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The phenomenon of resonant tunneling transport through polar double-barrier heterostructures is systematically investigated using a combined experimental and theoretical approach. On the experimental side, GaN/AlN RTDs are grown by MBE. In-situ electron diffraction is employed to monitor the number of monolayers incorporated into each tunneling barrier. Using this precise epitaxial control at the monolayer level, we demonstrate exponential modulation of the resonant tunneling current as a function of barrier thickness. Both the peak voltage and characteristic threshold bias exhibit a dependence on barrier thickness as a result of the intense electric fields present in the polar heterostructures. To get further insight into the asymmetric tunneling injection, we present an analytical theory for tunneling transport across polar heterostructures. A general expression for the resonant tunneling current with contributions from coherent and sequential tunneling processes is introduced. After applying this theory to the case of GaN/AlN RTDs, their experimental current-voltage characteristics are reproduced over both bias polarities, with tunneling currents spanning several orders of magnitude. This agreement allows us to elucidate the role played by the internal polarization fields on the magnitude of the tunneling current and broadening of the resonant line shape. Under reverse bias, we identify new tunneling features originating from highly attenuated resonant tunneling phenomena, which are completely captured by our model. Our analytical model, provides a simple expression which reveals the connection between the polar RTD design parameters and its current-voltage characteristics. This new theory paves the way for the design of polar resonant tunneling devices exhibiting efficient resonant current injection and enhanced tunneling dynamics, as required in various practical applications., 13 pages, 3 figures

International audience; To improve the read/write margin in perpendicular spin transfer torque magnetic random access memory (STT-MRAM), a concept of the double-magnetic tunnel junction (MTJ) MRAM cell is proposed in which the STT efficiency can be changed between read and write modes. In conventional double-MTJ stacks, the storage layer magnetization is submitted to two additive STT contributions, one from the reference layer below the bottom tunnel barrier and the other from an additional polarizing layer above the top tunnel barrier. In the proposed stack, the magnetization of the top polarizing layer can be switched between the read and write mode by domain wall propagation or spin orbit torque. This allows us to maximize the STT on the storage layer during write and minimize it during read. The associated advantages are a lower write current, reduced read disturb, maximal magnetoresistance amplitude during read, and faster read thanks to larger read current. We report here the experimental demonstration of this concept on perpendicular double-MTJ stacks.

The usage of Lévy processes involving big moves or jumps over a short period of time has proven to be a successful strategy in financial analysis to capture such rare or extreme events of stock price dynamics. Models that follow the Lévy process are FMLS, Kobol, and CGMY models. Such simulations steadily raise the attention of researchers in science because of the certain best options they produce. Thus, the issue of resolving these three separate styles has gained more interest. In the new paper, we introduce the computational method of such models. At first, the left and right tempered fractional derivative with arbitrary order is approximated by using the basis function of the shifted Chebyshev polynomials of the third kind (SCPTK). In the second point, by implementing finite difference approximation, we get the semi-discrete structure to solve the tempered fractional B–S model (TFBSM). We show that this system is stable and [Formula: see text] is the convergence order. In practice, the processing time and the calculation time per iteration will be reduced by a quickly stabilized system. Then we use SCPTK to approximate the spatial fractional derivative to get the full design. Finally, two numerical examples are provided to illustrate the established system’s reliability and effectiveness.

As the basic storage unit of spin transfer torque magnetic random-access memory (STT-MRAM), the perpendicular magnetic anisotropy (PMA) magnetic tunnel junction (MTJ) has been extensively studied in recent years. Lowering the critical switching current and improving the data retention are two crucial pathways to optimize the performance of STT-MRAM. However, the conventional MTJ can merely achieve both. In this paper, we present a physics-based compact model of Ta/CoFeB/MgO PMA double-barrier MTJ (DMTJ) with enhanced thermal stability recording structure. Combination of double-barrier and synthetic double-free layers can heighten the STT effect and enhance the thermal stability simultaneously. A larger STT switching efficiency, compared with conventional MTJ, can thus be realized. The modeling results show great agreement with experimental results. A 1-bit magnetic full adder (MFA) based on DMTJ, as a hybrid logic-in-memory circuit example, has been designed and simulated to validate its functionality. This SPICE-compatible compact model will be useful for high-performance hybrid MTJ/CMOS circuit and system designs.

