Rashba Energy Research Articles

Switching Rashba spin-splitting by reversing electric-field direction

The manipulation of the Rashba spin-splitting is crucial for the development of nanospintronic technology. Here, it is proposed that the Rashba spin-splitting can be turned on and off by reversing electric-field direction. By the first-principles calculations, our proposal is illustrated by a concrete example of Janus monolayer RbKNaBi. The designed RbKNaBi possesses dynamical, thermal, and mechanical stabilities, and is a large-gap quantum spin Hall insulator (QSHI) with Rashba spin-splitting near the Fermi level. A small built-in electric field is predicted due to very small electronegativity difference between the bottom and top atoms, which is very key to switch Rashba spin-splitting through the experimentally available electric field intensity. Due to out-of-plane structural asymmetry, the Janus monolayer has distinctive behaviors by applying external electric field $E$ with the same magnitude but different directions ($z$ or $\ensuremath{-}z$). Our results reveal that the Rashba energy (${E}_{R}$) and Rashba constant (${\ensuremath{\alpha}}_{R}$) are increased by the positive $E$, while a negative $E$ suppresses the Rashba splitting to disappear, and then appears again. In a certain $E$ region (0.15 $\mathrm{V}/\AA{}$ to 0.25 $\mathrm{V}/\AA{}$), switching Rashba spin-splitting can be achieved by only reversing electric-field direction. Besides, the piezoelectric strain coefficients ${d}_{11}$ and ${d}_{31}$ (5.52 pm/V and --0.41 pm/V) are predicted, which are higher than or compared with those of many 2D materials. By piezoelectric effect, the strain can also be used to tune Rashba spin-splitting of RbKNaBi. In Janus RbKNaBi monolayer, the combination of piezoelectricity and Rashba spin-splitting with topological insulating phase can promote the integration of various physical phenomena. Moreover, a possible spintronic device is proposed to realize the function of spintronic switch. Our proposed manipulation of the Rashba spin-splitting may make a special contribution to semiconductor spintronics.

Spectroscopic ellipsometry and raman spectroscopy of Bi1-xSbxTeI solid solutions with x≤0.1

Spectroscopic ellipsometry supported by reflectivity measurements and Raman spectroscopy are applied at room temperature to n-type Rashba semiconductors BiTeI and Bi1-xSbxTeI with nominal compositions x = 0.05 and 0.1. Complementary four probe Hall measurements are made using standard ac technique and the concentration of free carriers is determined. The Raman spectra, including TO-LO resonances are found to occupy a frequency range below 250 cm−1 in the studied materials. The pseudodielectric function, retrieved at different angles of incidence is analyzed focusing on the free carrier absorption (intraband transitions) and the optical transitions between the Rashba-split branches of the conduction band (intersubband vertical transitions). The former transitions with screened plasma frequency anchored to the zero-crossing point of the real part of the pseudodielectric function are described within a simple Drude model and the important parameters such as electron effective mass, electron mobility and high frequency dielectric constant are obtained. Anchored to the Rashba energy, the intersubband transitions obtained for each material by refining the pseudodielectric function from Drude contribution, appear in the imaginary part as a broad peak in the photon energy range between 0.15 and 0.4 eV. A noticeable red shift of this peak for Bi0.9Sb0.1TeI as compared to BiTeI is proposed to be a manifestation of the reduction of the spin splitting after part of Bi atoms is replaced by lighter Sb atoms.

Giant resonances in topological spin Hall effect due to electron-skyrmion scattering in two-dimensional Rashba spin-orbit ferromagnets

