Spin-orbit Interaction Constant Research Articles

Weak Antilocalization Effect in an AlAs/AlGaAs Quantum Well

Weak antilocalization in a narrow AlAs quantum well containing a two-dimensional electron system with a large effective mass at low temperatures has been studied. Such quantum corrections are due to a strong spin–orbit coupling in it. The spin–orbit interaction constant has been determined from the approximation of experimental data by a theoretical model in the diffusion approximation. Additionally, this constant has also been independently measured from the modification of the single-particle g-factor in the quantum Hall effect regime in the same sample using electron paramagnetic resonance. Electron paramagnetic resonance spectroscopy and analysis of the weak antilocalization effect yield close values of the interaction constants β = 7.6 and 10.1 meV Å, respectively. Agreement between β values thus obtained becomes full if effects of the strong electron–electron interaction are taken into account in the weak antilocalization model by renormalizing the effective mass of the electron.

Identification of a state of persistent spin helix in a parallel magnetic field, and exploration of its transport properties

The tensors of conductivity and spin susceptibility of a two-dimensional electron gas (2DEG) with equal Rashba and Dresselhaus spin-orbit interaction constants [the persistent spin helix (PSH) state] in a parallel magnetic field are calculated. Applying a parallel magnetic field to the PSH state leads to the appearance of a saddle point in the spectrum and, accordingly, to a Van Hove singularity (VHS), whose amplitude increases indefinitely as the magnetic field strength $(\mathbf{b})$ approaches to some critical value ${b}_{cr}$. The presence of a VHS in the density of states is an important factor determining the conductivity and spin susceptibility tensors. When only the lower spin subband is filled, the off-diagonal elements of the conductivity tensor are nonzero; that is, a Hall voltage arises due to the anisotropy of the Fermi surface and scattering. In the region where two spin subbands are filled, the diagonal and off-diagonal components of the spin susceptibility tensor are equal, and the off-diagonal terms of the conductivity tensor vanish. A sharp decrease in the conductivity and spin susceptibility at the beginning of the filling of the second spin subband, the ratio of the diagonal component of the spin susceptibility to the off-diagonal one, and also the number of critical points in the spectrum make it possible to establish the PSH 2DEG state.

Infrared spectroscopy of difference and combination bands of the NO3 radical and anharmonicity analysis

The 2ν3-ν4 difference bands of 14NO3 and 15NO3 have been observed in the 1643.6 cm−1 and 1622.0 cm−1 region, respectively, and analyzed to determine molecular constants in the v3 = 2 state. The present paper also reports re-analysis of high-resolution spectra of the 15NO3 radical from 2000 to 2500 cm−1, which have been reported previously without vibrational assignments [J. Phys. Chem. A 114(2010), 980]. Three bands at 2004, 2128, and 2492 cm−1 are analyzed as the ν1 + ν3, 2ν3, and ν1 + ν3 + ν4 bands, including perturbations from nearby states. All vibrational states of 14NO3 and 15NO3 so far observed by infrared spectroscopy and laser induced fluorescence (LIF) are analyzed by using a vibrational energy matrix including cubic and quartic anhamonic effects, to determine anharmonicity constants and eigenvector coefficients. The first-order Coriolis coupling constants Cζ and the effective spin–orbit interaction constants aeff are calculated by using the eigenvector coefficients and compared with the observed values.

Фотогальванический эффект в ферромагнетике со спин-орбитальным взаимодействием

The effect of the appearance of an electric current induced by the electromagnetic radiation at the interface of a ferromagnet and a non-magnetic material is calculated theoretically, taking into account the Rashba spin-orbit coupling. It is shown that the electric dipole transitions between the spin subbands of the conduction electrons of a ferromagnet due to the Rashba interaction lead to a photocurrent. This current has a resonance at a frequency corresponding to the energy of the exchange splitting of spin subbands. The resonance width is determined by the spin-orbit interaction constant. The estimates made show the possibility of experimental observation of this effect in specially prepared multilayer systems.

Photovoltaic effect in a ferromagnet with spin-orbit coupling

The effect of the appearance of an electric current induced by the electromagnetic radiation at the interface of a ferromagnet and a non-magnetic material is calculated theoretically, taking into account the Rashba spin-orbit coupling. It is shown that the electric dipole transitions between the spin subbands of the conduction electrons of a ferromagnet due to the Rashba interaction lead to a photocurrent. This current has a resonance at a frequency corresponding to the energy of the exchange splitting of spin subbands. The resonance width is determined by the spin-orbit interaction constant. The estimates show the possibility of experimental observation of this effect in specially prepared multilayer systems. Keywords: Ferromagnet, exchange coupling, Rashba spin-orbit coupling, photovoltaic effect.

