The effects of electron–phonon interaction on anisotropic RKKY interaction in graphene nanoribbon

We study the Ruderman–Kittle–Kasuya–Yosida (RKKY) interaction in doped armchair graphene nanoribbon. The effects of both external magnetic field and electron-Holstein phonon on RKKY interaction have been addressed. RKKY interaction as a function of distance between localized moments has been analyzed. It has been shown that a magnetic field along the z-axis mediates an anisotropic interaction which corresponds to a XXZ model interaction between two magnetic moments. In order to calculate the exchange interaction along arbitrary direction between two magnetic moments, we should obtain both transverse and longitudinal static spin susceptibilities of armchair graphene nanoribbon in the presence of electron-phonon coupling and magnetic field. The spin susceptibility components are calculated using the spin dependent Green’s function approach for Holstein model Hamiltonian. The effects of spin polarization on the dependence of exchange interaction on distance between moments are investigated via calculating correlation function of spin density operators. Our results show the influences of magnetic field on the spatial behavior of in-plane and longitudinal RKKY interactions are different in the presence of magnetic field.     

Indirect RKKY interaction in doped armchair nanotube due to electron phonon interaction effects

We study the Ruderman-Kittle-Kasuya-Yosida (RKKY) interaction in doped armchair nanotube in the presence of gap parameter. The effects of both next nearest neighbor hopping parameter and electron-Holstein phonon on RKKY interaction have been addressed. RKKY interaction as a function of distance between localized moments have been analyzed. In order to calculate the exchange interaction along arbitrary direction between two magnetic moments, we should obtain the transverse static spin susceptibility of armchair graphene nanoribbon in the presence of electron-phonon coupling and gap parameter. The spin susceptibility components are calculated using Green’s function approach for Holstein model Hamiltonian. The effects of electron doping on dependence of exchange interaction on distance between moments are investigated via calculating correlation function of spin density operators. Our results show the influences of next nearest neighbor hopping parameter on the spatial behavior of RKKY interactions are different in the presence of electron phonon coupling.     

Effect of kinematic interaction in the renormalized spin wave theory for isotropic ferromagnet

The procedure of calculating within the frame-work of renormalized spin wave approximation the contribution from kinematic interaction of ferromagnons to the partition function and magnetization of the isotropic cubic ferromagnet is established. The investigation seen here through extends Dysons's spin wave approach to higher temperatures up to the critical point. In contradistinction to the graphs due to dynamic interaction of spin waves which effect the renormalization of the energy of non-interacting ferromagnons, the diagrams resulting from kinematic interaction are shown to correct the average spin wave population numbers only. That correction proves to be a solution of an integral equation and its quantity depends both on the temperature and the atomic spin quantum numberS, and it tends to zero with increasingS.     

The thermodynamic one-particle Green function in the renormalized spin wave approximation for isotropic cubic ferromagnets

The thermodynamic one-particle Green function in the renormalized spin wave approximation for isotropic cubic ferromagnetic insulators with Dyson's spin wave theory as a base is derived. In quantitative respect, dynamic and kinematic effects of spin waves are approximated by the graphs deficient in the energy denominators, wherefore at low temperature kinematic interaction turns out to be too strong. As against the one-particle Green function for independent spin waves, dynamic interaction of ferromagnons is shown to effect the renormalization of the spin wave energy, whereas kinematic interaction directly modifies the average ferromagnon population numbers. In the matter of magnetization, its formula based on the Green function assumes a similar form as in the spin wave theory without interactions on the understanding that it remains valid within the entire range of temperatures from absolute zero up to the critical point.     

Spin Hall and spin Nernst effects in graphene with intrinsic and Rashba spin-orbit interactions

The spin Hall and spin Nernst effects in graphene are studied based on Green’s function formalism.We calculate intrinsic contributions to spin Hall and spin Nernst conductivities in the Kane-Mele model with various structures.When both intrinsic and Rashba spin-orbit interactions are present,their interplay leads to some characteristics of the dependence of spin Hall and spin Nernst conductivities on the Fermi level.When the Rashba spin-orbit interaction is smaller than intrinsic spin-orbit coupling,a weak kink in the conductance appears.The kink disappears and a divergence appears when the Rashba spin-orbit interaction enhances.When the Rashba spin-orbit interaction approaches and is stronger than intrinsic spin-orbit coupling,the divergence becomes more obvious.     

