Intrinsic Spin-orbit Interaction Research Articles

Nonadiabatic spin-transfer torque in real materials

The motion of simple domain walls and of more complex magnetic textures in the presence of a transport current is described by the Landau-Lifshitz-Slonczewski (LLS) equations. Predictions of the LLS equations depend sensitively on the ratio between the dimensionless material parameter $\ensuremath{\beta}$ which characterizes nonadiabatic spin-transfer torques and the Gilbert damping parameter $\ensuremath{\alpha}$. This ratio has been variously estimated to be close to zero, close to one, and large compared to one. By identifying $\ensuremath{\beta}$ as the influence of a transport current on $\ensuremath{\alpha}$, we derive a concise, explicit, and relatively simple expression which relates $\ensuremath{\beta}$ to the band structure and Bloch state lifetimes of a magnetic metal. Using this expression we demonstrate that intrinsic spin-orbit interactions lead to intraband contributions to $\ensuremath{\beta}$ which are often dominant, and can be (i) estimated with some confidence and (ii) interpreted using the ``breathing Fermi-surface'' model.

Influence of strain on band structure of semiconductor nanostructures

The influence of the mechanical strain on the electronic structure of the asymmetric (In,Ga)As/GaAs quantum well is considered. Both the direct influence of strain on the orbital part of the electronic structure and an indirect influence through the strain dependent Rashba and Dresselhaus Hamiltonians are taken into account. The analyzed quantum well is taken to have a triangular shape, and is oriented along the <110> direction. For this direction, there exists both the intrinsic and strain-induced spin-orbit interaction. For all analyzed types of spin-orbit interaction, subband splittings depend linearly on the in-plane wave vector. On the other hand, the electronic structure for the Rashba type of the strain-induced spin-orbit interaction shows isotropic dependence in the k-space, while the electronic structure due to the Dresselhaus type shows anisotropy. Furthermore, the Rashba strain-induced spin-orbit interaction increases subband splitting, while the effect of the Dresselhaus Hamiltonian on the electronic structure is opposite to the intrinsic spin-orbit interaction for certain polar angles.

Unscreened Coulomb Interactions and the Quantum Spin Hall Phase in Neutral Zigzag Graphene Ribbons

A study of the effect of unscreened Coulomb interactions on the quantum spin Hall phase of finite-width neutral zigzag graphene ribbons is presented. By solving a tight-binding Hamiltonian that includes the intrinsic spin-orbit (ISO) interaction, exact expressions for band structures and edge-state wave functions are obtained. These analytic results, supported by tight-binding calculations, show that chiral spin-filtered edge states are composed of localized and damped oscillatory wave functions, reminiscent of the ones obtained in armchair ribbons. The addition of long-range Coulomb interactions opens a gap in the charge sector with a gapless spin sector. In contrast to armchair terminations, the charge gap vanishes exponentially with the ribbon width and its amplitude and decay length are strongly dependent on the ISO coupling. Comparison with reported ab initio calculations are presented.

Asymmetries in intrinsic spin-Hall effect in low in-plane magnetic field

Effects of low in-plane magnetic field on bulk spin densities and edge spin accumulations of a diffusive two-dimensional semiconductor stripe are studied. Focusing upon the Dresselhaus-type intrinsic spin-orbit interaction (SOI), we look for the symmetry, or asymmetry, characteristics in two magnetic-field orientations: along and transverse to the stripe. For longitudinal field, the out-of-plane spin density ${S}_{z}$ exhibits odd parity across the stripe and even parity in the magnetic field and is an edge accumulation. For transverse field, the out-of-plane ${S}_{z}$ becomes asymmetric in both spatial and field dependencies and has finite bulk values for finite magnetic fields. Our results support utilizing low in-plane magnetic fields for the probing of the underlying SOI.

Mott Relation for Anomalous Hall and Nernst Effects inGa1−xMnxAsFerromagnetic Semiconductors

The Mott relation between the electrical and thermoelectric transport coefficients normally holds for phenomena involving scattering. However, the anomalous Hall effect (AHE) in ferromagnets may arise from intrinsic spin-orbit interaction. In this work, we have simultaneously measured AHE and the anomalous Nernst effect (ANE) in Ga1-xMnxAs ferromagnetic semiconductor films, and observed an exceptionally large ANE at zero magnetic field. We further show that AHE and ANE share a common origin and demonstrate the validity of the Mott relation for the anomalous transport phenomena.