We study a topological spin Hall effect where conduction electrons are scattered by N\'eel-type skyrmions in two-dimensional Rashba spin-orbit ferromagnets. We find the resonance structures in direct and Hall electric conductivities. The resonances strongly depend on the skyrmion size, the Rashba spin-orbit coupling vector value, and the relative direction between magnetization and Rashba vectors. The antiparallel arrangement of the Rashba spin-orbit coupling vector with respect to the magnetization determines the resonance structure and increases the direct conductivity by about two orders of magnitude. For the parallel arrangement the electric conductivities decrease by one to three orders of magnitude and the Hall conductivity changes the sign. The Rashba spin-orbit coupling also modifies electron bands depending on the ratio ${\ensuremath{\varepsilon}}_{R}/J$, where ${\ensuremath{\varepsilon}}_{R}$ is Rashba energy and $J$ is an exchange integral between conduction and localized electrons. If ${\ensuremath{\varepsilon}}_{R}/J\ensuremath{\le}1$, each energy band has the single minimum while for ${\ensuremath{\varepsilon}}_{R}/J>1$ the lower band has the ``Mexican-hat'' shape with the maximum at $k=0$. We focus on the dependencies of direct and Hall electric conductivities on Fermi energy, ${\ensuremath{\varepsilon}}_{F}$, skyrmion sizes, and Rashba spin-orbit coupling constant values and its relative direction with the magnetization. Analyzing both types of the energy bands, in general, we find two types of resonances: at the minimum of the upper band and behaviors, we employ the scattering pattern analysis. The resonance dependencies on skyrmion sizes and Rashba, a spin-orbit coupling contestant, can be qualitatively explained in terms of the Ramsauer-Townsend scattering of the upper band electrons by the skyrmion quantum well. The resonance properties can be used in spin transistors. To discover the resonances it is necessary to know the specific range of the parameters. At some values of the parameters the electric conductivity changes by about two orders of magnitude in the narrow range of ${\ensuremath{\varepsilon}}_{F}$ ($<0.01$ eV). To detect the resonances it is also important to identify the relative direction of the Rashba spin-orbit coupling vector with respect to the magnetization.

Valley spin polarization in two-dimensional h−MN (M=Nb,Ta) monolayers: Merger of valleytronics with spintronics

The search for new two-dimensional (2D) semiconductors with strong spin-orbit coupling, merging Rashba effect with valley physics, is essential for advancing the emerging fields of spintronics and valleytronics. $h\text{\ensuremath{-}}M\mathrm{N}$ $(M=\mathrm{Nb},\mathrm{Ta})$ monolayers are found to host valley physics together with Rashba effect. $h$-NbN (TaN) monolayers show Zeeman-type valley spin splitting of 32 (112) meV and 130 (406) meV at valence-band and conduction-band edges, respectively, based on density-functional theory calculations. One of the three degenerate valleys around the $K/{K}^{\ensuremath{'}}$ point in the first Brillouin zone (BZ) lies fully enclosed within the first BZ. Berry curvature $\ensuremath{\sim}50(73)\phantom{\rule{0.16em}{0ex}}{\AA{}}^{2}$ shown by h-NbN (TaN) monolayers is much higher than that in ${\mathrm{MoS}}_{2}$ monolayer $(\ensuremath{\sim}11\phantom{\rule{0.16em}{0ex}}{\AA{}}^{2})$, owing to the lower band gap and wave vector magnitude in $h$-NbN (TaN) monolayers. The Rashba energy splitting and Rashba constant induced by strong spin-orbit coupling (SOC) in $h$-NbN (TaN) monolayer is found to be 52 (74) meV and 2.9 (4.23) eV \AA{} respectively, which are amongst the giant Rashba spin-splitting parameters observed so far in 2D materials. The degree of Zeeman-type valley spin splitting and Rashba-type spin splitting is substantially tunable via in-plane biaxial strain and out of-plane electric field. Higher SOC in $h$-TaN monolayer relative to $h$-NbN monolayer caused by the heavier Ta atoms gives rise to a higher Berry curvature, valley-, and Rashba spin splitting in the former as compared to the latter. Valleytronic and spintronic properties in the studied monolayers are found to be superior to that in $h\text{\ensuremath{-}}{\mathrm{MoS}}_{2}$ and Janus MoSSe monolayers and are therefore proposed for an effective coupling of spin and valley physics.

