Strong Spin-orbit Coupling Strength Research Articles

Relativistic calculation of the orbital hyperfine splitting in complex microscopic structures

Theoretical spectroscopy based on double perturbation theory is typically challenged by systems with large orbital hyperfine splitting. Therefore, we here derive a rigorous, non-perturbative scheme starting from Dirac’s equation which allows to calculate the contribution of the orbital HFI for complex structures including heavy atoms with strong spin-orbit coupling (SOC). Using the PAW formalism, the method has been implemented in the software package Quantum ESPRESSO. We show that the ‘orbital part’ actually scales with SOC strength if orbital quenching is hindered by low local symmetry, i.e. in case of dimers or atoms at surfaces. This holds true in particular when the unpaired electron is localized in quasi-atomic p-like orbitals. Here, the orbital part is by far not negligible, but becomes dominant by surpassing the dipolar contribution by a factor of five.

Ballistic transport spectroscopy of spin-orbit-coupled bands in monolayer graphene on WSe2

Van der Waals interactions with transition metal dichalcogenides were shown to induce strong spin-orbit coupling (SOC) in graphene, offering great promises to combine large experimental flexibility of graphene with unique tuning capabilities of the SOC. Here, we probe SOC-driven band splitting and electron dynamics in graphene on WSe2 by measuring ballistic transverse magnetic focusing. We found a clear splitting in the first focusing peak whose evolution in charge density and magnetic field is well reproduced by calculations using the SOC strength of ~ 13 meV, and no splitting in the second peak that indicates stronger Rashba SOC. Possible suppression of electron-electron scatterings was found in temperature dependence measurement. Further, we found that Shubnikov-de Haas oscillations exhibit a weaker band splitting, suggesting that it probes different electron dynamics, calling for a new theory. Our study demonstrates an interesting possibility to exploit ballistic electron motion pronounced in graphene for emerging spin-orbitronics.

Topological band gap in intercalated epitaxial graphene

The study of functional manipulation of graphene is a critical subject, both for fundamental research and practical applications. In this study, we present that the intercalation of 5d transition metals into epitaxial graphene on SiC is a promising strategy for the realization of topologically nontrivial phases with a finite band gap in graphene. Employing first-principles calculations, grounded in density functional theory, we demonstrate that Re- and Ta-intercalated graphene evolve into two-dimensional topological insulators. These exhibit linear Dirac cones and quadratic bands with topological band gaps, respectively. The emergence of these topological states is attributed to the strong spin–orbit coupling strength of the intercalants. We show that the corresponding topological edge states persist within the finite bulk band gap, aligning with the bulk-boundary correspondence. Furthermore, we explore the spin splitting of the band structure, brought about by the inversion symmetry breaking and the spin–orbit coupling. Our study underscores that the intercalation of graphene is an effective and a feasible approach for manipulating the band gap and the topological nature of graphene. Such intercalated graphene systems hold potential utility for spintronics and low-dimensional quantum device applications.

Zoo of silicon-based quantum bits

Zoo of silicon-based quantum bits

Two-dimensional valleytronic semiconductor with spontaneous spin and valley polarization in single-layer Cr2Se3

Two-dimensional (2D) valleytronic materials, exhibiting valley-contrasting physics, are both fundamentally intriguing and practically appealing to be used in nanoscale devices. In this work, through first-principles calculations and model analysis, we identify single-layer ${\mathrm{Cr}}_{2}{\mathrm{Se}}_{3}$ as a promising 2D valleytronic semiconductor. We reveal that single-layer ${\mathrm{Cr}}_{2}{\mathrm{Se}}_{3}$ is a ferromagnetic semiconductor and harbors valley features. In contrast to most previously reported similar systems suffering from a natural in-plane magnetization, it favors the robust out-of-plane magnetization. This, combined with the broken inversion symmetry and strong spin-orbit coupling strength, renders that a sizable valley polarization occurs spontaneously in single-layer ${\mathrm{Cr}}_{2}{\mathrm{Se}}_{3}$, thus facilitating the observation of intriguing anomalous valley Hall effect. More remarkably, by employing strain and ferroelectric substrate, the on-off switching of the valley polarization is realized in single-layer ${\mathrm{Cr}}_{2}{\mathrm{Se}}_{3}$. The underlying physics is discussed in detail. Our work provides a tantalizing candidate for realizing and manipulating the valley and spin physics.