Spin-dependent resonant tunneling in CdTe/CdMnTe double-barrier heterostructures was theoretically investigated. The transfer-matrix method was employed to study the spin transport properties under zero applied field. The effect of Dresselhaus spin- orbit coupling was considered in the symmetrical heterostructure. The influences of the barrier width and height on the polarization efficiency, barrier transparency and dwell time of light and heavy holes were observed and discussed.

In this work, we have modelled and computed the transport properties of the double-barrier InGaAs/GaAsSb structure from the resonant tunnelling point of view. Based on the classical Tsu-Esaki formula for the tunnelling current, we have calculated the current density-voltage characteristic of a Al-free type-II $$\hbox {In}_{0.53}\hbox {Ga}_{0.47}\hbox {As/GaAs}_{0.51}\hbox {Sb}_{0.49}$$In0.53Ga0.47As/GaAs0.51Sb0.49 structure at different cryogenic and elevated temperatures. The tunnelling coefficient has been calculated in the framework of effective mass approximation with nonparabolicity included, using the transfer matrix approach. A good qualitative agreement of the position of resonant current peaks with the existing experimental data was achieved. Our calculation shows a very high sensitivity of the tunnelling current peak on monolayer-scale layer structure fluctuation which strongly affects peak to valley ratio in the resonant tunnelling structure.

In this work, recessed gate AlGaN/GaN metal-insulator-semiconductor high-electron-mobility transistors (MIS-HEMTs) with double AlGaN barrier designs are fabricated and investigated. Two different recessed depths are designed, leading to a 5 nm and a 3 nm remaining bottom AlGaN barrier under the gate region, and two different Al% (15% and 20%) in the bottom AlGaN barriers are designed. First of all, a double hump trans-conductance (gm)&ndash, gate voltage (VG) characteristic is observed in a recessed gate AlGaN/GaN MIS-HEMT with a 5 nm remaining bottom Al0.2Ga0.8N barrier under the gate region. Secondly, a physical model is proposed to explain this double channel characteristic by means of a formation of a top channel below the gate dielectric under a positive VG. Finally, the impacts of Al% content (15% and 20%) in the bottom AlGaN barrier and 5 nm/3 nm remaining bottom AlGaN barriers under the gate region are studied in detail, indicating that lowering Al% content in the bottom can increase the threshold voltage (VTH) toward an enhancement-mode characteristic.

The use of hydrogen and helium as a fuel requires well-developed technologies for the separation of gas mixtures, in particular, separation of isotopes of an element. The presence of quantum effects makes such processes possible, and the proposed system of two potential barriers enhances the differences in the passage of isotopes through two layers of matter providing high separation efficiency. The probability of atoms passing through composite barriers is derived from the solving of stationary Schroedinger equation.

In this paper, we have theoretically investigated the impact of different composition ‘x’ of the barrier height on transmission coefficient and IV characteristics of GaAs/Ga1−xAlxAs double barrier heterostructure. In this study, GaAs/Ga1−xAlxAs based double barrier heterostructure is selected at operating temperature 10 K. The calculated results show that IV characteristic and transmission coefficient are the crucial measurable quantity to anticipate the double barrier heterostructure property. When the height of barrier is less, then the transmission coefficient and IV characteristics of GaAs/Ga1−xAlxAs double barrier heterostructure are high. The calculated results are in good agreement with the available reported results from the other workers.

The Seebeck coefficients are studied in asymmetric double-barrier magnetic tunnel junctions (DBMTJs) with the structures as CoFeB/MgO/ZnO/MgO/LSMO. In the linear response regime, oscillatory behavior is observed with change in the ZnO layer thickness because of the resonant tunneling in the DBMTJs. Effects of average temperature and magnetizations orientation are also discussed. It is found that the Seebeck coefficients are greater in the DBMTJs than asymmetric single-barrier MTJs (SBMTJs). Therefore, it is to be achieved the greater Seebeck coefficients by choosing a proper thickness for the ZnO layer in the proposed asymmetric DBMTJs.