Rashba effect and flat band property in one-dimensional helical Se atomic chain

Tuning the electronic properties of low-dimensional materials is helpful in building nano electronic devices. Here, we investigate the structural and electronic structures of one-dimensional helical Se atomic chain by using first-principles calculations. Our results show that this structure has a much lower energy than the one with a straight-line structure. Our phonon calculations and <i>ab initio</i> molecular dynamics simulations suggest that this structure is both dynamically and thermally stable. The band structure shows that it is a semiconductor with a gap of about 2.0 eV and Rashba-type splitting near the <i>X</i> point. The helical structure is good for tuning the electronic properties by using strains. As a result, a 5% strain leads to a 20% change in the band gap while the Rashba energy offset is doubled. Moreover, we find that the valence band is a flat band, over which hole doping can induce ferromagnetism and the system becomes half-metallic. Further increasing the doping level can transform the system into a ferromagnetic metal. Such a strategy is then applied to one-dimensional helical Te atomic chain and similar results are obtained.

What Dictates Rashba Splitting in 2D van der Waals Heterobilayers.

Rashba spin-orbit coupling enables electric control of spin states, promising enormous advances from conventional charge-based computing. Until now, a general scheme or a descriptor to find an optimal system with isolated spin states with large tunable splitting is still lacking. Here, based on first-principles calculations, we explore the microscopic physicochemical mechanism responsible for the Rashba effect in 2D van der Waals heterobilayers. We find that the difference in the Born effective charge of atoms at the interface can be used as a single-layer descriptor to predict heteropairs with large Rashba splitting, thus reducing the scaling factor in materials search. Moreover, we discover that for most 2D materials, the routinely used Rashba parameter αR is not a good gauge of the effect's strength. From our general scheme, MoTe2|Tl2O and MoTe2|PtS2, with spin splitting above 120 meV, Rashba energy ER = 94 meV, and wavenumber difference 2k0 = 0.36 Å-1 ("effective" αR > 1 eVÅ), emerge as the best candidates for spin transistors at room temperature.

Large Rashba unidirectional magnetoresistance in the Fe/Ge(111) interface states

The structure inversion asymmetry at surfaces and interfaces gives rise to the Rashba spin-orbit interaction (SOI), that breaks the spin degeneracy of surface or interface states. Hence, when an electric current runs through a surface or interface, this Rashba effect generates an effective magnetic field acting on the electron spin. This provides an additional tool to manipulate the spin state in materials such as Si and Ge possessing inversion symmetry in their bulk form. The existence of Rashba states could be demonstrated by photoemission spectroscopy at the interface between different metals and Ge(111) and by spin-charge conversion experiments at the Fe/Ge(111) interface even though it is made of two light elements. In this paper, we identify the fingerprint of the Rashba states at the Fe/Ge(111) interface by magnetotransport measurements in the form of a large unidirectional magnetoresistance of up to $0.1%$. From its temperature dependence, we find that the Rashba energy splitting is larger than in pure Ge(111) subsurface states.

Observation of Large Unidirectional Rashba Magnetoresistance in Ge(111).

Relating magnetotransport properties to specific spin textures at surfaces or interfaces is an intense field of research nowadays. Here, we investigate the variation of the electrical resistance of Ge(111) grown epitaxially on semi-insulating Si(111) under the application of an external magnetic field. We find a magnetoresistance term that is linear in current density j and magnetic field B, hence, odd in j and B, corresponding to a unidirectional magnetoresistance. At 15K, for I=10 μA (or j=0.33 A m^{-1}) and B=1 T, it represents 0.5% of the zero field resistance, a much higher value compared to previous reports on unidirectional magnetoresistance (UMR). We ascribe the origin of this magnetoresistance to the interplay between the externally applied magnetic field and the pseudomagnetic field generated by the current applied in the spin-splitted subsurface states of Ge(111). This unidirectional magnetoresistance is independent of the current direction with respect to the Ge crystal axes. It progressively vanishes, either using a negative gate voltage due to carrier activation into the bulk (without spin-splitted bands), or by increasing the temperature due to the Rashba energy splitting of the subsurface states lower than ∼58k_{B}. We believe that UMR could be used as a powerful probe of the spin-orbit interaction in a wide range of materials.

