Hall effect, opening a route for engineering the spin–torque generator by oxygen control and manipulating magnetization without using heavy metals.

Addendum to ‘Existence of Dirac cones in the Brillouin zone of diperiodic atomic crystals according to group theory’

In our paper (Damljanović and Gajić 2016 J. Phys.: Condens. Matter 28 085502) we have analyzed sufficient conditions for the existence of Dirac cones in the Brillouin zone of non-magnetic, two-dimensional atomic crystals with weak spin–orbit coupling. We have provided a list of diperiodic groups hosting Dirac-like dispersion in the vicinity of Brillouin zone corners (K-points), where the orbital degeneracy at the vertex of the cones is caused by the crystal symmetry. In this addendum, we add to our list three more hexagonal diperiodic groups, in which the mentioned double degeneracy is caused by the time reversal symmetry.

Manifestation of chirality in the vortex lattice in a two-dimensional topological superconductor

We study the vortex lattice in a two-dimensional s-wave topological superconductor with Rashba spin-orbit coupling and Zeeman field by solving the Bogoliubov-de Gennes equations self-consistently for the superconducting order parameter. We find that when spin-orbit coupling is relatively weak, one of the two underlying chiralities in the topological superconducting state can be strongly manifest in the vortex core structure and govern the response of the system to vorticity and a nonmagnetic impurity where the vortex is pinned. The Majorana zero mode in the vortex core is found to be robust against the nonmagnetic impurity in that it remains effectively a zero-energy bound state regardless of the impurity potential strength and the major chirality. The spin polarization of the Majorana bound state depends on the major chirality for weak spin-orbit coupling, while it is determined simply by the vorticity when spin-orbit coupling is relatively strong.