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We present a general method for modeling spin-lasers such as spin-polarized vertical cavity surface emitting laser (spin-VCSELs) with multiple quantum wells including anisotropic effects such as i) the emission of elliptically-polarized photons and originating from unbalanced spin-up and spin-down pumps, ii) the linear gain dichroism originating from the reduction from Td to C2v symmetry group at the III-V ternary interfaces and iii) the locally linear birefringence due to the anisotropic strain field at surface of ½ VECSELs an optical birefringence of quantum wells from the Henry’s factor. New recurrence calculations, together with analytically gain tensor derived from Maxwell-Bloch equations, enable to model emission from multiple quantum well active zones to find the laser resonance conditions and properties of eigenmodes. The method is demonstrated on real semiconductor laser structures. It is used for the extraction of optical permittivity tensors of surface strain and of quantum wells (QWs). The laser structures are also experimentally studied via ellipsometry methods by measurement of the rotation spectra of complete Mueller matrix in the reflection geometry. The anisotropic optical permittivity constants in the spectral range from 0.73 to 6.4 eV are modeled in order to disantangle surface and QWs contributions to the linear optical birefringence of the structures.

We report on theoretical investigations and k.p calculations of carrier tunneling, both electrons and holes, in model systems and heterostructures composed of exchange-split III-V semiconductors, involving spin-orbit interactions. The two media are separated-or not-by a thin tunnel barrier made out of a (III-V) semiconductor. In a 2x2 exchange-split band model, we show that, when Dresselhaus interactions are included in the conduction band of two exchange-split semiconductors in contact in the antiparallel states of magnetization, the electrons are differently transmitted with respect to an axis orthogonal to both normal axis of the interface and of the magnetization. The transmission asymmetry (A) between +k// and -k// incidence is shown to be maximal (A=100%) at some points of the Brillouin zone corresponding to a totally quenched transmission at some given incidence angles. More generally, we derive a universal character of the transmission asymmetry A vs. the in-plane incidence wavevector, the reduced kinetic energy and exchange parameter, A being universally scaled by a unique function, independent of the spin-orbit strength and of material parameters. This particular asymmetry feature is reproduced by a more complete 14x14 band model involving coupling with the conduction band. On the other hand, calculations performed in the valence-band of equivalent model heterostructures and including tunnel barriers in both 6x6 (without inversion) and 14x14 k.p band model more astonishingly highlight, the same trends in the transmission asymmetry (A) which is related to the difference of orbital chirality and to the related branching (overlap) of the corresponding evanescent wavefunctions responsible for tunneling current. In both cases of electrons and holes, the asymmetry appears to be robust and persists only when a single electrode is magnetic.

We report on theoretical investigations of scattering asymmetry vs. incidence of carriers through exchange barriers and magnetic tunnel junctions made of semiconductors involving spin-orbit interaction. By an analytical 2?2 spin model, we show that, when Dresselhaus interaction is included in the conduction band of antiparallel magnetized electrodes, the electrons can undergo a large difference of transmission depending on the sign of their incident in-plane wavevector. In particular, the transmission is fully quenched at some points of the Brillouin zone for specific in-plane wavevectors and not for the opposite. Moreover, it is universally scaled by a unique function independent of the spin-orbit strength. This particular feature is reproduced by a 14 ? 14 band k ? p model showing, in addition, corresponding effects in the valence band and highlighting the robustness of the effect, which even persists for a single magnetic electrode. Upon tunneling, electrons undergo an asymmetrical deflection which results in the occurrence of a transverse current, giving rise to a so-called Tunnel Hall Effect.

Magnetization switching provoked by spin-injection is studied in Ni nanowires of various size and morphology. The response of the magnetization to the spin-injection is studied as a function of the amplitude of the current, the temperature, and the symmetry of the interfaces. The amplitude of the response of the magnetization to spin-injection is a decreasing function of the temperature, does not depend on the current sign, and occurs only in the case of asymmetric interfaces. It is shown that the spin-injection does not act on small magnetic inhomogeneities inside the layer. Some consequences in terms of longitudinal spin-transfer are discussed.