In-plane crystallographic orientations related spin-orbit torque in epitaxial Pt(111)/Co/Ta heterostructures

Current induced spin–orbit torque (SOT) in heavy metals with strong spin–orbit coupling strength has attracted considerable attention due to its potential applications in spintronic technology. Pt, as one of the mostly used heavy metals in SOT-based spintronic devices, shows large spin Hall angle (θSH) with its single phase and alloy counterparts. In this work, the in-plane crystallographic orientations related θSH of epitaxial Pt(111) layer is reported in MgO(111)/Pt(111)/Co/Ta heterostructures with strong perpendicular magnetic anisotropy. The θSH shows a quite large difference with values, respectively, around 0.083 and 0.057 when the current applied along the [11¯0] and [112¯] crystallographic directions of Pt(111) by the damping-like SOT efficiency using the harmonic Hall voltage measurement technique. The critical switching current densities also show large difference between these two orthogonal crystallographic orientations with the trend of that the larger SOT efficiency leads to the smaller critical switching current density. It independently confirms the generation of different damping-like SOT efficiency when current along [11¯0] and [112¯] directions of Pt(111). Moreover, a perpendicularly magnetized Pt/Co/Ta reference heterostructures with Pt having polycrystalline phase shows tiny variation of damping-like SOT efficiency in in-plane two orthogonal directions, which also indirectly indicates the crystallographic orientations related θSH in epitaxial Pt(111) layers. This study indicates that the θSH of epitaxial Pt is a crystallographic orientations related parameter.

Promising valleytronic materials with strong spin-valley coupling in two-dimensional MN2X2 (M = Mo, W; X = F, H)

The valley degree of freedom of electrons in two-dimensional systems enables the unprecedented exploration of some physical properties as well as promising device applications. However, suitable two-dimensional valleytronic materials, especially with strong spin-valley coupling, are rare. In this work, based on first-principles calculations, we demonstrate a class of promising two-dimensional valleytronic materials in monolayer MN2X2 (M = Mo, W; X = F, H). Monolayer MN2X2 exhibits a semiconducting nature with the valence band maximum located at the K/K′ points, forming a pair of degenerate valleys. Importantly, upon including spin-orbital coupling, the valleys in these systems experience a significant spin splitting (601 meV), which gives rise to the long-sought strong spin-valley coupling. Such significant spin splitting is attributed to the strong spin–orbit coupling strength within the W-dx2−y2/dxy orbitals as well as the inversion asymmetry. Moreover, under hole doping and optical illumination, the valley Hall effect can be achieved in these systems.

Large valley-polarized state in single-layer NbX2 (X = S, Se): Theoretical prediction

Exploring two-dimensional valleytronic crystals with large valley-polarized state is of considerable importance due to the promising applications in next-generation information related devices. Here, we show first-principles evidence that single-layer NbX2 (X = S, Se) is potentially the long-sought two-dimensional valleytronic crystal. Specifically, the valley-polarized state is found to occur spontaneously in single-layer NbX2, without needing any external tuning, which arises from their intrinsic magnetic exchange interaction and inversion asymmetry. Moreover, the strong spin-orbit coupling strength within Nb-d orbitals renders their valley-polarized states being of remarkably large (NbS2 ∼ 156 meV/NbSe2 ∼ 219 meV), enabling practical utilization of their valley physics accessible. In additional, it is predicted that the valley physics (i.e., anomalous valley Hall effect) in single-layer NbX2 is switchable via applying moderate strain. These findings make single-layer NbX2 tantalizing candidates for realizing high-performance and controllable valleytronic devices.

Spin-2 Bose–Einstein condensates in an annular trap with spin–orbit coupling

We study the ground-state phases of spin–orbit coupled spin-2 Bose–Einstein condensates in a two-dimensional concentrically coupled annular trap with the attractive and repulsive spin-exchange interactions, respectively. For the system with the attractive spin-exchange interaction, the ground-state phase densities in the inner ring show the bright solitons along the azimuthal direction with the weak spin–orbit coupling strength and the vortex line along the radial direction with the strong spin–orbit coupling strength. For the system with the repulsive spin-exchange interaction, the necklace-like state is shown. The number of petals of the necklace-like state continuous growth as the spin–orbit coupling strength enhanced. The momentum distributions of the ground-state phases are also studied.

