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We consider a transverse electrical and spin current response to a longitudinal electric field in a metallic or semiconductor system characterized by various types of chirality. Using the similar theoretical approach we study a skew scattering on magnetic skyrmions leading to topological Hall effect, tunneling anomalous Hall effect (TAHE) of electrons and holes across an interface between magnetic semiconductors and electron scattering on a magnetic center in a semiconductor. We demonstrate how the chiral symmetry of the system manifests itself in the Hall response and its dependence on the electron spin polarization.

Non-coplanar spatial or momentum-space distribution of an effective magnetic field acting on a free electron due to exchange or spin-orbit interaction couples electron spin precession with its motion. This coupling gives rise to a skew scattering underlying anomalous and topological Hall effects. We show that in a non-adiabatic interaction regime the emergent skew scattering can be expressed in terms of chirality in real or momentum space. The approach appears to be rather universal for transport phenomena in systems with broken time reversal symmetry. We show that scattering on a chiral spin texture produces a transversal current proportional to the real space spin chirality. Using the similar approach combined with tunneling Hamiltonian formalism we explain the chirality-driven skew tunneling of electrons and holes at a semiconductor interface. The theory can be relevant for unidirectional magnetoresistance in dilute magnetic semiconductors and magnetic topological insulators.

In this talk, we will present our general multiband k. p approach to describe the properties of spin-polarized transport and spin-dependent tunneling within semiconductors interfaces and related heterostructures. Hereafter, we will apply our formalism and platform to describe the properties of spin-dependent tunneling along the particular [110]-direction. This represents a nontrivial case for the description of the spin-current because of the presence of order terms in the wave vector k higher than two in the effective Hamiltonian. We demonstrate here that the multiband techniques employed and developed here beyond the actual state of the art also appear to be a perfect numerical tool to check and validate some analytical developments e.g. based on perturbation technique approaches, also allowing to alleviate some fundamental analytical issues.

We extend our layer-by-layer model of photonic eigenmodes (resonance, polarization) of semiconductor laser and VCSELs (Fordos PRA 2017) by considering local optical properties in order to describe the above-threshold lasing even in the multimode regime. Such generalization, consistent with the semi-classical description based on the optical Bloch equations, allows to describe the optical gain and the wave propagation within the cavity in a more realistic way. The formalism is suitable to study the mode competition, since the important physical effects such as spatial-hole burning or cross-saturation mechanisms are included self-consistently. The only input parameters are those describing geometrical and local material properties of the cavity and the gain media, without using any mean-field approximations. We will present our generalized approach for modelling real devices and will show how it can serve in determining the main optical and physical properties of such devices.

Spinorbitronics in III-V semiconductors, e.g. involving the GaMnAs ferromagnetic semiconductors, uses the properties of spin-orbit coupling (SOC) to generate currents of angular momentum [1-2]. Thoses are now essential to control the magnetization state of a magnet [3], or moving a domain wall [4] via the generalized spin-Hall effect of III-V possibly involving Rashba and Dresselhaus terms [4]. The interplay between particle spin and orbital motion is also at the basis of new families of effects played e. g. by the Anomalous Tunnel Hall effect described by the appearance of a lateral charge current transverse to a tunneling spin-current [5–7] ; or the spin-galvanic effects [8]. The ensemble of those complex phenomena requires a clear description of the spin-currents anatomy with advance calculation tools. In this work, as an extension to previous contributions [5], we study unconventional quantum effects resulting in a giant transport asymmetry of carriers and spin-to-charge conversion in semiconductor interfaces, tunnel barriers or quantum wells. Those are composed of ferromagnets and strong spin-orbit materials, e. g. III-V compounds with magnetizations of opposite direction (AP) or in the geometry of spin-injection devices. The symmetry of the structure allows a difference of transmission upon respective positive or negative incidence vs. the reflection plane defined by the magnetization and the surface normal. We will restrict ourself to the effect of bulk Dresselhaus terms by using the simplest form of the quantum boundary conditions. We will first detail the robustness of our advanced 30-band and 40 band tunneling codes free of spurious states effects and involving the higher electronic bands involving the relevant spin-orbit contributions. We will demonstrate that refined boundary conditions involving surface potentials, like Rashba terms, arising from the symmetry breaking at interfaces may lead to equivalent effects by their own. In a second part, we emphasize on the perturbation calculation techniques needed to understand this phenomena and to the case of the core SOI in the valence band (VB). References: [1] Tomasz Dietl and Hideo Ohno, Rev. Mod. Phys. 86, 187 (2014). [2] T. Jungwirth et al., Rev. Mod. Phys. 86, 855 (2014). [3] M. Elsen et al., Phys. Rev. B 73, 035303 [4] L. Thevenard et al., Phys. Rev. B 95, 054422 (2017). [5] T. Huong Dang, H. Jaffres, T. L. Hoai Nguyen, and H.-J. Drouhin, Phys. Rev. B 92, 060403(R) (2015). [6] A. Matos-Abiague and J. Fabian, Phys. Rev. Lett. 115, 056602 (2015). [7] M. Jamet, A. Barski, T. Devillers, V. Poydenot et al., Nat. Mat. 5, 653-659 (2006). [10] S. D. Ganichev et al., Spinpolarization by current, ""Handbook of spin-transport & magnetism"", (Chapman and Hall), 2016.