Determination of the Rashba and Dresselhaus Spin–Orbit Interaction Parameters and g‐Factor from the Critical Points of the Spectrum in a 2D Electron Gas in an In‐Plane Magnetic Field

A 2D electron gas with spin–orbit interaction (SOI) is known to form an anisotropic system with van Hove singularities controllable by a parallel magnetic field. The conductivity tensors of this system in the presence of both Rashba and Dresselhaus SOIs is studied. It is found that the diagonal elements of the conductivity tensor have sharp dips when the Fermi level passes through the singularity point of a spectrum. The energy position of these dips at different orientations of the magnetic field allows one to determine both SOI constants and the Landé g‐factor. The dependencies of the surface charge concentration on the Fermi level show a sharp change in the slope near the minimum of the spectrum due to the jumps of the density of states, while the van Hove singularities are not noticeable. In a zero magnetic field, the conductivity tensor has off‐diagonal terms which change the sign when the Fermi level passes the saddle points of the spectrum. The off‐diagonal terms evidence the appearance of the Hall voltage caused by the anisotropy of the Fermi surface and the scattering process.

Magnetic field driven topological transitions in the noncentrosymmetric energy spectrum of the two-dimensional electron gas with Rashba-Dresselhaus spin-orbit interaction

Spin orbit interaction (SOI) having a complicated energy spectrum with a conical point and four critical points are promising candidates to observe electron topological transitions. In the present paper we have investigated the evolution of the electron spectrum and isoenergetic contours under the influence of parallel magnetic field. General formulas for energies of critical points for arbitrary values of SOI constants and magnetic field are found. The existence of critical magnetic fields at which a number of critical points is changed has been predicted. The magnetic field driving topological Lifshitz transitions in the geometry of isoenergetic contours have been studied. Van Hove's singularities in the electron density of states are calculated. The obtained results can be used for theoretical investigations of different electron characteristics of such 2D systems.

Coulomb pairing of electrons in thin films with strong spin-orbit interaction

In low-dimensional structures with strong Rashba spin-orbit interaction (SOI), the Coulomb fields between moving electrons produce a SOI component of the pair interaction that competes with the potential Coulomb repulsion. If the Rashba SOI constant of the material is sufficiently high, the total electron-electron interaction becomes attractive, which leads to the formation of the two-electron bound states. We show that because of the dielectric screening in a thin film the binding energy is significantly higher as compared to the case of the bulk screening.

Experimental Study and Analysis of Absorption Spectra of Ni2+ Ions in Nickel Orthoborate Ni3(BO3)2

The results of studies of the absorption spectra of nickel orthoborate Ni3(BO3)2 in the range of electronic d–d-transitions are reported. The obtained data are analyzed in the framework of the crystal field theory. The Ni2+ ions are located in two crystallographically nonequivalent positions 2a and 4f with point symmetry groups C2h and C2, respectively, surrounded by six oxygen ions forming deformed octahedra. The absorption spectra exhibit three intense bands corresponding to spin-resolved transitions from the ground state of nickel ion 3A2g (3F) to the sublevels of the 3T2g (3F), 3T1g (3F) and 3T1g (3P) triplets split by the spinorbit interaction and the rhombic component of the crystal field. At temperatures below 100 K, the spectra exhibit a thin structure, in which phonon-free lines can be distinguished. Comparison of the calculated frequencies of the zero-phonon transitions with the experimental data allows estimating parameters of the crystal field acting on the nickel ions in the 2a- and 4f-positions, as well as the parameters of electrostatic interaction between the 3d electrons and spin-orbit interaction constants.

Spin-orbit-driven electron pairing in two dimensions

We show that the spin-orbit interaction (SOI) arising due to the in-plane electric field of the Coulomb repulsion between electrons in a two-dimensional quantum well produces an attractive component in the pair interaction Hamiltonian that depends on the spins and momenta of electrons. If the Rashba SOI constant of the material is high enough the attractive component overcomes the Coulomb repulsion and the centrifugal barrier, which leads to the formation of the two-electron bound states. There are two distinct types of two-electron bound states. The relative bound states are formed by the electrons orbiting around their common barycenter. They have the triplet spin structure and are independent of the center-of-mass momentum. In contrast, the convective bound states are formed because of the center-of-mass motion, which couples the electrons with opposite spins. The binding energy in the meV range is attainable for realistic conditions.