Possible Rashba band splitting and thermoelectric properties in CuI-doped Bi2Te2.7Se0.3 bulk crystals

We investigated thermoelectric properties of the CuI-doped (CuI)xBi2Te2.7Se0.3 bulk crystals grown by the Bridgman method. From the formation energy calculation and lattice parameter expansion along the c-axis, we confirm that the Cu-atom intercalates at the van der Waals layer while iodine substitutes at the Te(2) site which donates two electrons per CuI doping. The band structure calculation in iodine doped bismuth telluride monolayer shows band splitting along the momentum direction implying the Rashba type band splitting near the Fermi level. The Seebeck coefficient as a function of Hall carrier concentration on the compounds does not follow the Pisarenko's relation, whereas it follows the Rashba type Seebeck coefficient. The theoretical fitting with the Rashba type Seebeck coefficient indicates that the Rashba energy is increased with increasing CuI doping concentration. Owing to the enhancement of power factor near room temperature and reduction of lattice thermal conductivity by atomic scattering of phonon, the CuI doped compound (CuI)xBi2Te2.7Se0.3 (x= 0.3 mol.%) exhibited high ZT value over a wide temperature range.

Superconductivity in the Surface State of Noble Metal Gold and its Fermi Level Tuning by EuS Dielectric.

The induced superconductivity (SC) in a robust and scalable quantum material with strong Rashba spin-orbit coupling is particularly attractive for generating topological superconductivity and Majorana bound states (MBS). Gold (111) thin film has been proposed as a promising candidate because of the large Rashba energy, the predicted topological nature, and the possibility for large-scale MBS device fabrications. We experimentally demonstrate two important steps towards achieving such a goal. We successfully show induced SC in the Shockley surface state (SS) of ultrathin Au(111) layers grown over epitaxial vanadium films, which is easily achievable on a wafer scale. The emergence of SC in the SS, which is physically separated from a bulk superconductor, is attained by indirect quasiparticle scattering processes instead of by conventional interfacial Andreev reflections. We further show the ability to tune the SS Fermi level (E_{F}) by interfacing SS with a high-κ dielectric ferromagnetic insulator EuS. The shift of E_{F} from ∼550 to ∼34 mV in superconducting SS is an important step towards realizing MBS in this robust system.

Giant tunable Rashba spin splitting in a two-dimensional BiSb monolayer and in BiSb/AlN heterostructures

Search of novel two-dimensional giant Rashba semiconductors is a crucial step in the development of the forthcoming nano-spintronics technology. Using first-principle calculations, we study a stable two-dimensional crystal phase of BiSb having buckled honeycomb lattice geometry, which is yet unexplored. The phonon, room temperature molecular dynamics and elastic constant calculations verify the dynamical and mechanical stability of the monolayer at 0~K and at room temperature. The calculated electronic bandstructure reveals the direct bandgap semiconducting nature of BiSb monolayer with presence of highly mobile two-dimensional electron gas (2DEG) near Fermi-level. Inclusion of spin-orbit coupling (SOC) yields the giant Rashba spin-splitting of 2DEG near Fermi-level. The calculated Rashba energy and Rashba splitting constant are 13 meV and 2.3 eV\AA, respectively. The strength of the Rashba splitting is amongst the largest yet known 2D Rashba semiconductors. We demonstrate that the strength of the Rashba spin-splitting can be significantly tuned by applying in-plane bi-axial strain on the BiSb monolayer. Presence of the giant Rashba spin-splitting together with the large electronic bandgap (1.6 eV) makes this system of peculiar interest for optoelectronics applications. Furthermore, we study the electronic properties of BiSb/AlN heterostructures having a lattice mismatch of 1.3\% at the interface. Our results suggest that BiSb monolayer and heterostructure systems could be potentially used to develop highly efficient spin field-effect transistors, optoelectronics and nano-spintronics devices. Thus, this comprehensive study of two-dimensional BiSb systems can expand the range of possible applications in the future spintronics technology.

