A review of current research on spin currents and spin–orbit torques

Spintronics is a new discipline focusing on the research and application of electronic spin properties. After the discovery of the giant magnetoresistance effect in 1988, spintronics has had a huge impact on scientific progress and related applications in the development of information technology. In recent decades, the main motivation in spintronics has been efficiently controlling local magnetization using electron flow or voltage rather than controlling the electron flow using magnetization. Using spin–orbit coupling in a material can convert a charge current into a pure spin current(a flow of spin momenta without a charge flow) and generate a spin–orbit torque on the adjacent ferromagnets. The ability of spintronic devices to utilize spin-orbit torques to manipulate the magnetization has resulted in large-scale developments such as magnetic random-access memories and has boosted the spintronic research area. Here in, we review the theoretical and experimental results that have established this subfield of spintronics. We introduce the concept of a pure spin current and spin-orbit torques within the experimental framework, and we review transport-, magnetization-dynamics-, and opticalbased measurements and link then to both phenomenological and microscopic theories of the effect. The focus is on the related progress reported from Chinese universities and institutes, and we specifically highlight the contributions made by Chinese researchers.     

Thermoelectric transport and spin density of graphene nanoribbons with Rashba spin–orbit interaction

In the present paper, we have theoretically investigated thermoelectric transport properties of armchair and zigzag graphene nanoribbons with Rashba spin–orbit interaction, as well as dephasing scattering processes by applying the nonequilibrium Green function method. Behaviors of electronic and thermal currents, as well as thermoelectric coefficients are studied. It is found that both electronic and thermal currents decrease, and thermoelectric properties been suppressed, with increasing strength of Rashba spin–orbit interaction. We have also studied spin split and spin density induced by Rashba spin–orbit interaction in the graphene nanoribbons.     

Nuclear spin–spin constants,rotational g factor and susceptibility of sulphur hexafluoride

Following our previous study on spin–rotation and shielding constants of the SF₆ molecule, the rotational g factor and the magnetic susceptibility are calculated here, using ab initio methods to evaluate the electronic contribution to the nuclear hyperfine constants, and compared with experimental results. It is shown, for the first time, that the electronic component of the rotational g factor is proportional to a constant, which is given by a sum over electronic states. We also evaluate for the SF₆ molecule the indirect, or electron-coupled spin–spin interaction, theoretically described by Ramsey, and show that it gives non-negligible corrections to direct coupling constants d ₁ and d ₂. The contributions of the terms included in this interaction (DSO, PSO, SD and FC) are also analysed.     

Density-functional calculations of the nuclear magnetic shielding and indirect nuclear spin–spin coupling constants of three isomers of C20

The parameters of the nuclear magnetic resonance (NMR) spectrum – shielding constants and indirect spin–spin coupling constants – of three isomers of C₂₀ are studied using density-functional theory. The performance of different exchange–correlation functionals is analysed by optimising the geometry for the ring, bowl and cage isomers, followed by a computation of the NMR constants at the optimised structure. The results are analysed and rationalised by performing comparisons of the three isomers with one another and with related systems such as polyynes (for the ring), o-benzyne (for the bowl) and C₆₀ (for the cage). The shielding and spin–spin parameters calculated using the Perdew–Burke–Ernzerhof (PBE) exchange–correlation functional are sufficiently reliable to assist in future experimental NMR studies of C₂₀ and, in particular, the identification of its isomers.     

Influences of spin–orbit interaction on quantum speed limit and entanglement of spin qubits in coupled quantum dots

Quantum speed limit and entanglement of a two-spin Heisenberg XYZ system in an inhomogeneous external magnetic field are investigated. The physical system studied is the excess electron spin in two adjacent quantum dots. The influences of magnetic field inhomogeneity as well as spin–orbit coupling are studied. Moreover, the spin interaction with surrounding magnetic environment is investigated as a non-Markovian process. The spin–orbit interaction provides two important features: the formation of entanglement when two qubits are initially in a separated state and the degradation and rebirth of the entanglement.     