Tuning Magnetization Dynamics with Strong Spin-Orbit Coupling in Transition-Metal Dichalcogenide/ Co - Fe - B Heterostructures

Spintronic materials with two-dimensional (2D) transition-metal dichalcogenide (TMD)/ferromagnet (FM) interfaces have received a great deal of interest recently due to strong modulation of the magnetic properties, which provide attractive opportunities for magnetic information storage. Here, we demonstrate the strong spin-orbit coupling (SOC) effect and great interfacial tuning of magnetization dynamics in $M{X}_{2}$/$\mathrm{Co}\text{\ensuremath{-}}\mathrm{Fe}\text{\ensuremath{-}}\mathrm{B}$ thin films by means of a time-resolved magneto-optical Kerr approach, where M is chosen as $\mathrm{Mo}$ or $\mathrm{W}$ and X is $\mathrm{S}$ or $\mathrm{Se}$. The significant drop of demagnetization time, ${\ensuremath{\tau}}_{m}$, and increase of magnetic damping factor, ${\ensuremath{\alpha}}_{s}$, clearly highlight the presence of high interfacial SOC strength in just one monolayer of ${\mathrm{Mo}\mathrm{S}}_{2}$. Compared with the single $\mathrm{Co}\text{\ensuremath{-}}\mathrm{Fe}\text{\ensuremath{-}}\mathrm{B}$ film, the precession frequency, f, is lowered after inserting a $M{X}_{2}$ layer, suggesting a reduction of the effective magnetization, $4\ensuremath{\pi}{M}_{\mathrm{eff}}$, originating from the interfacial d-d hybridization effect. The role of SOC strength on ${\ensuremath{\tau}}_{m}$, ${M}_{\mathrm{eff}}$, and ${\ensuremath{\alpha}}_{s}$ is confirmed by using different TMD materials, and thus, demonstrates that the element M plays a dominant role. The samples with ${\mathrm{WS}}_{2}$ or ${\mathrm{W}\mathrm{Se}}_{2}$ have much shorter ${\ensuremath{\tau}}_{m}$, smaller ${M}_{\mathrm{eff}}$, and larger ${\ensuremath{\alpha}}_{s}$ values due to the strong SOC interaction of heavier atoms. The observed efficient control of dynamic magnetic behavior will further promote the development of TMD/FM materials for practical spintronic applications with ultrafast manipulation speed and low energy consumption.

Pb-doped p -type Bi2Se3 thin films via interfacial engineering

Due to high density of native defects, the prototypical topological insulator (TI), Bi$_2$Se$_3$, is naturally n-type. Although Bi$_2$Se$_3$ can be converted into p-type by substituting 2+ ions for Bi, only light elements such as Ca have been so far effective as the compensation dopant. Considering that strong spin-orbit coupling (SOC) is essential for the topological surface states, a light element is undesirable as a dopant, because it weakens the strength of SOC. In this sense, Pb, which is the heaviest 2+ ion, located right next to Bi in the periodic table, is the most ideal p-type dopant for Bi$_2$Se$_3$. However, Pb-doping has so far failed to achieve p-type Bi$_2$Se$_3$ not only in thin films but also in bulk crystals. Here, by utilizing an interface engineering scheme, we have achieved the first Pb-doped p-type Bi$_2$Se$_3$ thin films. Furthermore, at heavy Pb-doping, the mobility turns out to be substantially higher than that of Ca-doped samples, indicating that Pb is a less disruptive dopant than Ca. With this SOC-preserving counter-doping scheme, it is now possible to fabricate Bi$_2$Se$_3$ samples with tunable Fermi levels without compromising their topological properties.

Lifshitz-Transition-Driven Metal-Insulator Transition in Moderately Spin-Orbit-Coupled Sr_{2-x}La_{x}RhO_{4}.