High-resolution energy distribution curves and spin polarization versus energy distribution curves from an AlInGaAs layer, capped by a heavily doped thin GaAs quantum well layer has been measured. Polarization P of up to 83% in conjunction with quantum yield Y=0.5% at T=130 K has been obtained. These results are compared to polarization and quantum yield spectra at high excitation power. The narrow-band quantum well is shown to provide large effective negative electron affinity values with no harm to electron polarization. The studies in linear and nonlinear excitation regimes bring insight into the kinetics of photoemission and favor the photoemission model with elastic electron tunneling through the surface barrier.

Spin transport and dynamics is one of the crucial issues of spintronics, regardless of whether the system of interest is magnetic or nonmagnetic: semiconductors are of special interest because in such systems the charge carrier dynamics can be accurately treated through single-particle approximation, making use of the precise knowledge of wavefunctions. Here the single-electron, possibly spin-dependent wavefunction is well suited to provide reliable fully quantum mechanical models, or to derive semiclassical theoretical models, which eventually can be extended to other kinds of systems. In this context transport operators play a key role and, in particular, the probability current is a fundamental concept in quantum mechanics, which connects the wave-like description of a quasi-particle to the notion of transport current.

High resolution energy distribution curves (EDC) and a polarisation versus energy distribution curves (PEDC) of the electrons, photoemitted from strained GaAs/GaAsP layers are experimentally studied. The basic structures of the spectra are found to vary with temperature and illuminating wavelength. The ageing of the activation layer changes the EDC shape as well. Nevertheless, in the vicinity of the photoexcitation threshold the polarisation does not vary across the energy distribution both at room and 120 K temperatures of the cathode, which means that no depolarisation occurs during energy relaxation in the band bending region. The electron energy distribution is interpreted in terms of the electron energy relaxation in the band tail states of the quantum well formed by the band-bending region.

A quasimonoenergetic spin-polarized electron beam, emitted in vacuum from a GaAs photocathode, is injected into a thin ferromagnetic metal layer deposited on an $n$-doped GaAs substrate. The current transmitted through this Schottky barrier is measured. The striking feature of this hot-electron transistorlike system is a current gain spin dependency as high as $20%$. The measured variations of the current gain and its spin dependency with the injection energy are well explained by a very simple analytical model describing the transport of hot electrons in metallic thin films.

A simple model is presented to estimate the low-energy electron mean free path in transition metals and to calculate its spin dependence. In this model, the electron-scattering rate is directly related to the number of holes in the $d$ bands; its spin asymmetry is almost proportional to the spin magnetic moment. These quantities show a weak energy dependence from the vacuum level up to a few tens of eV above the metal Fermi level.

Thermokinetic considerations are appled to the case of a generic spintronic device in which a magneto-voltaic response is measured, in the absence of electric current, on an electrode placed perpendicular to a ferromagnetic layer (see Fig. 1). The magnetovoltaic signal is a response to a power excitation, that is related to the ferromagnetic degrees of freedom. This excitation can be performed by ferromagnetic resonance (electromagnetic excitations), by a temperature gradient, by magnetomechanical coupling or by magneto optic coupling (see these proceedings). The description of this generic device allows the so-called spin-Seebeck effects and spin-pumping effects17-16 to be addressed.

Based on a proper definition of the current operators for non-quadratic Hamiltonians, we derive the expression for the transport current which involves the derivative of the imaginary part of the free-electron current, highlighting peculiarities of the extra terms. The expression of the probability current, when Spin-Orbit Interaction (SOI) is taken into account, requires a reformulation of the boudary conditions. This is especially important for tunnel heterojunctions made of non-centrosymmetric semiconductors. Therefore, we consider a model case: tunneling of conduction electrons through a [110]-oriented GaAs barrier. The new boundary conditions are reduced to two set of equations: the first one expresses the discontinuity of the envelope function at the interface while the other one expresses the discontinuity of the derivative of the envelope function.

We propose a novel set of boundary conditions, based on the continuity of a generalized velocity and on the continuity of the probability current at the interface of heterojunctions, which is well suited to construct the solution of the tunneling problem when spin-orbit interaction is taken into account. We illustrate this procedure in a model case: tunneling of conduction electrons through a [110]-oriented GaAs barrier. In that case, the new boundary conditions reduce to two set of equations: the first one expresses the discontinuity of the envelope function at the interface while the other one is close to the standard condition on the derivative of the envelope function.