Prediction of the 1H NMR spectra of epoxy-fused cyclopentane derivatives by calculations of chemical shifts and spin–spin coupling constants

¹H NMR spectra of epoxy-fused cyclopentane derivatives have been computationally investigated with density functional calculations in order to unravel the shielding effect of the epoxy ring on the ¹H NMR chemical shifts of N-substituted epoxy-fused cyclopentane-3, 5-diol derivatives. Both ¹H NMR chemical shifts and spin–spin coupling constants have been calculated with the WP04/cc-pVTZ level of theory in solution. The WP04/cc-pVTZ// B3LYP/6-31+G(d) methodology has been found to reproduce the best experimental results on epoxy-fused cyclopentane derivatives. This study is expected to lead experimentalists in their endeavour to characterize epoxy-fused cyclic systems with ease.     

Characteristics of persistent spin current components in a quasi-periodic Fibonacci ring with spin–orbit interactions: Prediction of spin–orbit coupling and on-site energy

In the present work we investigate the behavior of all three components of persistent spin current in a quasi-periodic Fibonacci ring subjected to Rashba and Dresselhaus spin–orbit interactions. Analogous to persistent charge current in a conducting ring where electrons gain a Berry phase in presence of magnetic flux, spin Berry phase is associated during the motion of electrons in presence of a spin–orbit field which is responsible for the generation of spin current. The interplay between two spin–orbit fields along with quasi-periodic Fibonacci sequence on persistent spin current is described elaborately, and from our analysis, we can estimate the strength of any one of two spin–orbit couplings together with on-site energy, provided the other is known.     

Acoustic phonons mediated non-equilibrium spin current in the presence of Rashba and Dresselhaus spin–orbit couplings

Influence of electrons interaction with longitudinal acoustic phonons on magnetoelectric and spin-related transport effects are investigated. The considered system is a two-dimensional electron gas system with both Rashba and Dresselhaus spin–orbit couplings. The works which have previously been performed in this field, have revealed that the Rashba and Dresselhaus couplings cannot be responsible for spin current in the non-equilibrium regime. In the current Letter, a semiclassical method was employed using the Boltzmann approach and it was shown that the spin current of the system, in general, does not go all the way to zero when the electron–phonon coupling is taken into account. It was also shown that spin accumulation of the system could be influenced by electron–phonon coupling.     

Effects of charge on the structures and spin moments of Nil3 cluster

The structural stability and magnetic properties of the icosahedral Ni13, Ni13^＋1 and Ni13^-1 clusters have been obtained by utilizing all-electron density functional theory with the generalized gradient approximations for the exchange-correlation energy. The calculated results show that the ground states of neutral and charged clusters all favour a D3d structure, a distorted icosahedron, due to the Jahn-Teller effect. The radial distortions caused by doping one electron and by doping one hole are opposite to each other. Doping one electron will result in a 1/2 decrease and doping one hole will result in a 1/2 increase of the total spin. Both increasing interatomic spacing and decreasing coordination will lead to an enhancement of the spin magnetic moments for Nil3 clusters.     

Imposing changes of band and spin–orbit gaps in GaNBi

We present first-principles pseudopotential plane-wave calculations to explore the effects of alloying of non conventional III–V compound GaN with bismuth. We found a highly nonlinear reduction of the energy gap of GaN for small Bi composition. Consequently the optical band gap bowing is found extremely important and composition dependent. The stronger contribution is due principally to structural and, to less extent, to charge transfer effects. Moreover, because of strong relativistic effects caused by bismuth, we found a giant bowing for the spin–orbit splitting energy of valence band, by far the largest of any III–V ternary alloys.     

Theory of spin polarization in mesoscopic spin–orbit coupling systems

We establish a general formalism of the bulk spin polarization (BSP) and the current-based spin polarization (CSP) for mesoscopic ferromagnetic and spin–orbit interaction (SOI) semiconducting systems. Based on this formalism, we reveal the basic properties of BSP and CSP and their relationships. The BSP describes the intrinsic spin polarized properties of devices. The CSP depends on both intrinsic parameters of device and the incident current. For the non-spin-polarized incident current with the in-phase spin-phase coherence, CSP equals to BSP. We give analytically the BSP and CSP of several typical nanodevice models, ferromagnetic nanowire, Rashba nanowire and rings. These results provide basic physical behaviors of BSP and CSP and their relationships.     