We successfully improved the tunnel magnetoresistance ratio (TMR) of an MgO/CoFeB/MgO-based double-barrier magnetic tunnel junction (DMTJ) by inserting ultra-thin Fe into a CoFeB middle electrode. The Fe played as an absorber of B diffused out of the CoFeB and thereby facilitated the crystallization of the CoFeB at the interface. Changes in resistivity of the middle electrode with Fe insertion calculated by the modified current-in-plane tunneling method suggested that they can be explained by the formation of Fe borides, which is ascribed to the fact that Fe indeed promoted the diffusion of B by providing places for the B diffusion. As a result, Fe insertion improved the (001) texture of the middle electrode and thereby increased the TMR of the junction due to enhanced coherent tunneling. However, when inserted Fe was thick, the tunnel properties of DMTJs were degraded because of the absence of strong (001) texture of MgO. Materials and their thickness for a middle electrode are key parameters to successful application of DMTJs for spin devices.

Spin-dependent thermoelectric (TE) effects are studied in MgO-based double-barrier magnetic tunnel junctions with a non-magnetic metal spacer (DBMTJs-NM) in the linear response regime. Using non-equilibrium Green’s function (NEGF) formalism, the results show resonant peaks at specific thicknesses of the NM spacer because of the resonant tunneling effect through the DBMTJs-NM. Effects of average temperature and magnetization alignment are also described. Therefore, thermally charge and spin voltage lead to large spin-dependent TE effects by the DBMTJs-NM structures.

Charge current and thermal spin-transfer torque (TSTT) in asymmetric double-barrier magnetic tunnel junctions (DBMTJs) with a non-magnetic metal (NM) spacer as CoFeB/MgO/NM/MgO/LSMO are studied by non-equilibrium Green’s function (NEGF) formalism. It is found that the results show oscillatory behavior with an increase of the NM spacer thickness due to the resonant tunneling effect through the DBMTJs structures. About the dependence of the temperature difference and angle between the magnetizations, the charge current and TSTT are larger at the specific thicknesses (resonant positions) of the NM spacer than the others. The results also illustrate a magnitude enhancement for asymmetric DBMTJs compared with asymmetric single-barrier MTJs (SBMTJs). Therefore, it is possible to achieve a large TSTT for magnetization dynamics by new asymmetric DBMTJs.

Thermopower is studied in double-barrier magnetic tunnel junctions (DBMTJs) with a non-magnetic metal (NM) spacer by considering structural asymmetry—related to the different thicknesses of the MgO insulators—in the linear response regime. Using non-equilibrium Green’s function (NEGF) formalism, it is found that the thermopower is larger in the case with thicker left insulator than the other cases which is related to the voltage drop within the insulator layer. The thermopower has shown its maximum value as large as S = 482μ V/K in the anti-parallel configuration of the magnetizations and T = 300K. Therefore, it is possible to achieve the large thermopower in the thermoelectric devices based on MTJs.

The charge and spin thermopower in double-barrier magnetic tunnel junctions with a semiconductor (e.g. GaAs) spacer (DBMTJs-SC) are studied using non-equilibrium Green’s function (NEGF) formalism in the linear response regime. The results show oscillatory behavior with an increase of the SC spacer thickness due to the resonant tunneling effect through the DBMTJs-SC. Effects of the average temperature of the junctions and the spin-splitting of the ferromagnetic (FM) contacts on the charge and spin thermopower are also described. It is found that the results show a magnitude enhancement at the specific thicknesses of the SC spacer (resonant positions) compared with the other thicknesses.

The substitution effect of a Ferro-magnet (FM) electrode by a half-metallic FM material La0.7Sr0.3MnO3 (LSMO) on charge current and spin-transfer torque (STT) components is studied in MgO-based double barrier magnetic tunnel junctions (DBMTJs) with a middle non-magnetic metal (NM) layer. Using non-equilibrium Green’s function (NEGF) formalism, it is observed that the current and STT components show oscillatory behavior due to quantum well states in the middle NM layer and resonant tunneling effect. We also study effect of difference in the thickness of the MgO insulators. Bias dependence demonstrate the magnitude enhancement of the current and in-plane STT in new asymmetric DBMTJs (A-DBMTJs) compared with symmetric DBMTJs (S-DBMTJs), however, perpendicular STT decreases in the A-DBMTJs. Results also show different behavior compared with conventional asymmetric MTJs and spin valves (SVs). Therefore, one can design new memory devices by means of suitable insulator and FM electrodes with proper thicknesses.