Экспериментальное исследование и анализ спектров поглощения ионов Ni-=SUP=-2+-=/SUP=- в ортоборате никеля Ni-=SUB=-3-=/SUB=-(BO-=SUB=-3-=/SUB=-)-=SUB=-2-=/SUB=-

AbstractThe results of studies of the absorption spectra of nickel orthoborate Ni_3(BO_3)_2 in the range of electronic d – d -transitions are reported. The obtained data are analyzed in the framework of the crystal field theory. The Ni^2+ ions are located in two crystallographically nonequivalent positions 2 a and 4 f with point symmetry groups C _2 h and C _2, respectively, surrounded by six oxygen ions forming deformed octahedra. The absorption spectra exhibit three intense bands corresponding to spin-resolved transitions from the ground state of nickel ion ^3 A _2 g (^3 F ) to the sublevels of the ^3 T _2 g (^3 F ), ^3 T _1 g (^3 F ) and ^3 T _1 g (^3 P ) triplets split by the spinorbit interaction and the rhombic component of the crystal field. At temperatures below 100 K, the spectra exhibit a thin structure, in which phonon-free lines can be distinguished. Comparison of the calculated frequencies of the zero-phonon transitions with the experimental data allows estimating parameters of the crystal field acting on the nickel ions in the 2 a - and 4 f -positions, as well as the parameters of electrostatic interaction between the 3 d electrons and spin-orbit interaction constants.

High-resolution Fourier transform emission spectroscopy of the A∼2Πi-X∼2Πi band of the OCS+ ion.

High resolution Fourier transform emission spectroscopy of the A∼2Πi-X∼2Πi band of the OCS+ ion was performed in the UV region to observe the ν1 (CO stretch) progression bands (υ1 = 0 → 2-5) for both the Ω=3/2 and 1/2 spin components. Accurate molecular constants including the rotational constants, B0 = 0.194 765(13) and 0.187 106(13) cm-1, and the spin-orbit interaction constants, A0 = -381.0(56) and -126.5(56) cm-1, were determined for the X∼2Π and A∼2Π states, respectively, by the simultaneous analysis of the observed progression bands. The CO bond length (rCO = 1.2810 Å) for the A∼2Π state, derived from the rotational constant B0 and Franck-Condon factors, is longer by 0.1756 Å than that (1.1054 Å) for the X∼2Π state, while the CS bond length for the A∼2Π state is shorter by 0.0905 Å than that for the X∼2Π state. Pure rotational transition frequencies in the ground X∼2Π state are predicted, as well as transition frequencies of the ν1 fundamental band, with the present molecular constants.

Experimental and theoretical investigation of the vibrational band structure of the 1 Πu5-1 Πg5 high-spin system of C2.

Vibrational levels of the recently observed high-spin transition (1 Πu5-1 Πg5) of dicarbon [P. Bornhauser et al., J. Chem. Phys. 142, 094313 (2015)] are explored by applying non-linear double-resonant four-wave mixing and laser-induced fluorescence methods. The deperturbation of the d Πg3, υ = 8 and 1 Πg5, υ = 3 states results in accurate molecular constants for the υ = 3 "dark" quintet state. In addition, the spin-orbit interaction constant is determined and parameters for the upper Swan level d Πg3, υ = 8 are improved. The first excited vibrational state of 1 Πu5 is observed by performing perturbation-assisted intersystem crossing via "gateway" states in the d Πg3, υ=6∼1 Πg5,υ= 0 system. The rotationally resolved spectra yield 11 transitions to 1 Πu5, υ = 1 that include four spin-substates. Data reduction results in accurate molecular constants of this vibrational level in the shallow potential energy surface of this state. Finally, υ = 1 and 2 of the lower quintet state (1 Πg5) are measured by performing perturbation-assisted double-resonant excitation to the 1 Πu5, υ = 0 state and observing dispersed fluorescence. The obtained molecular constants are compared with high level ab initio computations at the multi-reference configuration interaction (MRCI) level of theory by using a large correlation consistent basis set or, alternatively, by applying the computationally less demanding method of explicitly correlated multi-reference configuration interaction (MRCI-F12). The spectroscopic accuracy of both methods is evaluated by comparison with the experimental findings.