Apart from classical and anomalous Hall effects, an appearance of transverse current in chiral systems has been recently discovered named as topological Hall effect (THE) as it was thought to be possible solely for topologically charged spin textures such as magnetic skyrmions. In this talk we focus on asymmetric electron scattering on chiral spin textures and tunnel transport across a semiconductor interface with account for exchange and spin-orbit interactions. We distinguish between chiral Hall effect (CHE) which requires local chirality of an effective magnetic field and the THE which requires also a non-zero topological charge. THE emerges in adiabatic regime of scattering, which can be described via geometrical Berry phase. With semi-classical approach we clarify why the spin Hall current in this case is proportional to the topological charge of a spin texture and does not depend on its size. For non-adiabatic regime we expand the scattering T-matrix in Born series and show that the scattering cross section acquires an asymmetric part, which depends on the local chirality of the spin texture leading to CHE independently of the topological charge. The analysis allowed us to clarify the reason for the spin Hall effect to vanish in this regime while preserving the charge Hall effect. We have also found theoretically the spin swapping effect for the exchange scattering on chiral spin textures. Further, with the T-matrix analysis we explain the asymmetry in the tunneling across a semiconductor interface emerging due to chiral configuration of exchange and spin-orbit fields leading to generation of transverse current.

Recent technological and scientific interest in spin-polarized vertical-cavity surface emitting lasers (spin-VCSELs) leads to development of advanced laser modeling tools [1]. The models describes arbitrary multilayer structure of spin-VCSELs including general anisotropy of optical properties of individual layers, and also anisotropy of gain. This important generalization allows not only for precise description of static properties of the resonant cavity, but can also be used to precisely calculate effective parameters used in dynamical models. [2] Applications of spin-lasers for high modulation and switching up to GHz/THz frequencies, advanced output beam shape manipulation, and use of active quantum dot structures leads to necessity to model spin-VCSELs with active and passive laterally periodic structures such as gratings, photonic crystals, and diffractive structures. In this paper, we will show the generalization of existing matrix-based models to describe spin-lasers with lateral periodicity. The generalized rigorous coupled-wave analysis (RCWA) will be discussed in details and it will be compared with grid-based techniques such as finite element methods (FEM) and finite-difference time-domain analysis (FDTD). We will also discuss effects of incoherent propagation and random phase during light propagation in the structure. The method will be applied to structures of practical interest consisting of anisotropic grating used for ultrafast laser modulation and photonic structure. [1] T. Fordos, et. al., J. Opt. 16 (2014) 065008, Phys. Rev. A 96, (2017) 043828. [2] M. Drong, et al. Proc. SPIE 10926, (2019) 1092614.

We report on theoretical investigations of carrier scattering asymmetry at ferromagnet-semiconductor junctions. By an analytical $2\times 2$ spin model, we show that, when Dresselhaus interactions is included in the conduction band of III-V $T_d$ symmetry group semiconductors, the electrons may undergo a difference of transmission vs. the sign of their incident parallel wavevector normal to the in-plane magnetization. This asymmetry is universally scaled by a unique function independent of the spin-orbit strength. This particular feature is reproduced by a multiband $\mathbf{k}\cdot \mathbf{p}$ tunneling transport model. Astonishingly, the asymmetry of transmission persists in the valence band of semiconductors owing to the inner atomic spin-orbit strength and free of asymmetric potentials . We present multiband $14\times 14$ and $30\times 30$ $\mathbf{k}\cdot \mathbf{p}$ tunneling models together with tunneling transport perturbation calculations corroborating these results. Those demonstrate that a tunnel spin-current normal to the interface can generate a surface transverse charge current, the so-called Anomalous Tunnel Hall Effect., 6 pages, 3 figures, conference MIMS 2017 Moscow (submitted), Journal of Magnetism and Magnetic Materials (JMMM), 2017

Electrically and optically pumped spin-polarized vertical-cavity surface-emitting lasers (spin-VCSELs) seem to attain improved performance compared to their conventional counterparts. Their dynamical properties are studied mostly in the framework of effective rate equations containing parameters that are difficult to directly relate with fundamental material properties. Consequently, such approaches are not suitable for the precise design and optimization of future spin-lasers with desirable dynamical properties. We propose a method for extraction of dynamics-related parameters for the spin-flip model, which is widely used for the description of spin-laser dynamics. This method is based on the correspondence between robust local computational tools and effective models. A general matrix formalism based on S-matrices and generalized Maxwell–Bloch equations is used to determine approximate values of parameters such as cavity decay rate or birefringence rate. This would allow us to tune laser properties by changing the optical properties of the laser cavities and active media according to our needs. The method is demonstrated on realistic anisotropic spin-VCSEL structures containing a 12-quantum-well InGaAs/GaAsP active region. The potential limitations of already existing effective models are discussed.