Directional excitation of surface plasmon polaritons (SPPs) by electrical means is important for the integration of plasmonics with molecular electronics or steering signals toward other components. We report electrically driven SPP sources based on quantum mechanical tunneling across molecular double-barrier junctions, where the tunneling pathway is defined by the molecules' chemical structure as well as by their tilt angle with respect to the surface normal. Self-assembled monolayers of S(CH

The hot carrier cell (HCSCs) is a promising advanced photovoltaic concept. It aims to minimize major losses in p-n junction solar cells and is predicted to have energy conversion efficiency over 65% at one sun. Energy selective contacts (ESCs) is a critical component of the HCSC. In this paper, potential of ESCs based on quantum dot and quantum well double barrier resonant tunneling structures is presented. Results of I-V measurements these show negative differential resistance (NDR) characteristics both at low temperature and room temperature, thus indicating that these structures can be suitable for ESC application.

We study the resistance states and spin dynamics in a Ag/Fe(8)/MgO(3)/Fe(8)/MgO(5)/Fe/Ag junction based on a first-principles scattering theory. Spin dynamics simulations show that up to four resistance states with noticeable difference can be achieved via manipulating the voltage bias scheme and the position of the reference magnetization. The study indicates possible multiple-valued logic applications in an asymmetric MgO-based double-barrier magnetic tunnel junction.

This paper describes the physical simulation of Al0.3Ga0.7N/GaN-based double barrier resonant tunnelling diode (RTD) with cubic-GaN structure using Silvaco ATLAS. Cubic-GaN is interesting for vertical transport devices due to the absence of internal polarization. Proper selection of material parameters is vital in order to optimize the device performance. The relationship between current-voltage (I-V) characteristic, particularly the negative differential resistance (NDR) with respect to variation in barrier composition, well width and barrier thickness are studied in detail. RTDs with clear NDR are demonstrated with peak-to-valley-current ratio (PVCR) of 7.19 and peak current density of 3.77 mA/cm2 at room temperature. The optimum barrier thickness for a given composition is determined by using the ratio of current magnitude at resonant peak to the width of the resonance, and also used as figure of merit for the device. Finally, optimum parameters for the promising cubic Al0.3Ga0.7N/GaN RTD are proposed.

Spin-polarized currents in double-barrier magnetic tunnel junctions (MTJs) as CoFeB/MgO/InP/MgO/CoFeB (MTJs-InP) are investigated by non-equilibrium Green’s function formalism. The asymmetric structures with a half-metal LSMO contact are studied and a spin-diode behavior is found compared to the MTJs-InP. Charge and spin currents as well as spin polarization as a function of bias voltage, angle between magnetizations and quantum-well thickness are also described. A nearly 100% spin polarization is observed at a certain range of bias voltage. Therefore, one can design excellent spin-filter devices based on new MTJs-InP.

Glass-ceramics are well known for the excellent combination properties provided by their components, a glassy matrix and crystalline phases, and have promising applications in the immobilization and detoxification of solid waste containing toxic metals. Glass-ceramic products were successfully synthesized in CaO-MgO-SiO2-Al2O3 -Cr2O3 system. Two key measures--partitioning ratio of Cr in the spinel and Cr leaching ratio--were used to investigate the mechanism of Cr immobilization in the glass-ceramic products. The results of powder X-ray diffraction revealed that both spinel and diopside were major crystalline phases in the products. The value of x in the MgCr(x)Al(2-x)O4 spinel was highly related to the amount of Cr2O3 added to the glass-ceramic system. As Cr2O3 content increased, the proportion of spinel phase increased, while that of glass phase decreased. The partitioning ratio of Cr in spinel phase was about 70% for 2 wt.% Cr2O3, and increased to 90% when loaded with 10 wt.% of Cr2O3. According to the results of the prolonged toxicity characteristic leaching procedure, the Cr leaching ratio decreased with the increase of Cr partitioning ratio into the spinel phase. The findings of this study clearly indicate that glass-ceramic formed by spinel structure and residual glass successfully immobilized Cr.