The new investigation of the [formula omitted] system of AlH

The b3Σ−–a3Π visible system of AlH was observed at high resolution by using a high accuracy, dispersive optical spectroscopy technique. The emission spectrum was excited in an aluminum hollow-cathode lamp with two anodes, filled with a static Ne/NH3 gas mixture. In the 25,900–26,500cm−1 spectral region, the rotational structure of the two overlapped 0–0 and 1–1 bands was clearly observed and precisely measured. In total, 260 transition wavenumbers have been assigned with an estimated accuracy of about 0.005cm−1. The open rotational structure of the Q branches in both bands has been measured for the first time, and the Λ-doubling in the a3Π,v=0,1 levels has been described by o,p and q parameters. For example, the values for the v=0 level are p0=1.754(14)×10−2cm−1, q0=3.264(28)×10−3cm−1 and o0=9.34(20)×10−2cm−1. Moreover, the spin–orbit interaction constants for the a3Π state have been obtained experimentally as follows: A0=40.6040(42)cm−1 and A1=40.419(59)cm−1. The a3Π,v=0,1 levels are considered as regular, while for the b3Σ−,v=0,1 levels considerable perturbations in the rotational structure have been observed. Consequently, these states have been represented in a different way in our least-squares treatment: a3Π state by molecular constants and b3Σ− state by term values. The observed irregularities in the b3Σ− state have been graphically described by plotting experimental minus calculated term values versus quantum number N for the v=0 level, as well as by plotting reduced term values versusN(N+1) for the v=1 level.

The possibility of determining the spin-orbit interaction constants using scanning tunneling microscopy

A study of electron tunneling from quasi-two-dimensional (surface) states with spin-orbit interaction into bulk-mode states, within the framework of a model of an infinitely thin inhomogeneous tunnel magnetic barrier between two conductors. We analyze how the scattering of quasi-two-dimensional electrons on a single magnetic defect affects the tunneling current in this system. We also obtain an analytical expression for the conductance of the tunnel point-contact, as a function of its distance from the defect. It is shown that analyzing local magnetization oscillations around the defect using spin-polarized scanning tunneling microscopy allows us to determine the spin-orbit interaction constant.

Anisotropic spin–orbit stark effect in cubic semiconductors without an inversion center

The effect of external electric and magnetic fields on shallow donor levels in a semiconductor of the Td crystallographic class is analyzed. Application of an electric field eliminates the symmetry of the donor potential with respect to space inversion; as a result, corrections from the momentum-odd spin–orbit Dresselhaus term appear in the donor levels. In a strong electric field, such corrections determine the anisotropy of spin splitting of the donor levels relative to the directions of the external fields in the crystallographic coordinate system. Analytic expressions are derived for the spin splitting anisotropy for various relations between the magnitudes of the magnetic and electric fields. The results of this study can be used to determine the Dresselhaus spin–orbit interaction constant by a new method (in experiments on spin splitting of donor levels).

Spectroscopic and theoretical studies of the low-lying states of BaO(+).

The BaO(+) cation is of interest from the perspectives of electronic structure and the potential for cooling to ultra-cold temperatures. Spectroscopic data for the ion have been obtained using a two-color photoionization technique. The ionization energy for BaO was found to be 6.8123(3) eV. The ground state of BaO(+) was identified as X(2)Σ(+), and both vibrational and rotational constants were determined. Vibrationally resolved spectra were recorded for A(2)Π, the first electronically excited state. These data yielded the term energy, vibrational frequency, and the spin-orbit interaction constant. Relativistic electronic structure calculations were carried out using multi-reference configuration interaction (MRCI), coupled cluster and density functional theory methods. Transition moments for the pure vibrational and A(2)Π-X(2)Σ(+) transitions were predicted using the MRCI method.

Millimeter-wave spectroscopy of the FeCO radical in the ν2 and ν3 vibrationally excited states.