Spin Hall effect in a Josephson contact

The spin Hall effect on the Josephson tunneling through a two-dimensional normal contact with a spin-orbit split conduction band has been studied in the diffusive regime and at the zero electric bias. Linearized Usadel equations for triplet components of the pairing function in the presence of intrinsic spin-orbit interaction have been derived. These equations have been employed for analysis of the spin Hall effect induced by the supercurrent. We predict that a nondissipative out-of-plane spin Hall polarization accumulates at lateral edges and an in-plane polarization is induced throughout the entire normal region. At the same time, in contrast to the spin Hall effect in normal systems, the spin current is absent in the considered case of the stationary Josephson effect.

Electron-Electron and Spin-Orbit Interactions in Armchair Graphene Ribbons

The effects of intrinsic spin-orbit and Coulomb interactions on low-energy properties of finite width graphene armchair ribbons are studied by means of a Dirac Hamiltonian. It is shown that metallic states subsist in the presence of intrinsic spin-orbit interactions as spin-filtered edge states, in contrast with the insulating behavior predicted for graphene planes. A charge-gap opens due to Coulomb interactions in neutral ribbons, that vanishes as Delta approximately 1/W, with a gapless spin sector. Weak intrinsic spin-orbit interactions do not change the insulating behavior. Explicit expressions for the width-dependent gap and various correlation functions are presented.

Electronic spin transport and spin precession in single graphene layers at room temperature

Electronic transport in single or a few layers of graphene is the subject of intense interest at present. The specific band structure of graphene, with its unique valley structure and Dirac neutrality point separating hole states from electron states, has led to the observation of new electronic transport phenomena such as anomalously quantized Hall effects, absence of weak localization and the existence of a minimum conductivity. In addition to dissipative transport, supercurrent transport has also been observed. Graphene might also be a promising material for spintronics and related applications, such as the realization of spin qubits, owing to the low intrinsic spin orbit interaction, as well as the low hyperfine interaction of the electron spins with the carbon nuclei. Here we report the observation of spin transport, as well as Larmor spin precession, over micrometre-scale distances in single graphene layers. The 'non-local' spin valve geometry was used in these experiments, employing four-terminal contact geometries with ferromagnetic cobalt electrodes making contact with the graphene sheet through a thin oxide layer. We observe clear bipolar (changing from positive to negative sign) spin signals that reflect the magnetization direction of all four electrodes, indicating that spin coherence extends underneath all of the contacts. No significant changes in the spin signals occur between 4.2 K, 77 K and room temperature. We extract a spin relaxation length between 1.5 and 2 mum at room temperature, only weakly dependent on charge density. The spin polarization of the ferromagnetic contacts is calculated from the measurements to be around ten per cent.

Gilbert damping and spin Coulomb drag in a magnetized electron liquid with spin-orbit interaction

We present a microscopic calculation of the Gilbert damping constant for the magnetization of a two-dimensional spin-polarized electron liquid in the presence of intrinsic spin-orbit interaction. First we show that the Gilbert constant can be expressed in terms of the auto-correlation function of the spin-orbit induced torque. Then we specialize to the case of the Rashba spin-orbit interaction and we show that the Gilbert constant in this model is related to the spin-channel conductivity. This allows us to study the Gilbert damping constant in different physical regimes, characterized by different orderings of the relevant energy scales -- spin-orbit coupling, Zeeman coupling, momentum relaxation rate, spin-momentum relaxation rate, spin precession frequency -- and to discuss its behavior in various limits. Particular attention is paid to electron-electron interaction effects,which enter the spin conductivity and hence the Gilbert damping constant via the spin Coulomb drag coefficient.

GRAPHENE AND THE QUANTUM SPIN HALL EFFECT

We show that the intrinsic spin orbit interaction in a single plane of graphene converts the ideal two dimensional semi metallic groundstate of graphene into a quantum spin Hall (QSH) state. This novel electronic phase shares many similarities with the quantum Hall effect. It has a bulk excitation gap, but supports the transport of spin and charge in gapless "spin filtered" edge states on the sample boundary. We show that the QSH phase is associated with a Z2 topological invariant, which distinguishes it from an ordinary insulator. The Z2 classification, which is defined for any time reversal invariant Hamiltonian with a bulk excitation gap, is analogous to the Chern number classification of the quantum Hall effect. We argue that the QSH phase is topologically stable with respect to weak interactions and disorder. The QSH phase exhibits a finite (though not quantized) dissipationless spin Hall conductance even in the presence of weak disorder, providing a new direction for realizing dissipationless spin transport. We will discuss various proposals for experimentally observing the QSH phase, along with generalizations of this effect in three dimensional systems.