We study the quantum size effects of an MgO-based double barrier magnetic tunnel junction with a nonmagnetic-metal (DBMTJ-NM) (semiconductor (DBMTJ-SC)) spacer on the charge current and the spin-transfer torque (STT) components using non-equilibrium Green's function (NEGF) formalism. The results show oscillatory behavior due to the resonant tunneling effect depending on the structure parameters. We find that the charge current and the STT components in the DBMTJ-SC demonstrate the magnitude enhancement in comparison with the DBMTJ-NM. The bias dependence of the STT components in a DBMTJ-NM shows different behavior in comparison with spin valves and conventional MTJs. Therefore, by choosing a specific SC spacer with suitable thickness in a DBMTJ the charge current and the STT components significantly increase so that one can design a device with high STT and faster magnetization switching.

Resonant tunneling quantum structures consist of asymmetric wells and barriers have been investigated to find their optimized geometrical parameters and potential profile by the numerical calculations. The results show that the widths and the depths of the asymmetric wells have a significant effect on the transmission coefficient and the dwell time. The properties exhibited in this work may establish guidance to the device applications.

We report large tunnel magnetoresistance (TMR) ratios of up to 219% at 300 K and 366% at 3.7 K obtained for a high-quality fully epitaxial double-barrier magnetic tunnel junction (MTJ) composed of Fe/MgO/Fe/γ-Al2O3/Nb-doped SrTiO3. The obtained TMR ratios are among the highest values reported in Fe/MgO/Fe structures. This result may be attributed to the small in-plane wave vectors of the tunneling electrons injected from the Nb-doped SrTiO3 electrode with a small carrier density, demonstrating good compatibility between the Fe-based MTJ and SrTiO3.

The Co-Fe-B/MgO system with perpendicular magnetic anisotropy finds extensive application in modern magnetic memories. Critical issues for the practical usage of magnetic tunnel junctions (MTJs) include the limited thermal stability of bit storage, and low switching efficiency. This study elucidates the deterministic influence of Co-Fe-B composition and the MgO interface on an MTJ's fundamental magnetic properties, which affect both thermal stability and switching current. Furthermore, the authors observe an anomalous trend in saturation magnetization, which is attributed to a change in magnetic anisotropy.

Shot noise reveals spin dependent transport properties in a magnetic tunnel junction. We report measurement of shot noise in CoFeB/MgO/CoFeB/MgO/CoFeB double barrier magnetic tunnel junctions, which shows a strong temperature dependence. The Fano factor used to characterize shot noise increases with decreasing temperature. A sequential tunneling model can be used to account for these results, in which a larger Fano factor results from larger spin relaxation length at lower temperatures.

In recent years, transmission and reception systems of optical signals are widely used. Receiving the optical signal in such systems is carried by photoreceiving modules based on a photodetector, which defines the quality of the received signal, the range and speed of the entire system. However, hitherto used p–i–n- and avalanche photodiodes do not fully meet the growing demands. The present work is devoted to investigate the photovoltaic characteristics of semiconductor thin base transistor structure based on germanium, which is superior the silicon counterparts by speed and gain. Investigated p+–n–p-structures were obtained by diffusion of antimony onto the substrate of p-type germanium to a depth of 1 micron and alloying of indium to the part of its surface which creates diffusion layer of ?+-type and with thickness of 0,5 microns. Experiments have shown that the reverse biasing of a single p+-n-emitter-base junction leads to a smooth increase in reverse current, at the same time when it is connected in series to forward biased collector p-n-junction there is a sharp increase in the current by voltage, giving properties of voltage surge suppressor. This behavior of the current-voltage characteristics can be explained by the punch-through effect when the space charge regions of the emitter junction and the space charge region of collector junction touch each other and the conditions are realized for double carrier injection into a fully depleted region of the transistor. At the same time giving small fixed voltages 0,1—0,15 V to the collector-base junction the output static characteristics can be received with an operating voltage of 3—3,5 V. A characteristic feature of the investigated transistor is that when the base region under illumination by integrated light intensity (50 and 3000 lux) light current appears, whose magnitude with the increase of operating voltage (up to 1.7 V) increases nonlinearly, resulting in increased current photosensitivity up to 17 µA/lux, which is one and a half orders of magnitude greater than photosensitivity of germanium phototransistor “OOA-5”.