Experimental determination of the bulk Rashba parameters in BiTeBr

Shubnikov-de Haas (SdH) oscillations, Hall effect, and optical reflectance measurements have been performed on single crystals of BiTeBr. Under magnetic fields up to 32 tesla and at temperatures as low as 0.4 K, the SdH data shows a single oscillation frequency . The combined transport and optical studies establish that the SdH effect originates from the Rashba spin-split bulk conduction band, with the chemical potential situated about 13 meV below the crossing (Dirac) point. The bulk carrier concentration was and the effective mass . Combining SdH and optical data, we reliably determine the Rashba parameters for the bulk conduction band of BiTeBr: the Rashba energy and the momentum spin-split . Hence, the bulk Rashba coupling strength is found to be 1.7 eVÅ.

Interesting pressure dependence of power factor in BiTeI

We investigate pressure dependence of electronic structures and thermoelectric properties in BiTeI by using a modified Becke and Johnson exchange potential. Spin–orbit coupling (SOC) effects are also included due to giant Rashba splitting. Thermoelectric properties are illuminated through solving Boltzmann transport equations within the constant scattering time approximation. The calculated energy band gap of 0.36 eV agrees well with the experimental value of 0.38 eV. As the pressure increases, the energy band gap first decreases, and then increases. The Rashba energy has the opposite trend with the energy band gap. SOC has obvious detrimental influence on the power factor in both n-type and p-type doping. For low doping concentration, the power factor has the same trend with the energy band gap with increasing pressure, but shows a monotonic changing trend in high doping. It is found that the pressure can induce a significantly enhanced power factor in high n-type doping, which can be understood as pressure leading to two-dimensional-like density of states in the conduction bands. These results suggest that BiTeI may be a potential candidate for efficient thermoelectricity in n-type doping by pressure, turning an ordinary insulator into a topological insulator.

Tunneling conductance of a metal/two-dimensional electron gas with Rashba spin–orbit coupling junction within a lattice model

The charge transport in an infinite two-dimensional system of a normal metal and a two-dimensional electron gas with Rashba spin–orbit coupling was studied. The square lattice model is used to describe the electronic properties in each region. Especially, we developed an appropriate way to take into account the quality of the interface to calculate the transport properties of a particle in the junction. We focused on the effects of the spin-conserved and the spin-flip scattering potential on the overall tunneling conductance. It was found that the conductance spectrum can be enhanced by increasing equally the two types of the interfacial scattering value. The conductance spectrum appears to have characteristic kink features when the Fermi level reaches the coincidence of the Rashba band interaction for both the top and bottom of the band. The kinks reflect the difference in the nature of the electron-like and hole-like energy contours of the energy band. In addition, the Rashba energy is predicted not only from the energy spacing between the onset and the first kink of the conductance spectrum, but also from the energy spacing between the second kink and the offset of the conductance spectrum.

Engineering topological surface states and giant Rashba spin splitting in BiTeI/Bi2Te3 heterostructures.

The search for strongly inversion asymmetric topological insulators is an active research field because these materials possess distinct properties compared with the inversion symmetric ones. In particular, it is desirable to realize a large Rashba spin-splitting (RSS) in such materials, which combined with the topological surface states (TSS) could lead to useful spintronics applications. In this report, based on first principles calculations, we predict that the heterostructure of BiTeI/Bi2Te3 is a strong topological insulator with a giant RSS. The coexistence of TSS and RSS in the current system is native and stable. More importantly, we find that both the invariants and the Rashba energy can be controlled by engineering the layer geometries of the heterostructure, and the Rashba energy can be made even larger than that of bulk BiTeI. Our work opens a new route for designing topological spintronics devices based on inversion asymmetric heterostructures.

Charge and spin transport through the two-dimensional electron gas/ferromagnet junctions with Rashba spin–orbit coupling

Using the method of Blonder, Tinkham and Klapwijk, the conductance spectra of two-dimensional electron gas (2DEG) and ferromagnet (F) junctions in the presence of Rashba spin–orbit coupling (RSOC) are theoretically studied. Two distinguishing features are predicted. This predicted effect allows a direct measurement of the exchange energy of the ferromagnet and the Rashba energy of the 2DEG. The influence of the interfacial scattering is also considered on the differential conductance and spin polarization of the conductance. Surprisingly, the combined effect of both types of scattering (spin-conserving and spin-flip) can actually result in an increase in conductance and spin polarization under certain conditions. The transport properties of 2DEG/F and metal (M)/F junctions are compared. It is implied that Rashba spin–orbit coupling can enhance spin polarization.