A single molecule spin pump

We theoretically put forward a single molecule spin pump, which can generate spin current, even pure spin current. The intrinsic spin–orbit interaction allowed by the molecular symmetry plays a key role in this device. Numerical calculations show the pumped spin current can be modulated by the pumping frequency, the external magnetic flux, and the gate voltage. Such a single molecule device can be realized within the reach of the present-day technology.

Exchange interaction of magnetic impurities in graphene

The indirect exchange interaction between magnetic impurities localized in a graphene plane is considered theoretically, with the influence of intrinsic spin-orbit interaction taken into account. Such an interaction gives rise to an energy gap at the Fermi level, which makes the usual RKKY model not applicable. The results show that the effective indirect exchange interaction is described by a range function which decays exponentially with the distance between magnetic moments. The interaction is also shown to depend on whether the two localized moments belong to the same sublattice or are located in two different sublattices.

Intrinsic and Rashba spin-orbit interactions in graphene sheets

Starting from a microscopic tight-binding model and using second order perturbation theory, we derive explicit expressions for the intrinsic and Rashba spin-orbit interaction induced gaps in the Dirac-like low-energy band structure of an isolated graphene sheet. The Rashba interaction parameter is first order in the atomic carbon spin-orbit coupling strength $\xi$ and first order in the external electric field $E$ perpendicular to the graphene plane, whereas the intrinsic spin-orbit interaction which survives at E=0 is second order in $\xi$. The spin-orbit terms in the low-energy effective Hamiltonian have the form proposed recently by Kane and Mele. \textit{Ab initio} electronic structure calculations were performed as a partial check on the validity of the tight-binding model.

Prohibition of equilibrium spin currents in multiterminal ballistic devices

We show that in the multi-terminal ballistic devices with intrinsic spin-orbit interaction connected to normal metal contacts there are no equilibrium spin currents present at any given electron energy. Obviously, this statement holds also after the integration over all occupied states. Based on the proof of this fact, a number of scenarios involving nonequilibrium spin currents is identified and further analyzed. In particular, it is shown that an arbitrary two-terminal device cannot polarize transient current. The same is true for the output terminal of an N-terminal device when all N-1 inputs are connected in parallel.

Mean-field magnetization relaxation in conducting ferromagnets

Collective ferromagnetic motion in a conducting medium is damped by the transfer of the magnetic moment and energy to the itinerant carriers. We present a calculation of the corresponding magnetization relaxation as a linear-response problem for the carrier dynamics in the effective exchange field of the ferromagnet. In electron systems with little intrinsic spin-orbit interaction, a uniform magnetization motion can be formally eliminated by going into the rotating frame of reference for the spin dynamics. The ferromagnetic damping in this case grows linearly with the spin-flip rate when the latter is smaller than the exchange field and is inversely proportional to the spin-flip rate in the opposite limit. These two regimes are analogous to the “spin-pumping” and the “breathing Fermi-surface” damping mechanisms, respectively. In diluted ferromagnetic semiconductors, the hole-mediated magnetization can be efficiently relaxed to the itinerant-carrier degrees of freedom due to the strong spin-orbit interaction in the valence bands.

Quantum beating in the conductance of ballistic rings

We propose and demonstrate experimentally a novel configuration for observing spin interference effects in the conductance of quantum rings. Our configuration, in which the conducting ring and the tangential current lead form a single collimating contact, precludes spin rotation in the contact region. We have observed the spin quantum beating in the Aharonov–Bohm (AB) conductance oscillations. This beating is the result of a superposition of two independent interference signals associated with the intrinsic spin–orbit interactions. Our work provides conclusive evidence of the spin Berry phase in the ring conductance.

Hall Effect, Magnetic Resistivity, and Magnetic Susceptibility of Nickel and Nickel-Copper Alloys

Hall-effect, electrical-resistivity, and magnetic-susceptibility measurements have been made on polycrystalline specimens of nickel-copper alloys. The temperature range covered is 100 to 700\ifmmode^\circ\else\textdegree\fi{}K. The spontaneous Hall coefficient ${R}_{p}$ in the paramagnetic region has been separated out by simultaneous measurement of the Hall resistivity per unit field and the atomic susceptibility. The magnetic resistivity of the same specimen has also been determined. It has been shown that, for pure nickel, intrinsic spin-orbit interaction provides the right order of magnitude of the spontaneous Hall coefficient ${R}_{p}$. A linear relationship between ${R}_{\mathrm{pi}}$, the impurity part of the paramagnetic Hall coefficient, and ${\ensuremath{\rho}}_{\mathrm{mi}}$, the impurity part of the magnetic resistivity, with a constant of proportionality 4.5 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}5}$ ${\mathrm{G}}^{\ensuremath{-}1}$, has been observed in alloys.