The results of the fabrication and study of a double-barrier resonant tunneling structure grown on the basis of GaN and AlN wide-gap materials on a (0001)-oriented sapphire substrate are given. It is shown that, at voltages of ∼3 V, the current-voltage characteristics of resonant tunneling diode samples exhibit a region of negative differential conductivity that disappears upon multiple cyclic measurements. It is also shown that the reversal of sign of the applied voltage restores the initial shape of the current-voltage characteristics and an increase in the temperature of the structure from room temperature to 200°C yields irreversible degradation of the device and a shift of the region of negative differential conductivity to lower voltages

The considerable power consumption on logic and memory circuit system will be an unavoidable bottleneck with the shrinking of complementary metal oxide semiconductor (CMOS) technology size. One promising solution is to build non-volatile spintronic device, e.g. spin transfer torque magnetic random access memory (STT-MRAM). The basic storage unit of STT-MRAM, i.e. magnetic tunnel junction (MTJ), has thus been extensively studied. Double-barrier MTJ (DMTJ), as an optimized structure, enhances the STT effect with a second MgO barrier layer and reduces its critical switching current. In this paper, we present a physics-based compact model of CoFeB/MgO DMTJ with perpendicular magnetic anisotropy (PMA). The modeling results show a great agreement with experimental results. More efficient STT switching and similar magnetoresistance features compared with single-barrier MTJ (SMTJ) can be realized. Mixed circuits simulations have also been carried out to validate its functionality. This SPICE-compatible compact model will be useful for high-performance hybrid DMTJ/CMOS circuit and system designs.

Various negative photoelectric effects in films of alloys of II–VI compounds deposited from a solution are studied depending on the deposition mode and heat treatment. A combined electronic-molecular mechanism of the negative photocapacitance effect, which is for the first time found in Cd1 − xZnxS and CdS1 − xSex films, and negative slowly relaxing photoelectric effects is established. The latter are caused by the transition of electrons arranged in a nanoscale surface layer from shallow energy levels of attachment centers to deeper levels with lower polarizability and by the presence of nanoscale clusters playing the role of a “reservoir” for minority carriers in these materials. A model, which makes it possible to interpret the main regularities of negative photoconductivity in Cd1 − xZnxS and CdS1 − xSex films deposited from a solution, is suggested. It is established that the negative residual photoconductivity is explained on the basis of a double barrier profile, while the negative differential photoconductivity is explained by the presence of nanoscalel electric domains.

Thin film transistors with nanoparticles silicon floating-gate are fabricated by plasma enhanced chemical vapor deposition. It should be noted that SiO2acts as both a tunneling and a blocking layer. Meanwhile, some np-Si dots are embedded within SiO2layers. The electrical characteristic of the devices are measured by semiconductor parameter analyzer at room temperature. These Thin film transistors show a good device performance with a high charge-carrier mobility of 33 cm2/vs and a large on/off ratio of 1.2×106. Moreover, the capability of written and erasing was demonstrated. This indicates that thin film transistors can be operated as rewritable nonvolatile floating gate memory devices.

The simulation is done for electron tunneling through the insulating layer of the magnetic tunnel junction with non-magnetic embedded nanoparticles (npMTJs). The distribution of the nanoparticles by size (DNPS) was important part of the solution for tunnel magnetoresistance (TMR) which was calculated on the basement of the double barrier tunneling model. It was found that theoretical agreement with experimental data can be influenced not only from DNPS but also due to different cases of the quantization. A few cases of the quantization related with a redistribution over quantum well (QW) states of the nanoparticles (NPs) (with diameter d) were considered (one of the possible DNPS and related TMR is shown in Fig. 1a and Fig. 1b).

We study the tunneling of Dirac fermions in graphene through a double barrier potential allowing the carriers to have an effective mass inside the barrier as generated by a lattice miss-match with the boron nitride substrate. The consequences of this gap opening on the transmission are investigated. The realization of resonant tunneling conditions is also analyzed., Comment: 17 pages, 6 figures

In this paper, we study the value of the tunnel magnetoresistance (TMR) as a function of the applied voltage in double barrier magnetic tunnel junctions (DMTJs) with the left and right ferromagnetic (FM) layers being pinned and numerically estimate the possible difference of the TMR curves for negative and positive voltages in the homojunctions (equal barriers and electrodes). DMTJs are modeled as two single barrier junctions connected in series with consecutive tunneling (CST). We investigated the asymmetric voltage behavior of the TMR for the CST in the range of a general theoretical model. Significant asymmetries of the experimental curves, which arise due to different annealing regimes, are mostly explained by different heights of the tunnel barriers and asymmetries of spin polarizations in magnetic layers.