General relativistic spin-orbit and spin–spin effects on the motion of rotating particles in an external gravitational field

We analytically compute the orbital effects induced on the motion of a spinning particle geodesically traveling around a central rotating body by the general relativistic two-body spin–spin and spin-orbit leading-order interactions. Concerning the spin-orbit term, we compute the long-term variations due to the particle’s spin by finding secular precessions for the inclination I of the particle’s orbit, its longitude of the ascending node Ω and the longitude of pericenter v{\varpi} . Moreover, we generalize the well-known Lense-Thirring precessions to a generic orientation of the source’s angular momentum by obtaining an entirely new effect represented by a secular precession of I, and additional secular precessions of Ω and v{\varpi} as well. The spin–spin interaction is responsible of gravitational effects à la Stern-Gerlach consisting of secular precessions of I, W, v{I, \Omega, \varpi} and the mean anomaly M{\mathcal{M}} . Such results are obtained without resorting to any approximations either in the particle’s eccentricity e or in its inclination I; moreover, no preferred orientations of both the system’s angular momenta are adopted. Their generality allows them to be applied to a variety of astronomical and astrophysical scenarios like, e.g., the Sun and its planets and the double pulsar PSR J0737-3039A/B. It turns out that the orbital precessions caused by the spin–spin and the spin-orbit perturbations due to the less massive body are below the current measurability level, especially for the solar system and the Stern-Gerlach effects. Concerning the solar Lense-Thirring precessions, the slight misalignment of the solar equator with respect to the ecliptic reduces the gravitomagnetic node precession of Mercury down to a 0.08 mas per century level with respect to the standard value of 1 mas per century obtained by aligning the z axis with the Sun’s angular momentum. The new inclination precession is as large as 0.06 mas per century, while the perihelion’s rate remains substantially unchanged, amounting to −2 mas per century. Further studies may be devoted to the extrasolar planets which exhibit a rich variety of orbital and rotational configurations.     

Zero- and low-temperature behavior of the two-dimensional ±J Ising spin glass

Scaling arguments and precise simulations are used to study the square lattice ±J Ising spin glass, a prototypical model for glassy systems. Droplet theory explains, and our numerical results show, entropically stabilized long-range spin-glass order at zero temperature, which resembles the energetic stabilization of long-range order in higher-dimensional models at finite temperature. At low temperature, a temperature-dependent crossover length scale is used to predict the power-law dependence on temperature of the heat capacity and clarify the importance of disorder distributions.     

Nuclear spin–lattice relaxation and complex motion of macromolecules in solution

The NMR spectral densities of a complex motion consisting of a combination of anisotropic overall motion and internal motion have been derived. Two approximations of the equations derived for the cases of slow, J_slow (ω), and fast, J_fast (ω), internal motions are presented. These equations imply that reduction in spectral density of overall motion can be observed if the maxima of internal and overall motions spectral densities versus temperature are well separated, as for fast internal motion. Slow intramolecular motion influences the values of spectral densities of the overall motion if one of the two spins performs a motion, for example a proton in double minimum of the ¹⁵N-H?···?N hydrogen bond. The analysis presented reveals small differences between the temperature dependencies of spectral densities of the isotropic and anisotropic overall motions. The theory is illustrated by the ¹³C protonated carbon spin-lattice relaxation of α-cyclodextrin macromolecule, using the expected motional parameters: D _∥/D _⊥?≈?5 at room temperature and for a fast or slow internal motion.     

Effects of vibrational averaging on coupled cluster calculations of spin–spin coupling constants for hydrocarbons

We present vibrationally corrected nuclear spin–spin coupling constants for four hydrocarbons with different types of carbon–carbon bonds calculated with coupled cluster (CC) theory. First, we perform a systematic basis set investigation on acetylene for all of the four contributions (Fermi-contact, spin-dipole, para- and diamagnetic spin–orbit) to the spin–spin coupling constants and subsequently choose basis sets of sufficient flexibility to describe converged electronic properties. Then, in order to describe the effects of vibrational motion for the studied molecules we perform a Taylor expansion in the normal coordinates up to second order – a method that is well known for both its quality and efficiency – and rigorously estimate the resulting contribution for all types of spin–spin coupling constants. Combined, this allows us to obtain highly accurate benchmark estimates of the spin–spin coupling constants for acetylene, ethylene, ethane, and cyclopropane. This work provides one of the first systematic benchmarks of zero-point vibrational contributions to spin–spin coupling constants in poly-atomic molecules using the reliable CC theory and it is thus an important reference for further research within in-silico spin–spin coupling constant determination. We note that earlier computational estimates of zero-point vibrational effects agree well with those presented here (for acetylene, ethylene, and cyclopropane) while vibrational corrections for ethane are reported for the first time.