Spin-Hall transport in a two-dimensional electron system with magnetic impurities

The spin Hall transport properties in a two-dimensional electron system with both Rashba spin-orbit coupling (SOC) and magnetic impurities are investigated. Electrons are scattered by impurities through an exchange interaction that leads to spin flip-flop processes and so changes the spin Hall effect induced by the SOC. The spin Hall conductance is calculated in a 4-terminal system using the Landauer-Buttiker formula and Green function approach. In comparison with the simulation results on nonmagnetic impurities doping systems, our results reveal that the spin Hall conductance is still nonzero in a system with a large density of magnetic impurities and a finite intensity of the exchange interaction between the electrons and impurities, and its sign may be altered when the doping density and interaction strength are large enough.     

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.     

Spin waves of a layered ferromagnetic electron gas

Using a first-order Green's function technique, the spin wave spectrum of a layered ferromagnetic electron system is determined in the long-wave length limit. It is shown that the spin wave stiffness is a highly anisotropic quantity. A discussion of the Stoner-Overhauser-Wohlfarth condition shows that both electron tunneling processes and a more sophisticated expression of the Coulomb interaction matrix element than the usual Hubbard form are important for the existence of ferromagnetic ordering.     

Interplay of Rashba spin orbit coupling and disorder in the conductance properties of a four terminal junction device

We report a thorough theoretical investigation on the quantum transport of a disordered four terminal device in the presence of Rashba spin orbit coupling (RSOC) in two dimensions. Specifically we compute the behaviour of the longitudinal (charge) conductance, spin Hall conductance and spin Hall conductance fluctuation as a function of the strength of disorder and Rashba spin orbit interaction using the Landauer Büttiker formalism via Green’s function technique. Our numerical calculations reveal that both the conductances diminish with disorder. At smaller values of the RSOC parameter, the longitudinal and spin Hall conductances increase, while both vanish in the strong RSOC limit. The spin current is more drastically affected by both disorder and RSOC than its charge counterpart. The spin Hall conductance fluctuation does not show any universality in terms of its value and it depends on both disorder as well as on the RSOC strength. Thus the spin Hall conductance fluctuation has a distinct character compared to the fluctuation in the longitudinal conductance. Further one parameter scaling theory is studied to assess the transition to a metallic regime as claimed in literature and we find no confirmation about the emergence of a metallic state induced by RSOC.     

Spin Hall effect on edge magnetization and electric conductance of a 2D semiconductor strip

The intrinsic spin Hall effect on spin accumulation and electric conductance in a diffusive regime of a 2D electron gas has been studied for a 2D strip of a finite width. It is shown that the spin polarization near the flanks of the strip, as well as the electric current in the longitudinal direction, exhibit damped oscillations as a function of the width and strength of the Dresselhaus spin-orbit interaction. Cubic terms of this interaction are crucial for spin accumulation near the edges. As expected, no effect on the spin accumulation and electric conductance have been found in case of Rashba spin-orbit interaction.     

Origin of magnetic anisotropy of Gd metal

Using first-principles theory, we have calculated the energy of Gd as a function of spin direction, theta, between the c and a axes and found good agreement with experiment for both the total magnetic anisotropy energy and its angular dependence. The calculated low temperature direction of the magnetic moment lies at an angle of 20 degrees to the c axis. The calculated magnetic anisotropy energy of Gd metal is due to a unique mechanism involving a contribution of 7.5 microeV from the classical dipole-dipole interaction between spins plus a contribution of 16 microeV due to the spin-orbit interaction of the conduction electrons. The 4f spin polarizes the conduction electrons via exchange interaction, which transfers the magnetic anisotropy of the conduction electrons to the 4f spin.     

Spin-polarized transport through the T-shaped double quantum dots

Using the Keldysh nonequilibrium Green function and equation-of-motion technique, this paper investigates the spin-polarized transport properties of the T-shaped double quantum dots （DQD） coupled to two ferromagnetic leads. There are both Fano effect and Kondo effect in the system, and due to their mutual interaction, the density of states, the current, and the differential conductance of the system depend sensitively on the spin-polarized strength. Thus the obtained results show that this system is provided with excellent spin filtering property, which indicates that this system may be a candidate for spin valve transistors in the spintronics.     

Parallel susceptibility of chain-like antiferromagnets

The parallel susceptibility of chain-like antiferromagnets is obtained by the spin wave theory considering kinematical interaction. The result obtained is very similar to that given by the Green function method for usual antiferromagnets. The correction due to kinematical interaction is expressed as a function of the spin reduction. It is found that the effect of kinematical interaction on the susceptibility is very large for chain-like antiferromagnets. Dynamical interaction is shown to contribute also greatly to the susceptibility. Numerical calculations are made for KCuF₃. Case of antiferromagnetic and ferromagnetic inter-chain exchange interaction are investigated numerically and it is concluded that the sign of the inter-chain exchange interaction is not important for chain-like antiferromagnets.     

