Double reflection of electron spin in 2D semiconductors

The reflection of spin-polarized electrons from a potential barrier inside a quantum well (QW) is analyzed. Using Clifford (geometric) algebra it is shown that the spin–orbit interaction brings about a double reflection at an oblique incidence of an electronic beam. The reflected beam is in a superposition of two beams having different wavelengths and reflection angles which produces a two-period spatial beating pattern that can be observed experimentally in the electron spin polarization component which is normal to the QW.     

Spin-dependent quantum interference from epitaxial MgO thin films on Fe(001)

Spin-dependent electron reflection from MgO thin films grown on Fe(001) was measured using spin-polarized low energy electron microscopy. The electron reflectivity exhibits quantum interference from which two MgO energy bands with Delta1 symmetry were determined in experiment. We found that a bulklike MgO energy gap is fully established for MgO film thicker than 3 atomic monolayers and that the electron reflectivity from the MgO/Fe interface exhibits a spin-dependent amplitude and a spin-independent phase change.     

Quantum-size-induced oscillations of the electron-spin motion in Cu films on Co(001)

We report on spin-polarized electron reflection experiments in which the electron-spin motion is studied in spin-dependent quantum well structures. Oscillations of the electron-spin motion due to quantum interference are observed in the model system Cu/Co(001) both as a function of electron energy and Cu overlayer thickness. The reflectivity as well as the spin-motion data can be well interpreted in terms of a Fabry-Pérot interferometer model. In particular, this opens the possibility of studying the spin-dependent reflection properties of the buried Cu/Co interface.     

Spin-dependent Fabry-Pérot interference from a Cu thin film grown on fcc Co(001)

Spin-dependent electron reflection from a Cu thin film grown on Co/Cu(001) was investigated using spin-polarized low-energy electron microscopy (SPLEEM). Fabry-Pe rot type interference was observed and is explained using the phase accumulation model. SPLEEM images of the Cu overlayer reveal magnetic domains in the Co underlayer, with the domain contrast oscillating with electron energy and Cu film thickness. This behavior is attributed to the spin-dependent electron reflectivity at the Cu/Co interface which leads to spin-dependent Fabry-Pe rot electron interference in the Cu film.     

Quantum oscillation of the tunneling conductance in fully epitaxial double barrier magnetic tunnel junctions

We investigated spin-dependent tunneling conductance properties in fully epitaxial double MgO barrier magnetic tunnel junctions with layered nanoscale Fe islands as a middle layer. Clear oscillations of the tunneling conductance were observed as a function of the bias voltage. The oscillation, which depends on the middle layer thickness and the magnetization configuration, is interpreted by the modulation of tunneling conductance due to the spin-polarized quantum well states created in the middle Fe layer. This first observation of the quantum size effect in the fully epitaxial double barrier magnetic tunnel junction indicates great potential for the development of the spin-dependent resonant tunneling effect in coherent tunneling regime.     

Electrical spin injection and threshold reduction in a semiconductor laser

A spin-polarized vertical-cavity surface-emitting laser is demonstrated with electrical spin injection from an Fe/Al0.1Ga0.9As Schottky tunnel barrier. Laser operation with a spin-polarized current results in a maximum threshold current reduction of 11% and degree of circular polarization of 23% at 50 K. A cavity spin polarization of 16.8% is estimated from spin-dependent rate equation analysis of the observed threshold reduction.     

Electron-spin motion: a new tool to study ferromagnetic films and surfaces

When electrons are interacting with a ferromagnetic material, their spin-polarization vector is expected to move. This spin motion, comprising an azimuthal precession and a polar rotation about the magnetization direction of the ferromagnet, has been studied in spin-polarized electron scattering experiments both in transmission and reflection geometry. In this review we show that electron-spin motion can be considered as a new tool to study ferromagnetic films and surfaces and we discuss its application to a number of different problems: (a) the transmission of spin-polarized electrons across ferromagnetic films, (b) the influence of spin-dependent gaps in the electronic band structure on the spin motion in reflection geometry, (c) interference experiments with spin-polarized electrons and (d) the influence of lattice relaxations in ferromagnetic films on the spin motion.     

Spin transport in graphene spin–orbit barrier structure

We studied spin-dependent transport in monolayer graphene with a spin–orbit barrier, a narrow strip in which the spin–orbit interaction is not zero. When the Fermi energy is between the two spin-split bands, the structure can be used to generate spin-polarized current. For a strong enough Rashba strength, a thick enough barrier or a low enough Fermi energy, highly spin-polarized current is generated (polarization ∼0.7–0.85$\sim 0.7\text{–}0.85$). Under these conditions, the spin direction of the transmitted electron is approximately perpendicular to the direction of motion. This shows that graphene spin–orbit nanostructures are useful for the development of graphene spintronic devices.     