Motivated by the novel insulating state of Sr_{2}IrO_{4} from strong spin-orbit coupling (SOC), we investigate, by means of angle resolved photoemission, the metal-insulator transition (MIT) mechanism in Sr_{2-x}La_{x}RhO_{4} whose mother compound is isovalent and isostructural but has smaller SOC strength compared to Sr_{2}IrO_{4}. Transport and angle resolved photoemission results from single crystalline Sr_{2-x}La_{x}RhO_{4} revealed that the MIT occurs coincidentally with a multi- to single-band transition (Lifshitz transition) at x=0.4. Starting from x=0.4, there is a gradual but anomalous enhancement in the band gap size with additional electron doping, suggesting that the insulating phase in Sr_{2-x}La_{x}RhO_{4} is a new type which has been rarely investigated. These results suggest that the insulating phase in Sr_{2-x}La_{x}RhO_{4} is likely induced by the moderate SOC strength and electron doping effect from the La. Our findings not only elucidate the MIT mechanism in Sr_{2-x}La_{x}RhO_{4}, but may also open new avenues for novel MIT research in moderate SOC regimes.

Composition-dependent topological-insulator properties of epitaxial (Bi1-xSbx)2(Te1-ySey)3 thin films

Due to strong spin-orbit coupling (SOC), topological insulators (TIs) have attracted much interest in developing novel energy-efficient electronic devices. (Bi1-xSbx)2(Te1-ySey)3 (BSTS) has been regarded as a prototypical TI because of the dominance of the surface channel in carrier transport. Nevertheless, the effect of the composition of BSTS on SOC has not been explored, which is important for the application in novel electronic devices. In this work, BSTS thin films with systematically varying compositions are examined to release composition-dependent maps for the bulk carrier density, the dominance of the surface states in carrier transport, and the strength of SOC. The maps show that the regions for optimizing each property are located in separate positions, with a narrow overlap between them. These results imply that a stringent control in composition of the BSTS thin film is required in order to take advantage of the spin-momentum-locked surface channel of TI in novel electronic devices.

Curvature of gap closing features and the extraction of Majorana nanowire parameters

Recent tunneling conductance measurements of Majorana nanowires show a strong variation in the magnetic field dependence of the superconducting gap among different devices. Here, we theoretically study the magnetic field dependence of the gap closing feature and establish that the degree of convexity (or concavity) of the gap closing as a function of Zeeman field can provide critical constraints on the underlying microscopic parameters of the semiconductor-superconductor hybrid system model. Specifically, we show that the gap closing feature is entirely concave only for strong spin-orbit coupling strength relative to the chemical potential. Additionally, the non-linearity (i.e. concavity or convexity) of the gap closing as a function of magnetic field complicates the simple assignment of a constant effective $ g $-factor to the states in the Majorana nanowire. We develop a procedure to estimate the effective $ g $-factor from recent experimental data that accounts for the non-linear gap closing resulting from the interplay between chemical potential and spin-orbit coupling. Thus, measurements of the magnetic field dependence of the gap closure on the trivial side of the topological quantum phase transition can provide useful information on parameters that are critical to the theoretical modeling of Majorana nanowires.

Weak Antilocalization at the Atomic-Scale Limit of Metal Film Thickness.

Creation of the 2D metallic layers with the thickness as small as a few atomic layers and investigation of their properties are interesting and challenging tasks of the modern condensed-matter physics. One of the possible ways to grow such layers resides in the synthesis of the so-called metal-induced reconstructions on silicon (i.e., silicon substrates covered with ordered metal films of monolayer or submonolayer thickness). The 2D Au-Tl compound on Si(111) surface having [Formula: see text] periodicity belongs to the family of the reconstructions incorporating heavy-metal atoms with a strong spin-orbit coupling (SOC). In such systems, strong SOC results in the spin-splitting of surface-state bands due to the Rashba effect, the occurrence of which was experimentally proved. Another remarkable consequence of a strong SOC that manifests itself in the transport properties is a weak antilocalization (WAL) effect, which has never been explored in the metal layers of atomic thickness. In the present study, the transport and magnetotransport properties of the 2D Au-Tl compound on Si(111) surface were investigated at low temperatures down to ∼2.0 K. The compound was proved to show behavior of the 2D nearly free electron gas system with metallic conduction, as indicated by Ioffe-Regel criterion. It demonstrates the WAL effect which is interpreted in the framework of Hikami-Larkin-Nagaoka theory, and possible mechanisms of the electron decoherence are discussed. Bearing in mind that besides the (Au, Tl)/Si(111)[Formula: see text] system, there are many other ordered atomic-layer metal films on silicon differing by composition, structure, strength of SOC, and spin texture, which provide a promising area for prospective investigations of the WAL effect at the atomic-scale limit when the film thickness is less than the electron wavelength.