In this study, we report magneto-resistance measurements on an n-doped InSb film, to separate the contributions of the electrical currents from the heat currents. We have demonstrated a prototype for a magnetic field sensor which is powered by heat currents and does not require any electrical current. We fabricated two Hall bars, where a low frequency (f = 0.05 Hz) AC current, was applied between the two contacts in one of the Hall bars. Separating the f and 2f components of the voltage measured across the second Hall bar was used to distinguish between the electrical and the heat contributions to the electron currents. Our observations can be modeled using a Gaussian distribution of mobility within the sample.

In order to understand some new spintronics experiments of spin-dependent voltage for which the electric conduction does not play a role, a model of two spin-conduction channel is proposed in which the ferromagnets (either electric conductors or insulators) are defined by an ensemble of non­ equilibrium heat carriers composed of a populations of heat carriers of spin up, and heat carriers of spin down. It is shown that a temperature gradient generates locally a spin-accumulation. The diffu­ sion equation of this thermal spin-accumulation is straightforwardly derived from the corresponding transport equations and conservation equations. The principle of the detection is described in terms of Spin-Nernst effect.

New boundary conditions are derived for tunnel-heterojunctions, where the effective Hamiltonian is a generic power of the momentum-operator. A novel expression of probability-current operator, which can be also applied in presence of the D'yakonov-Perel (DP) Hamiltonian, has to be used. We test our technique on the interface between two semi-infinite media, with on one side a free-electron-like material and on the other side the [110]- oriented GaAs barrier.

International audience; We present a systematic construction of the probability-and spin-current operators, based on a momentum power expansion of effective Hamiltonians. These operators play an essential role in transport problems related to semiconductor heterostructures, in particular when spin-orbit interaction is taken into account. The result, valid whatever the momentum power and including the linear (Bychkov-Rashba) term as well as the cubic (Dresselhaus or D'yakonov-Perel) term, is of special importance for spintronics.

We propose a procedure, based on momentum power series expansion Hamiltonian of nth general order, to obtain a coherent expression of the probability current operator that is valid also when Spin-Orbit Interaction (SOI) terms are included. We prove that we recover the standard definition when the free electron-like term is included in the Hamiltonian, but when taking into account higher order Spin-Orbit Interaction (SOI) terms, a more general definition of the probability current operator is mandatory, due to its different symmetrization, compared to the Hermitian velocity operator expression.

The intimate relation between the angular momentum and the magnetization - expressed through the gyromagnetic relation - is well known and is easy to evidenced at the macroscopic scale with magnetomechanical measurements. On the other hand, the conservation of the angular momentum find also a simple illustration in the behavior of a spinning top. Accordingly, the dynamics of a single domain ferromagnet should follow the same laws as a symmetrical spinning top. Paradoxically, this is not true since the equations that govern the dynamics of the magnetization do not contain inertial terms. We investigate under what conditions the inertial terms that are initially present in the conservation laws disappear, in order to lead to the well-known expressions of the Landau-Lifshitz-Gilbert equation

We show that effective Hamiltonians in solids lead to specific problems when dealing with spin-orbit interaction. We prove that the usual construction, where the velocity operator is simply deduced from the velocity calculated using the Hamilton relation, has a restricted validity and that there is an absolute necessity to modify the standard current-tensor definition. We derive proper symmetrized expressions in the case of a Hamiltonian which has linear and cubic dependence versus momentum components.

The spin-dependent electron inelastic mean free path (IMFP) in transition metals is studied in the energy range 5–50 eV above the Fermi level. It is shown that the spin-dependent IMFP is simply related to the number of holes in both d spin subbands, whatever the detail of the d-band structure. This analysis allows us to disentangle the different scattering channels. Many experimental determinations of the spin-dependent part of the electron scattering cross section, from several teams, are analyzed in the framework of this model. The strong energy dependence of the exchange matrix element is clearly evidenced.