Magnonics aims to utilize magnons (quanta of spin-waves) to process and transfer digital and analog information, promising high throughput, low power computing for the post-CMOS era. Any such future magnonic circuits will require spin wave signal sources and amplifiers. We propose that acoustic pumping of spin waves provides a mechanism to implement these functions in efficient and highly localized devices. In support of this, we have developed a general theoretical model of linear and parametric magneto-acoustic interactions, covering all possible polarizations of acoustic waves and spin wave modes. The model combines the predictive power of analytical techniques with numerical micromagnetic simulations and is thus well-suited for the design of complex physical devices. Based on this, we determine the configurations most amenable to spin wave generation and amplification. As an experimental prototype we demonstrate an acoustically-pumped amplifier for spin-waves. Our device consists of an yttrium-iron-garnet (YIG) film grown on a gallium gadolinium garnet (GGG) substrate, with a bulk acoustic waves (BAW) transducer fabricated on the top of the GGG substrate. We show experimentally that the amplitude of the propagating spin-waves increases with the application of the BAW. Moreover, this scheme can be used as a signal correlator, where the modulated spin-waves and acoustic waves serve as signal inputs and the resulting modulation of the amplified spin wave serves as the output.

We have studied an infinite Hubbard chain with a spin-orbit coupling term, submitted to a uniform magnetic field as well as local phonons. By means of a Lang-Firsov transformation, we show that an effective interacting fermion model emerges. Moreover, a self-consistent mean-field theory of this model, formulated in terms of thermal Green's functions, shows that a BCS term emerges, thus leading to a superconducting phase transition at zero temperature. We find analytical expressions for the phase boundary, that agree well with exact numerical diagonalization of the Hamiltonian.

We present a general method for the modeling of semiconductor lasers such as a vertical-cavity surface-emitting laser and a vertical-external-cavity surface-emitting laser containing multiple quantum wells and involving anisotropies that may reveal (i) a local linear birefringence due to the strain field at the surface or (ii) a birefringence in quantum wells due to phase amplitude coupling originating from the reduction of the biaxial ${D}_{2d}$ symmetry group to the ${C}_{2v}$ symmetry group at the III-V ternary semiconductor interfaces. From a numerical point of view, a scattering S-matrix recursive method is implemented using a gain or amplification tensor derived analytically from the Maxwell-Bloch equations. It enables one to model the properties of the emission (threshold, polarization, and mode splitting) from the laser with multiple quantum well active zones by searching for the resonant eigenmodes of the cavity. The method is demonstrated on real laser structures and is presently used for the extraction of optical permittivity tensors of surface strain and quantum wells in agreement with experiments. The method can be generalized to find the laser eigenmodes in the most general case of circular polarized pumps (unbalance between the spin-up and spin-down channels) and/or dichroism allowing an elliptically polarized light emission as recently demonstrated experimentally when the linear birefringence is almost compensated [Joly et al., Opt. Lett. 42, 651 (2017)].

In this presentation we will review the spintronic terahertz (THz) phenomena such as ultrafast transient demagnetization [1], generation of spin waves via THz Zeeman torque [2,3], Mott scattering [4], and ultrafast inverse spin-Hall effect [5]. [1] E. Beaurepaire, G. M. Turner, S. M. Harrel, M. C. Beard, J.-Y. Bigot, and C. A. Schmuttenmaer, "Coherent terahertz emission from ferromagnetic films excited by femtosecond laser pulses," Appl. Phys. Lett. 84, 3465 (2004) [2] T. Kampfrath, A. Sell, G. Klatt, A. Pashkin, S. Mahrlein, T. Dekorsy, M. Wolf, M. Fiebig, A. Leitenstorfer, and R. Huber, "Coherent terahertz control of antiferromagnetic spin waves," Nature Photonics 5, 31 (2011) [3] Z. Jin, Z. Mics, G. Ma, Z. Cheng, M. Bonn, and D. Turchinovich, "Single-pulse terahertz coherent control of spin resonance in the canted antiferromagnet YFeO3, mediated by dielectric anisotropy", Phys. Rev. B 87, 094422 (2013) [4] Z. Jin, A. Tkach, F. Casper, V. Spetter, H. Grimm, A. Thomas, T. Kampfrath, M. Bonn, M. Klaui, and D. Turchinovich, "Accessing the fundamentals of magnetotransport in metals with terahertz probes", Nature Physics 11, 761 (2015) [5] T. Seifert, S. Jaiswal, U. Martens, J. Hannegan, L. Braun, P. Maldonado, F. Freimuth, A. Kronenberg, J. Henrizi, I. Radu, F. Freimuth, E. Beaurepaire, Y. Mokrousov, P.M. Oppeneer, M. Jourdan, G. Jakob, D. Turchinovich, L. M. Hayden, M. Wolf, M. Munzenberg, M. Klaui, and T. Kampfrath, "Efficient metallic spintronic emitters of ultrabroadband terahertz radiation", Nature Photonics 10, 483 (2016)

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.

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.

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 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.

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

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.