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.     

Staggered potential and spin polarization effects on RKKY interaction in armchair graphene nanoribbon

Indirect exchange interaction between two magnetic external atoms, named by Ruderman–Kittle–Kasuya–Yosida (RKKY) interaction, has been presented in the staggered armchair graphene nanoribbon. We have studied RKKY interaction as a function of distance between localized moments. It has been shown that a magnetic ordering along the z-axis mediates an anisotropic interaction which corresponds to a XXZ model interaction between two magnetic moments. The static spin susceptibility components of armchair graphene nanoribbon have been calculated to find exchange interaction between arbitrary components of magnetic moments. We have exploited Green’s function approach in order to calculate spin susceptibility components of electronic gas in nanoribbon structure in the context of tight binding model Hamiltonian. The effects of parameter and ribbon width on the dependence of exchange interaction on distance between moments are investigated. Our results show the spin polarization along perpendicular to the plane leads to anisotropic behavior for exchange interaction between the two magnetic moments. In other words the spatial behavior of RKKY interaction between longitudinal components of magnetic moments is different from that of transverse components.     

Eigenwaves in a two-component system of particles with nonzero magnetic moments

Two-component systems of particles with nonzero intrinsic magnetic moments are shown to support not only the transverse electromagnetic and longitudinal waves, but also self-consistent spin waves and waves that propagate independently in each component and degenerate into oscillations for spin-zero systems. For all types of waves, the dispersion relations are obtained by solving the quantum hydrodynamics equations and field equations in linear approximation.     

Spin–lattice relaxation phenomena in the magnetic state of a suggested Weyl semimetal CeAlGe

ABSTRACT

In this work, we report the results of DC susceptibility, AC susceptibility and related technique, resistivity, transverse and longitudinal magnetoresistance and heat capacity on polycrystalline magnetic semimetal CeAlGe. This compound undergoes antiferromagnetic type ordering around 5.2 K (T¹). Under the application of external magnetic fields, parallel alignment of magnetic moments is favoured above 0.5?T. At low field and temperature, frequency and AC field amplitude response of AC susceptibility indicate the presence of spin–lattice relaxation phenomena. The observation of spin–lattice interaction suggests the presence of the Rashba–Dresselhaus spin–orbit interaction which is associated with inversion and time-reversal symmetry breaking. Additionally, the presence of negative and asymmetric longitudinal magnetoresistance indicates anomalous velocity contribution to the magnetoresistance due to the Rashba–Dresselhaus spin–orbit interaction which is further studied by heat capacity.     

Spin polarized threshold-photoemission from Ni(110) with transverse sample magnetization

A spin polarized photoemission experiment using transverse magnetized samples is described in detail. We discuss the advantages of this set-up in comparison to the one used so far which employed the longitudinal magnetization (polarization) geometry. Data on Ni(110) are presented including oxygen adsorption results, and discussed along current ideas in spin polarized photoemission theory.     

Spin diffusion in anisotropic Heisenberg chains: S≥1/2

In this paper, we investigate spin diffusion in Heisenberg chains with uniaxial nearest-neighbor interactions. The approach followed is based on an analysis of the infinite-temperature longitudinal spin density and spin current correlation functions. For S=1/2, exact results are presented for the time-dependent correlation functions in the XY limit. Away from this limit, the second and fourth moments of the Fourier transform of the spin density correlation function provide information about spin dynamics for arbitrary values of the spin. The moments are used in an assessment of the accuracy of the Gaussian approximation for the spin diffusion constant for S=1/2. The general behavior of the Gaussian approximation when S>1/2 is discussed, and numerical results for the spin diffusion constant are presented for S=1/2, 1, 3/2, 2 and in the classical limit. A moment-based criterion for the boundary in reciprocal space between diffusive and non-diffusive dynamics that applies to arbitrary values of the spin is presented.     

Spinor Boltzmann Equation with Two Momenta at the Fermi Level

Based on the formalism of Keldysh's nonequilibrium Green function, we establish a two momenta spinor Boltzmann equation for longitudinal scalar distribution function and transverse vector distribution function. The longitudinal charge currents, transverse spin currents and the continuity equations satisfied by them are then studied, it indicates that both the charge currents and spin currents decay oscillately along with position, which is due to the momenta integral over the Fermi surface. We also compare our charge currents and spin currents with the corresponding results of one momentum spinor Boltzmann equation, the differences are obvious.     

Spinor Boltzmann Equation with Two Momenta at the Fermi Level

Based on the formalism of Keldysh's nonequilibrium Green function, we establish a two momenta spinor Boltzmann equation for longitudinal scalar distribution function and transverse vector distribution function. The longitudinal charge currents, transverse spin currents and the continuity equations satisfied by them are then studied, it indicates that both the charge currents and spin currents decay oscillately along with position, which is due to the momenta integral over the Fermi surface. We also compare our charge currents and spin currents with the corresponding results of one momentum spinor Boltzmann equation, the differences are obvious.     

Spin dynamics in a site diluted finite spin cluster system probed by positive muons

The site diluted finite spin cluster system Rb₂CO _x Mg_1–x F₄ (x=0.15, 0.4, 0.5) has been investigated by the ⁺SR technique. Muon spin relaxation was observed in these diluted magnetic systems in a weak longitudinal field of 100 G. By reducing temperature below 100 K, the experimental data show features of slowing down phenomena of the Co electron moments in the finite spin clusters.     