A general definition of the Spintronics concept of spin-pumping is proposed as generalized forces conjugated to the spin degrees of freedom in the framework of the theory of mesoscopic non-equilibrium thermodynamics. It is shown that at least three different kinds of spin-pumping forces and associated spin-currents can be defined in the most simple spintronics system (the Ferromagnetic/Non-Ferromagnetic metal interface). Furthermore, the generalized force associated to the ferromagnetic collective variable is also introduced in an equal footing, in order to describe the coexistence of the spin of the conduction electrons (paramagnetic spins attached to $s$-band electrons) and the ferromagnetic-order parameter. The dynamical coupling between these two kinds of magnetic degrees of freedom is presented, and interpreted in terms of spin-transfer effects., Comment: 18 pages, 2 figures

Due to the absence of inversion symmetry, spin-orbit interaction leads to a very particular topology of the evanescent states in zinc-blende semiconductors, which may consist of loops connecting different spin sub-bands at the zone center. The spin-vector motion along such loops is analytically or numerically studied. A surprising picture emerges from this detailed analysis. Namely, the two spin sub-bands do not correspond to opposite spin states near the Brillouin-zone center and merge with identical spins at larger wave vector. This determines the spin-filtering capabilities of the semiconductor barrier.

In non-centrosymmetric semiconductors with zinc-blende structure grown along the [110] crystallographic direction, electrons with up and down spins undergo different quantum phase shifts upon tunneling, which can be wieved as resulting from spin precession around a complex magnetic field. There is no spin filtering but a pure spin dephasing. The phase shift of the transmitted wave is proportional to the overall barrier-material thickness. We show that a device incorporating a number of resonant tunnel barriers constitutes an efficient quantum-phase shifter.

We discuss possible tunneling phenomena associated with complex wave vectors along directions where the spin degeneracy is lifted in noncentrosymetric semiconductors. We show that the result drastically depends on the direction. In the [110] direction, no solution can be calculated in the usual way assuming that the wave function and its derivative are continuous. A method for obtaining physical solutions is given and consequences are drawn. As a result, there is no spin filtering in such a direction but the spin undergoes a precession through the barrier with the rotation angle being proportional to the barrier thickness. In a direction close to [001] we find a spin-filter effect in close agreement with the model discussed by Perel' et al. [Phys. Rev. B 67, 201304(R) (2003)].

An out-of-equilibrium description of spin-transfer effect is proposed, based on the spin-injection mechanism occurring at the junction with a ferromagnet. The effect of spin injection is to locally modify, in the ferromagnetic configuration space, the density of magnetic moments. The corresponding gradient leads to a currentdependent diffusion process of magnetization. In order to describe this effect, the dynamics of the magnetization of a ferromagnetic single domain is reconsidered in the framework of the thermokinetic theory of mesoscopic systems. Assuming an Onsager cross coefficient that couples the currents, it is shown that spindependent electric transport leads to a correction of the Landau–Lifshitz–Gilbert equation of the ferromagnetic order parameter with supplementary diffusion terms. The consequence of spin injection in terms of the activation process of the ferromagnet is deduced, and the expressions of the effective energy barrier and of the critical current are derived. Magnetic fluctuations are calculated: the correction to the fluctuations is similar to that predicted for the activation. These predictions are consistent with the measurements of spin transfer obtained both in the activation regime and for ferromagnetic resonance under spin injection.

Negative electron affinity GaAs photocathodes, excited by circularly polarized light with energy close to the band gap, have proved to be efficient sources of spin polarized electrons in vacuum. In this paper we clarify some of the depolarizing mechanisms which affect the polarization of the emitted electrons by analyzing the polarization versus energy distribution curves obtained for various excitation energies.

Using third and forth order perturbation, we have derived main GaAs band parameters (such as EP ) from both experimental results (m *, g *, ...) and theoretical results (overall band structure from Cohen-Chelikowski pseudo-potential calculations). The analysis of the set of data leads to a drastic change to the "admitted" value of some parameters (E'P ) from the only experimental results and show inconsistency if theoretical results are furthermore taken into account.© (2006) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Spin injection in metallic normal/ferromagnetic junctions is investigated taking into account the anisotropic magnetoresistance (AMR) occurring in the ferromagnetic layer. It is shown, on the basis of a generalized two channel model, that there is an interface resistance contribution due to anisotropic scattering, beyond spin accumulation and giant magnetoresistance (GMR). The corresponding expression of the thermopower is derived and compared with the expression for the thermopower produced by the GMR. First measurements of anisotropic magnetothermopower are presented in electrodeposited Ni nanowires contacted with Ni, Au and Cu. The results of this study show that while the giant magnetoresistance and corresponding thermopower demonstrates the role of spin-flip scattering, the observed anisotropic magnetothermopower indicates interband s-d relaxation mechanisms., 20 pages, 4 figures