Effect of Nb concentration on the spin-orbit coupling strength in Nb-doped SrTiO3 epitaxial thin films

Several oxide materials have attracted much interest for the application in spintronic devices due to unusual properties originating from the strongly correlated orbital and spin degrees of freedom. One missing part in oxide spintronics is a good spin channel featured by strong spin-orbit coupling (SOC) which enables an efficient control of the electron’s spin. We have systematically investigated the dependence of the SOC strength of Sr(NbxTi1−x)O3 thin films on Nb concentration (nNb = 2~20 at. %) as a deeper exploration of a recent finding of the strong SOC in a heavily Nb-doped SrTiO3 (Sr(Nb0.2Ti0.8)O3) epitaxial film. Apart from a finding of a proportionality of the SOC to nNb, we have observed an intriguing temperature dependence of the SOC strength and the anisotropic magnetoresistance (MR) in the intermediate nNb region. These phenomena are associated with the temperature dependence of Landé g-factor and the change of the band structure, which is consistent with the result of density functional theory (DFT) calculation.

Coupling a Germanium Hut Wire Hole Quantum Dot to a Superconducting Microwave Resonator.

Realizing a strong coupling between spin and resonator is an important issue for scalable quantum computation in semiconductor systems. Benefiting from the advantages of a strong spin-orbit coupling strength and long coherence time, the Ge hut wire, which is proposed to be site-controlled grown for scalability, is considered to be a promising candidate to achieve this goal. Here we present a hybrid architecture in which an on-chip superconducting microwave resonator is coupled to the holes in a Ge quantum dot. The charge stability diagram can be obtained from the amplitude and phase responses of the resonator independently from the DC transport measurement. Furthermore, we estimate the hole-resonator coupling rate of gc/2π = 148 MHz in the single quantum dot-resonator system and estimate the spin-resonator coupling rate gs/2π to be in the range 2-4 MHz. We anticipate that strong coupling between hole spins and microwave photons in a Ge hut wire is feasible with optimized schemes in the future.

Electronic structure of monolayer 1T′-MoTe2 grown by molecular beam epitaxy

Monolayer transition metal dichalcogenides (TMDCs) in the 1T′ structural phase have drawn a great deal of attention due to the prediction of quantum spin Hall insulator states. The band inversion and the concomitant changes in the band topology induced by the structural distortion from 1T to 1T′ phases are well established. However, the bandgap opening due to the strong spin-orbit coupling (SOC) is only verified for 1T′-WTe2 recently and still debated for other TMDCs. Here we report a successful growth of high-quality monolayer 1T′-MoTe2 on a bilayer graphene substrate through molecular beam epitaxy. Using in situ angle-resolved photoemission spectroscopy (ARPES), we have investigated the low-energy electronic structure and Fermi surface topology. The SOC-induced breaking of the band degeneracy points between the valence and conduction bands is clearly observed by ARPES. However, the strength of SOC is found to be insufficient to open a bandgap, which makes monolayer 1T′-MoTe2 on bilayer graphene a semimetal.

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.

Gate tunable spin-orbit coupling and weak antilocalization effect in an epitaxial La2/3Sr1/3MnO3 thin film

Epitaxial La$_{2/3}$Sr$_{1/3}$MnO$_3$ (LSMO) films have been grown on SrTiO$_3$ (001) substrates via pulsed laser deposition. In a 22-nm thick LSMO film with a low residual resistivity of $\rho_0$ = 59 $\mu \Omega$ cm, we found a zero-field dip in the magnetoresistance (MR) below 10 K, manifesting the weak antilocalization (WAL) effect due to strong spin-orbit coupling (SOC). We have analyzed the MR data by including the D'yakonov-Perel' spin-relaxation mechanism in the WAL theory. We explain that the delocalized spin-down electron subband states play a crucial role for facilitating marked SOC in clean LSMO. Moreover, we find that the SOC strength and gate voltage tunability is similar to that in the 2DEG at LaAlO$_3$/SrTiO$_3$ interface, indicating the presence of an internal electric field near the LSMO/SrTiO$_3$ interface. In a control measurement on a 5-nm thick high resistivity ($\rho_0$ = 280 $\mu \Omega$ cm) LSMO film, we observe only a small zero-field peak in MR from weak localization effect, indicating negligible SOC.