Mechanism of exchange switching of spin valves by an inverse current

The exchange switching of spin valves by an inverse current can be explained by the interaction of the charge carriers with the spin-injection effective magnetic field. Such an interaction gives rise to transverse spin components, which are transferred to the magnetic lattice and cause its instability and switching. The spin-injection field is produced by longitudinal spin components, but it opens up a channel for the transverse spin transfer to the lattice. The spin transfer to the lattice and the switching occur in the free layer of the spin valve.     

COMPASS and HERMES contributions to our understanding of the nucleon spin

An update is given on the ongoing experimental investigation of the spin structure of the nucleon, with particular emphasis on the results from the COMPASS and HERMES experiments. Both longitudinal and transverse spin phenomena are covered. In the first case, the hot topic is the direct measurement of the gluon polarization. Evidence is presented for ΔG/G being small around x_g?0.1, and the first moment of ΔG should not be larger than 0.2-0.3. About transverse spin effects, evidence is given for new phenomena, associated with transverse-momentum-dependent distribution and fragmentation functions, which might explain the transverse spin phenomena observed for a long time in pp scattering.     

Anisotropic Rayleigh scattering

Coherence transfer between heteronuclear spin species in the rotating frame is analysed in view of application to heteronuclear two-dimensional cross-correlation spectroscopy in liquids. The general formalism and applications to simple spin systems are presented. In particular, the longitudinal and transverse coherence transfer functions are evaluated and discussed in terms of transfer efficiency, oscillation frequencies, phase anomalies and multiplet effects.     

Magnetic properties of a mixed spin-1/2 and spin-3/2 transverse Ising model

A theoretical study of a mixed spin-1/2 and spin-3/2 Ising system with independent transverse fields is presented using an effective field method within the framework of a single-site cluster theory. In this approach the effective field equations are derived using a probability distribution method based on the use of generalized van der Waerden identities accounting exactly for the single-site kinematic relations. The effect of the transverse fields on the critical behaviour is studied. The thermal dependence of the longitudinal and transverse components of the magnetization and its higher moments is also studied.     

μSR on an induced‐moment spin glass system: Hg1-xFexSe

Zero and longitudinal field μSR have been used to examine the singlet ground state magnetism of the diluted magnetic semiconductor Hg_1-xFe_xSe. For x\geq 0.05\ μSR experiments indicate spin glass behaviour which is limited to sample regions with locally enhanced Fe²⁺ content. Longitudinal field spectra in the glassy state reveal a static local field \sim 50 mT due to induced moments of Fe²⁺. These are proposed to originate from a distribution of bound magnetic polaron energies. This revised version was published online in July 2006 with corrections to the Cover Date.     

Ferrimagnetic magnetizations of transverse Ising thin films with diluted surfaces

The temperature dependences of longitudinal and transverse magnetizations in transverse Ising thin films with diluted surfaces which are coupled antiferromagnetically to the bulk are studied by the use of the effective-field theory (EFT) with correlations. Novel features are obtained for the thermal variations of longitudinal magnetization, being different from those of the bulk ferrimagnetic materials, such as the possibility of two compensation points. They are depending on the thickness of a film and the surface dilution. These characteristic phenomena come from the competition between the surfaces and the bulk when the ratios of the physical parameters (transverse field and exchange interaction) between the surfaces and the bulk are selected as some large values.     

An introduced effective-field theory study of spin-1 transverse Ising model with crystal field anisotropy in a longitudinal magnetic field

A spin-1 transverse Ising model with longitudinal crystal field in a longitudinal magnetic field is examined by introducing an effective field approximation (IEFT) which includes the correlations between different spins that emerge when expanding the identities. The effects of the crystal field as well as the transverse and longitudinal magnetic fields on the thermal and magnetic properties of the spin system are discussed in detail. The order parameters, Helmholtz free energy, entropy and specific heat curves are calculated numerically as functions of the temperature and Hamiltonian parameters. A number of interesting phenomena such as reentrant phenomena originating from the temperature, crystal field, transverse and longitudinal magnetic fields have been found.     

Theoretical model of spin transfer torque in multilayers

We present a model of spin transport in a Co/Cu(1 1 1)/Co pseudo-spin-valve (PSV) structure where current is flowing in the current perpendicular-to-plane (CPP) geometry. The model considers ballistic spin-dependent transmission at the two Co–Cu interfaces, as well as diffusive spin relaxation within the Cu spacer and free Co layer. In the latter, the spin relaxation process is composed of the usual longitudinal spin relaxation due to spin flip scattering, as well as transverse spin relaxation due to spin precession. The resulting spin transfer torque exerted on the moments within the free Co layer is composed of two contributions, the main contribution coming from “absorbed” spins in the interfacial regions. The second contribution arises from the relaxation of spin accumulation within the free Co layer. The calculated critical current density for switching is estimated to be approximately between 3.3×10⁷ and 1.1×10⁸ A/cm², which is in agreement with available experimental results.     

The magnetic fields and rotation generators of free space electromagnetism

The relation is developed between rotation generators of the Lorentz group and the magnetic fields of free-space electromagnetism. Using these classical relations, it is shown that in the quantum field theory there exists a longitudinal photomagneton, a quantized magnetic flux density operator which is directly proportional to the photon spin angular momentum. Commutation relations are given in the quantum field between the longitudinal photomagneton and the usual transverse magnetic components of quantized electromagnetism. The longitudinal component is phase free, but the transverse components are phase dependent. All three components can magnetize material in general, but only the transverse components contribute to Planck's law. The photon therefore has three, not two, relativistically invariant degrees of polarization, an axial, longitudinal, polarization, and the usual right and left circular transverse polarizations. Since the longitudinal polarization is axial, it is a phase- free magnetic field.