Quantum Interference Mapping of Rashba-Split Bloch States inBi/Ag(111)

We report on low-temperature scanning tunneling spectroscopy investigations of the (sqrt[3]×sqrt[3]) Bi/Ag(111)R30° surface alloy which provides a giant Rashba-type spin splitting. We observed spectroscopic features that are assigned to two Rashba-split bands. Quantum interference mapping shows that backscattering is not only allowed below but also above the Rashba energy. We argue that the observed behavior can be understood within the Bloch picture where k refers to the crystal momentum and the velocity of an electronic state is defined as v(n)(E) = 1/ℏ ∇(k)E(n)(k). The analysis of the energy dispersion of scattering channels reveals a conventional Rashba splitting for the unoccupied Rashba bands, while hybridization is observed in the occupied states.

Tunability of giant Rashba spin splitting in BiTeI

Giant Rashba spin splitting was recently discovered in bismuth tellurohalide (BiTeI) [K. Ishizaka et al., Nat. Mater. 10, 521 (2011)]. In this work, biaxial strain is used to modify the interatomic interaction in BiTeI, and the strain dependence of spin splitting is determined theoretically by first-principles density functional calculations. Large tunability is found for the Rashba energy ${E}_{\mathrm{R}}$, momentum offset ${k}_{\mathrm{R}}$, and coupling constant ${\ensuremath{\alpha}}_{R}$, showing that the spin splitting in BiTeI can be significantly modified by atom-atom interaction in a solid. The maximum values of ${E}_{\mathrm{R}}$ and ${\ensuremath{\alpha}}_{R}$ occur at strain $\ensuremath{\eta}=\ensuremath{-}1.5%$. Furthermore, tensile strain is shown to favor the increase of ${k}_{\mathrm{R}}$, and compressive strain favors the increase of ${E}_{\mathrm{R}}$. Moreover, contrast of the spin splittings between the electron at CBM and the hole at VBM reveals that ${E}_{\mathrm{R}}^{e}$ of the electron and ${E}_{\mathrm{R}}^{h}$ of the hole display drastically different behaviors under tensile strains. However, under compressive strains, the strain dependencies of ${E}_{\mathrm{R}}^{e}$ and ${E}_{\mathrm{R}}^{h}$ are interestingly similar (so are the strain dependencies of ${k}_{\mathrm{R}}^{e}$ and ${k}_{\mathrm{R}}^{h}$). By examining microscopic electron states, the anomalous Bi-I interaction is found to be important for the spin splitting in BiTeI, and qualitative explanation for the strain dependence of the spin splitting is provided.

Mathematical Modelling of Bloch NMR to Explain the Rashba Energy Features

The Bloch NMR as an analytical tool was able to address the fundamental features in the learning of spintronics. Beside confirming past assertions on the Rashba spin-orbit interaction, thermal motion of hole and electron spin and features of the quantum well, it was also able to explain the condition necessary for Rashba splitting within the quantum well. When the Rashba energy is 43 meV, it modified the Ehrenfest’s theorem to hold for an external magnetic field. The confinement potential which is the strength of the Rashba spin-orbit interaction was shown to be controlled magnetically.

Two Anderson impurities in a two-dimensional host with Rashba spin-orbit interaction

We have studied the two-dimensional two-impurity Anderson model with additional Rashba spin-orbit interaction by means of the modified perturbation theory. The impurity Green's functions we have constructed exactly reproduce the first four spectral moments. We discuss the height and the width of the even/odd Kondo peaks as functions of the inter-impurity distance and the Rashba energy $E_R$ (the strength of the Rashba spin-orbit interaction). For small impurity separations the Kondo temperature shows a non-monotonic dependence on $E_R$ being different in the even and the odd channel. We predict that the Kondo temperature has only almost linear dependence on $E_R$ and not an exponential increase with $E_R$