Spin-dependent delay time and Hartman effect in asymmetrical graphene barrier under strain

We study the spin-dependent tunneling time, including group delay and dwell time, in a graphene based asymmetrical barrier with Rashba spin–orbit interaction in the presence of strain, sandwiched between two normal leads. We find that the spin-dependent tunneling time can be efficiently tuned by the barrier width, and the bias voltage. Moreover, for the zigzag direction strain although the oscillation period of the dwell time does not change, the oscillation amplitude increases by increasing the incident electron angle. It is found that for the armchair direction strain unlike the zigzag direction the group delay time at the normal incidence depends on the spin state of electrons and Hartman effect can be observed. In addition, for the armchair direction strain the spin polarization increases with increasing the RSOI strength and the bias voltage. The magnitude and sign of spin polarization can be manipulated by strain. In particular, by applying an external electric field the efficiency of the spin polarization is improved significantly in strained graphene, and a fully spin-polarized current is generated.     

Polarized beams for electron accelerators

NEA-GaAs based photocathodes allow the production of spin-polarized electron beams for fundamental research. We demonstrate how semiconductor properties influence salient parameters such as polarization and beam brightness. We present techniques that provide remedies for the extreme sensitivity to environmental factors. These are discussed for the specific installation that has provided spin-polarized beam at the MAMI facility during the last decade.     

Atomically resolved spin-dependent tunneling on the oxygen-terminated Fe3O4(111)

We employ spin-polarized STM to study the spin-dependent tunneling between a magnetite (111) sample and an antiferromagnetic tip through a vacuum barrier at room temperature. Atomic scale STM images show significant magnetic contrast corresponding to variations in the local surface states induced by oxygen vacancies. The estimated variations in tunneling magnetoresistance of 250% suggest that the spin-transport properties are significantly altered locally by the presence of surface defects.     

Tunable interlayer exchange coupling energy by modification of Schottky barrier potentials

We theoretically demonstrate that the interlayer exchange coupling (IEC) energy can be manipulated by means of an external bias voltage in a F₁/NM/F₂/S (F₁: ferromagnetic, NM: nonmagnetic metallic, F₂: ferromagnetic, S: semiconductor layers) four-layer system. It is well known that the IEC energy between two ferromagnetic layers separated by nanometer thick nonmagnetic layer depends on the spin-dependent electron reflectivities at the interface in F₁/NM/F₂ trilayer system. We apply such dependence to the F₁/NM/F₂/S four-layer system, where the reflectivity of NM/F₂ interface also depends on F₂/S interface due to the multiple reflection of an electron like optics. Finally, the IEC energy depends on the spin-dependent electron reflectivity not only at the interfaces of F₁/NM/F₂, but also at the interface of F₂/S. Naturally the Schottky barrier is formed at the interface between metallic ferromagnetic layer and semiconductor, the Schottky barrier height and thickness can be tailored by an external bias voltage, which causes the change of the spin-dependent reflectivity at F₂/S interface. We show that the IEC energy between two ferromagnetic layers can be controlled by an external bias voltage due to the electron-optics nature using a simple free-electron-like one-dimensional model.     

Goos–Hänchen shift for higher-order Hermite–Gaussian beams

We study the reflection of a Hermite–Gaussian beam at an interface between two dielectric media. We show that unlike Laguerre–Gaussian beams, Hermite–Gaussian beams undergo no significant distortion upon reflection. We report Goos–H?nchen shift for all the spots of a higher-order Hermite–Gaussian beam near the critical angle. The shift is shown to be insignificant away from the critical angle. The calculations are carried out neglecting the longitudinal component along the direction of propagation for a spatially finite, s-polarized, full 3D vector beam. We briefly discuss the difficulties associated with the paraxial approximation pertaining to a vector Gaussian beam.     

Nonlinear diffraction and total internal reflection in optical-beam interaction in defocusing media

We elaborate the theory of reflection of an optical signal beam from an inhomogeneous channel created by a high-power laser beam of different frequency in a nonlinear defocusing medium. We study the effects of total internal reflection and nonlinear diffraction in the interaction of these beams. We derive and analyze the equation for the trajectory of the reflected signal beam and obtain the expression for the critical value of beam-intersection angle below which the total internal reflection occurs. We discuss the results of numerical modeling of nonlinear Schr¨odinger equations for envelopes of the beams in media with quadratic, photorefractive, and thermal nonlinearities. We present experimental data on the interaction of beams of argon and helium–neon lasers in a cuvette with tinted alcohol.     