The pure rotational spectra of the FeCO radical in the ν2 (bending) and ν3 (Fe-C stretching) vibrational states of the ground X̃(3)Σ(-) electronic state were observed in the millimeter-wave region. The equilibrium rotational and centrifugal distortion constants were determined to be Be = 4374.631 (58) MHz and De = 1.1666 (20) kHz together with the spin-spin coupling constant λe = 691.89 (37) GHz and spin-rotation coupling constant γe = - 1079.4 (55) MHz with use of the millimeter-wave results and the ν1 IR data. The equilibrium bond length for Fe-C was derived to be 1.725 Å assuming that for C-O to be 1.159 Å. Since the vibronic symmetry of the excited state of bending vibration is (3)Π, the analysis of spectrum in the ν2 state required an effective spin-orbit interaction constant of A2 = 6.0219 (61) GHz together with three parity doubling constants of o2 = 36.168 (10) GHz, p2 = 85.18 (34) MHz, and q2 = 4.7024 (17) MHz. The effective spin-orbit interaction constant A2 is attributed to the vibronic mixing of the (3)Π excited electronic states. The vibronic mixing also cause the parity doubling constants o2 and p2, but the main contribution to q2 is given by the vibrational l-type doubling.

High-resolution laser spectroscopy and magnetic effect of the B̃(2)E(')←X̃(2)A2(') transition of the (15)N substituted nitrate radical.

Rotationally resolved high-resolution fluorescence excitation spectra of the 0-0 band of the B̃(2)E(')←X̃(2)A2(') transition of the (15)N substituted nitrate radical were observed for the first time, by crossing a jet-cooled molecular beam and a single-mode dye laser beam at right angles. Several thousand rotational lines were detected in the 15 080-15 103 cm(-1) region. We observed the Zeeman splitting of intense lines up to 360 G in order to obtain secure rotational assignment. Two, nine, and seven rotational line pairs with 0.0248 cm(-1) spacing were assigned to the transitions from the X̃(2)A2(') (υ″ = 0, k″ = 0, N″ = 1, J″ = 0.5 and 1.5) to the (2)E3/2(') (J' = 1.5), (2)E1/2(') (J' = 0.5), and (2)E1/2(') (J' = 1.5) levels, respectively, based on the ground state combination differences and the Zeeman splitting patterns. The observed spectrum was complicated due to the vibronic coupling between the bright B̃(2)E(') (υ = 0) state and surrounding dark vibronic states. Some series of rotational lines other than those from the X̃(2)A2(') (J = 0.5 and 1.5) levels were also assigned by the ground state combination differences and the observed Zeeman splitting. The rotational branch structures were identified, and the molecular constants of the B̃(2)E1/2(') (υ = 0) state were estimated by a deperturbed analysis to be T0 = 15 098.20(4) cm(-1), B = 0.4282(7) cm(-1), and DJ = 4 × 10(-4) cm(-1). In the observed region, both the (2)E1/2(') and (2)E3/2(') spin-orbit components were identified, and the spin-orbit interaction constant of the B̃(2)E(') (υ = 0) state was estimated to be -12 cm(-1) as the lower limit.

Simultaneous analysis of the Ballik-Ramsay and Phillips systems of C2 and observation of forbidden transitions between singlet and triplet states.

6229 lines of the Ballik-Ramsay system (b(3)Σg (-)-a(3)Πu) and the Phillips system (A(1)Πu-X(1)Σg (+)) of C2 up to v = 8 and J = 76, which were taken from the literature or assigned in the present work, were analyzed simultaneously by least-squares fitting with 82 Dunham-like molecular parameters and spin-orbit interaction constants between the b(3)Σg (-) and X(1)Σg (+) states with a standard deviation of 0.0037 cm(-1) for the whole data set. As a result of the deperturbation analysis, the spin-orbit interaction constant AbX was determined as 6.333(7) cm(-1) and the energy difference between the X(1)Σg (+) and a(3)Πu states was determined as 720.008(2) cm(-1) for the potential minima or 613.650(3) cm(-1) for the v = 0 levels with Merer and Brown's N(2) Hamiltonian for (3)Π states, which is about 3.3 cm(-1) larger than the previously determined value. Due to this sizable change, a new energy-level crossing was found at J = 2 for v = 3 (F1) of b(3)Σg (-) state and v = 6 of X(1)Σg (+) state, where the strong interaction causes a nearly complete mixing of the wave functions of the b(3)Σg (-) and X(1)Σg (+) states and the forbidden transitions become observable. Using the predictions of our deperturbation analysis, we were able to identify 16 forbidden transitions between the singlet and triplet states at the predicted frequencies with the expected intensities, which verifies our value for the energy difference between the X(1)Σg (+) and a(3)Πu states.