Experiments of spin injection, from a normal metal to a ferromagnet, show that the magnetization of the ferromagnet can be switched with high current pulses, without the need of a magnetic field. In order to describe the experimental observations, two different kinds of electronic populations are defined for the transport: the spin polarized current inside the normal metal (paramagnetic spin-polarized current) and the spin-polarized current inside the ferromagnet (ferromagnetic spin polarization). The redistribution of the electronic populations is then investigated in the framework of a four-channel approach (up and down spin polarization for paramagnetic and ferromagnetic currents). This mechanism couples the electronic transport (Boltzmann equations) to the dynamics of the magnetization (Landau-Lifehitz-Gilbert equation), and leads to define a magnetic temperature which depends on the current injection.

Within the band gap of a semiconductor no electronic propagating states are allowed, but there exist evanescent states which govern charge transport such as tunneling. In this Letter, we address the issue of their spin dependence in III-V semiconductors. Taking into account the spin-orbit interaction, we treat the problem using a k center dot p 14x14 Hamiltonian that we numerically compute for GaAs. Our results show that the removed spin degeneracy in the band gap can lead to giant energy splittings and induces forbidden zones in k space where evanescent states are suppressed

Integrated polarization and quantum yield spectra of the electrons, photoemitted from strained AlInGaAs layer, capped by heavily doped thin GaAs quantum well layer, as well as high resolution energy distriubtion curves and a polarization versus energy distribution curves are studied as a function fo light excitation energy and power. The polarization P of up to 83% in conjunction with quantum yield Y=0.5 at T=130K have been measured. At high excitation intensity decrease of Y and P is observed which is attributed to the surface photovoltage effects, i.e. decrease of the negative electron affinity, narrowing of the band-bending region and an increase of the hole concentration in the quatnum well layer. The narrow-band quantum well is shown to provide high effective negative electron afffinity values with no harm to electron polarization.

We determine the polarization vector of a spin-polarized electron beam emerging from a ferromagnet and we study the particular case of two uncoupled ferromagnetic layers with in-plane magnetizations in a perpendicular configuration. We show that the transmitted intensity depends on the three components of the primary polarization and we propose to use such a structure as a convenient spin detector for low- energy electrons.

This chapter describes ultrathin ferromagnetic layers as spinfilters, analogous to optical polarizers. Dealing with electrons offer more possibilities because the electron polarization possibly has both longitudinal and transverse components. The inelastic electron mean free path (IMFP) in metals, which characterizes the escape depth, plays a crucial role in these experiments, as in all electron spectroscopies. In transition metals, the IMFP variation is mostly determined by density of state effects, whereas the transition matrix elements introduce weaker corrections. Cobalt and iron thin films have been extensively studied in the chapter. The spin-dependent IMFP component is of particular interest as it mostly originates from electron-electron interaction and can be measured with accuracy. Spin-dependent electron transport of low-energy electrons in a ferromagnetic metal arises because majority- and minority-spin electrons have different relaxation channels due to different final densities of states in the d spin subbands. The chapter establishes simple relations between the number of holes in the d spin subbands and the IMFPs. This information is essential for the conception of devices based on spin filtering. In ballistic-electron devices like hot-electron transistors, only electrons that have undergone almost no energy loss are collected. An electron ballistically injected into the metal layer and that undergoes a change in its wave-vector direction will no longer travel along the device axis, and will thus travel a longer path. Finally, it will be lost due to inelastic scattering. This effect is well known and has supported undimensional transport equations in field-assisted photoemission. The manipulation of spin packets in solids, experiencing coherent spin precession, also brings technological challenges to new frontiers. The development of magnetic semiconductors at room temperature could be a crucial step towards spintronics. The absorption or emission of spin waves and their coupling with light waves may also lead to applications involving long wavelength excitations.

An asymmetrical ferromagnetic cobalt bilayer (18 nm Au/0.8 nm Co/2.2 nm Au/1.3 nm Co/1.5 nm Au) operates as a self-calibrated spin polarimeter with a high spin selectivity for free electrons injected at a few eV above the Fermi level. We present the analysis of transmitted currents as a function of the incident energy, based on a model of spin polarization dilution into the first gold layer and ballistic transport close to the vacuum level throughout the sample.