A tunable spatial spin splitter based on a spin–orbit-coupling modulated magnetic nanostructure

We investigate theoretically the spin-dependent Goos–Hänchen (GH) effect in a magnetic nanostructure modulated by spin–orbit coupling (SOC), which can be experimentally realized by depositing a ferromagnetic (FM) stripe and a Schottky-metal (SM) stripe on the top and bottom of an InAs/Al_xIn_1?xAs heterostructure, respectively. We consider two kinds of different SOCs (Rashba and Dresselhaus types), and calculate the GH shift and its spin polarization for the electrons across the device. Results show that the GH shift still is spin-polarized after including the SOC, and the behavior of the spin-polarized electrons can be manipulated by the Rashba and/or Dresselhaus SOC. These interesting properties provide an alternative scheme for spatially realizing spin injection into a semiconductor, and the magnetic nanostructure can be employed as a controllable spatial spin splitter for a spin-polarized source in spintronics.     

Spin Transport in a Rashba Ring-Quantum Dot System Pumped by Microwave Fields

We report a theoretical study on producing electrically spin-polarized current in the Rashba ring with parallel double dots embedded, which are subject to two time-dependent microwave fields. By means of the Keldysh Green's function method, we present an analytic result of the pumped current at adiabatic limit and demonstrate that the interplay between the quantum pumping effectand spin-dependent quantum interference can lead to an arbitrarily controllable spin-polarized current in the device. The magnitude and direction of the charge and spin current can be effectively modulated by system parameters such as the pumping phase difference, Rashba precession phase, and the dynamic phase difference of electron traveling in two arms of ring; moreover, thespin-polarization degree of the charge current can also be tuned in the range [-∞, +∞]. Our findings may shed light on the all-electric way to produce the controllable spin-polarized charge current in the field of spintronics.     

Spin-to-orbital angular momentum conversion and spin-polarization filtering in electron beams

We propose the design of a space-variant Wien filter for electron beams that induces a spin half-turn and converts the corresponding spin angular momentum variation into orbital angular momentum of the beam itself by exploiting a geometrical phase arising in the spin manipulation. When applied to a spatially coherent input spin-polarized electron beam, such a device can generate an electron vortex beam, carrying orbital angular momentum. When applied to an unpolarized input beam, the proposed device, in combination with a suitable diffraction element, can act as a very effective spin-polarization filter. The same approach can also be applied to neutron or atom beams.     

Anisotropic and valley-resolved beam-splitter based on a tilted Dirac system

We investigate theoretically valley-resolved lateral shift of electrons traversing an n–p–n junction bulit on a typical tilted Dirac system (8-Pmmn borophene). A gauge-invariant formula on Goos–Hänchen (GH) shift of transmitted beams is derived, which holds for any anisotropic isoenergy surface. The tilt term brings valley dependence of relative position between the isoenergy surface in n region and that in the p region. Consequently, valley double refraction can occur at the n–p interface. The exiting positions of two valley-polarized beams depend on the incident angle and energy of incident beam and barrier parameters. Their spatial distance D can be enhanced to be ten to a hundred times larger than the barrier width. Due to tilting-induced high anisotropy of the isoenergy surface, D depends strongly on the barrier orientation. It is always zero when the junction is along the tilt direction of Dirac cones. Thus GH effect of transmitted beams in tilted Dirac systems can be utilized to design anisotropic and valley-resolved beam-splitter.     

The Imbert-Fedorov shift of paraxial light beams

We present a solution to the problem of reflection and transmission of a polarized paraxial light beam at an interface between two homogeneous media by using a two-form amplitude and an extension matrix to represent the vectorial angular spectrum of a three-dimensional (3D) light beam. We derive general formulas for the Imbert-Fedorov (IF) shift of the reflected and transmitted beams of a polarized paraxial light beam. The IF shift of two different types of polarized beams is calculated, and the influence of the polarization state and the polarization feature of the vectorial angular spectrum on the IF shift is discussed.     

Resolution and sensitivity enhancements in strong grating based fiber Fabry–Perot interferometric sensor system utilizing multiple reflection beams

We investigate an asymmetric intensive fiber Bragg grating (FBG) defined Fabry–Perot (F–P) sensor system decoded by a multiple-path-matched Michelson interferometer. The interrogation of higher order reflection beams cannot only solve the problem of the degraded resolution induced by the spectral mismatch of the FBGs, but also amplify the effect of the fiber strain on the phase of the light. We demonstrate multiple reflection beams in the F–P cavity based on the concept of the FBG effective length for constructing respective interrogation interferometers, and present a cost function with optimized system parameters to improve noise properties. The performances of interrogating the second, third and fourth order reflection beams are compared in a strain sensing experiment arrangement. Under the condition of the same optical path length mismatch, the interrogation of the fourth order reflection beam can achieve 9.8 dB sensitivity enhancement and 3 dB resolution promotion compared with the result using the second order reflection beam.