Beta function and anomaly of the Fermi surface for a d=1 system of interacting fermions in a periodic potential

We derive a perturbation theory, based on the renormalization group, for the Fermi surface of a one dimensional system of fermions in a periodic potential interacting via a short range, spin independent potential. The infrared problem is studied by writing the Schwinger functions in terms of running couplings. Their flow is described by a Beta function, whose existence and analyticity as a function of the running couplings is proved. If the fermions are spinless we prove that the Beta function is vanishing and the renormalization flow is bounded for any small interaction. If the fermions are spinning the Beta function is not vanishing but, if the conduction band is not filled or half filled and the interaction is repulsive, it is possible again to control the flow proving the partial asymptotic freedom of the theory. This is done showing that the Beta function is partially vanishing using the exact solution of the Mattis model, which is the spin analogue of the Luttinger model. In both these cases Schwinger functions are anomalous so that the system is a Luttinger liquid. Our results extend the work in [B.G.P.S.], where neither spin nor periodic potential were considered; an explicit proof of some technical results used but not explicitly proved there is also provided.     

Weak localization and coulomb interaction in disordered systems

Interacting electrons, diffusing in a two-dimensional (2d) disordered system, are studied. The renormalization group equations, including both localization effects and Coulomb correlations, are derived. We encounter a qualitatively new situation: the constants describing electron interaction diverge as a result of the renormalization when a certain scale is achieved, whereas the resistence proves to be finite. Calculation of the spin density correlation function reveals that the system exhibits a tendency for spin density rearrangement.     

Conductance oscillations of a spin-orbit stripe with polarized contacts

We investigate the linear conductance of a stripe of spin-orbit interaction in a 2D electron gas; that is, a 2D region of length l\ell along the transport direction and infinite in the transverse one in which a spin-orbit interaction of Rashba type is present. Polarization in the contacts is described by means of Zeeman fields. Our model predicts two types of conductance oscillations: Ramsauer oscillations in the minority spin transmission, when both spins can propagate, and Fano oscillations when only one spin propagates. The latter are due to the spin-orbit coupling with quasibound states of the non propagating spin. In the case of polarized contacts in antiparallel configuration Fano-like oscillations of the conductance are still made possible by the spin orbit coupling, even though no spin component is bound by the contacts. To describe these behaviors we propose a simplified model based on an ansatz wave function. In general, we find that the contribution for vanishing transverse momentum dominates and defines the conductance oscillations. Regarding the oscillations with Rashba coupling intensity, our model confirms the spin transistor behavior, but only for high degrees of polarization. Including a position dependent effective mass yields additional oscillations due to the mass jumps at the interfaces.     

Third harmonic generation in quantum dot with Rashba spin orbit interaction

Here we have investigated the influence of magnetic field and confinement potential on nonlinear optical property, third harmonic generation (THG) of a parabolically confinement quantum dot in the presence of Rashba spin orbit interaction. We have used density matrix formulation for obtaining optical properties within the effective mass approximation. The results are presented as a function of confining potential, magnetic field, Rashba spin orbit interaction strength and photon energy. Our results indicate that an increase of Rashba spin orbit interaction coefficient produces strong effect on the peak positions of THG. The role of confinement strength and spin orbit interaction strength as control parameters on THG have been demonstrated.     

Exact Solution to Spin Squeezing of the Arbitrary-Range Spin Interaction and Transverse Field Model

We investigate spin squeezing effects of trapped ions in an off-resonance optical potential system using the arbitrary range spin-spin interaction and transverse Geld model.The collective spin noises at any time are analyzed exactly.The general expression of spin squeezing factor is presented for arbitrary-range spin interaction.For the nearest-neighbor and next-nearest neighbor spin interaction model,the analytic solutions are reduced from the general expressions.It is shown that the maximum spin squeezing is enhanced for the general arbitraryrange spin interaction compared with the nearest-neighbor interaction model as the long-range interaction with arbitrary sites enforces stronger correlation.     

Spiral spin state in high-temperature copper-oxide superconductors: evidence from neutron scattering measurements

An effective spiral spin phase ground state provides a new paradigm for the high-temperature superconducting cuprates. It accounts for the recent neutron scattering observations of spin excitations regarding both the energy dispersion and the intensities, including the "universal" rotation by 45 degrees around the resonance energy . The intensity has a 2D character even in a single twin crystal. The value of is related to the nesting properties of the Fermi surface. The excitations above are shown to be due to in-plane spin fluctuations, a testable difference from the stripe model. The form of the exchange interaction function reveals the effects of the Fermi surface, and the unique shape predicts large quantum spin fluctuations in the ground state.