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In this work we demonstrate explicit analytical expressions for both charge and spin currents which constitute the 2 × 2 spinor in magnetic tunnel junctions with noncollinear magnetizations under applied voltage. The calculations have been performed within the free electron model in the framework of the Keldysh formalism and WKB approximation. We demonstrate that spin/charge currents and spin transfer torques are all explicitly expressed through only three irreducible quantities, without further approximations. The conditions and mechanisms of deviation from the conventional sine angular dependence of both spin currents and torques are shown and discussed. It is shown in the thick barrier approximation that all tunneling transport quantities can be expressed in an extremely simplified form via Slonczewski spin polarizations and our effective spin averaged interfacial transmission probabilities and effective out-of-plane polarizations at both interfaces. It is proven that the latter plays a key role in the emergence of perpendicular spin torque as well as in the angular dependence character of all spin and charge transport considered. It is demonstrated directly also that for any applied voltage, the parallel component of spin current at the FM/I interface is expressed via collinear longitudinal spin current components. Finally, spin transfer torque behavior is analyzed in a view of transverse characteristic length scales for spin transport. [ABSTRACT FROM AUTHOR]

Nonequilibrium spin-dependent transport in magnetic tunnel junctions comprising a ferroelectric barrier is theoretically investigated. The exact solutions of the free electron Schrödinger equation for electron tunneling in the presence of interfacial screening are obtained by combining Bessel and Airy functions. We demonstrate that the spin transfer torque efficiency, and more generally the bias dependence of tunneling magneto- and electroresistance, can be controlled by switching the ferroelectric polarization of the barrier. In particular, the critical voltage at which the in-plane torque changes sign can be strongly enhanced or reduced depending on the direction of the ferroelectric polarization of the barrier. This effect provides a supplementary way to electrically control the current-driven dynamic states of the magnetization and related magnetic noise in spin transfer devices. [ABSTRACT FROM AUTHOR]

The perpendicular magnetic anisotropy (PMA) arising at the interface between ferromagnetic transition metals and metallic oxides was investigated via first-principles calculations. In this work very large values of PMA, up to 3 erg/cm2, at Fe∣MgO interfaces are reported, in agreement with recent experiments. The origin of PMA is attributed to overlap between O-pz and transition metal dz2 orbitals hybridized with dxz(yz) orbitals with stronger spin-orbit coupling-induced splitting around the Fermi level for perpendicular magnetization orientation. Furthermore, it is shown that the PMA value weakens in the case of over- or underoxidation due to the fact that oxygen pz and transition metal dz2 orbital overlap is strongly affected by disorder, in agreement with experimental observations in magnetic tunnel junctions. [ABSTRACT FROM AUTHOR]

The relative contributions of in-plane (damping-like) and out-of-plane (field-like) spin-transfer torques (STT) in the magnetization switching of out-of-plane magnetized magnetic tunnel junctions (pMTJ) has been theoretically analyzed using the transformed Landau-Lifshitz-Gilbert (LLG) equation with the STT terms. It is demonstrated that in a pMTJ structure obeying macrospin dynamics, the out-of-plane torque influences the precession frequency, but it does not contribute significantly to the STT switching process (in particular to the switching time and switching current density), which is mostly determined by the in-plane STT contribution. This conclusion is confirmed by finite temperature and finite writing pulse macrospin simulations of the current field switching diagrams. It contrasts with the case of STT switching in in-plane magnetized magnetic tunnel junction (MTJ) in which the field-like term also influences the switching critical current. This theoretical analysis was successfully applied to the interpretation of voltage field STT switching diagrams experimentally measured on pMTJ pillars 36 nm in diameter, which exhibit macrospin behavior. The physical nonequivalence of Landau and Gilbert dissipation terms in the presence of STT-induced dynamics is also discussed. [ABSTRACT FROM AUTHOR]

Using first-principles calculations, we investigated the impact of chromium (Cr) and vanadium (V) impurities on the magnetic anisotropy and spin polarization in Fe/MgO magnetic tunnel junctions. It is demonstrated, using layer resolved anisotropy calculation technique, that while the impurity near the interface has a drastic effect in decreasing the perpendicular magnetic anisotropy (PMA), its position within the bulk allows maintaining high interfacial PMA while reducing the bulk magnetization and correlatively the easy-plane demagnetizing energy. As a result, the effective magnetic anisotropy tends to increase as a function of the Cr or V concentration resulting in an increase in the critical magnetic thickness at which the crossover from out-of-plane to in-plane anisotropy takes place. At the same time, the interfacial spin polarization is not affected by the magnetic layer bulk doping by Cr or V impurities and even enhanced in most situations thus favoring an increase of tunnel magnetoresistance (TMR) amplitude. [ABSTRACT FROM AUTHOR]

The charge-mediated effect of electric field on the perpendicular magnetic anisotropy (PMA) of Fe/MgO interfaces is investigated using first-principles calculations. We present an approach by discussing this effect in relation to the intrinsic dipole field existing at the Fe/MgO interface. A firm correlation between the PMA and the interfacial dipole is established and further verified in the absence of an applied electric field. The on-site projected PMA analysis not only elucidates that the effect of electric field on the PMA extends beyond the interfacial Fe layer, but also shows that the second Fe layer carries the largest contribution to the effect. This observation is interpreted in relation to the orbital hybridization changes induced by applying an electric field. [ABSTRACT FROM AUTHOR]

Double-barrier heterostructures are model systems for the study of electron tunneling and discrete energy levels in a quantum well (QW). Until now resonant tunneling phenomena in metallic QWs have been observed for limited thicknesses (1-2 nm) under which electron phase coherence is conserved. In the present study we show evidence of QW resonance states in Fe QWs up to 12 nm thick and at room temperature in fully epitaxial double MgA10c barrier magnetic tunnel junctions. The electron phase coherence displayed in this QW is of unprecedented quality because of a homogenous interface phase shift due to the small lattice mismatch at the Fe-MgA10v interface. The physical understanding of the critical role of interface strain on QW phase coherence will greatly promote the development of spin-dependent quantum resonant tunneling applications. [ABSTRACT FROM AUTHOR]

Spin-transfer torque (STT) in tunnel junctions with ferromagnetic leads is one of the essential underlying phenomena of modem spintronics. Here, we present a theoretical study of STT in ferrimagnet- (FT-) based tunnel junctions where two FI metal electrodes are separated by a thin nonmagnetic insulating barrier. We show that electronic structure parameters, such as bandwidths and exchange splittings of the FI leads strongly influence STT. In particular, the STT spatial distribution within the leads shows a striking spin-modulated wavelike behavior resulting from the interplay between the exchange splittings of the two FI sublattices. Additionally, we identify the fundamental parameter for quantifying STT characteristic lengths in FI metals, which will also be accessible to experiments, for instance, by ferromagnetic resonance and spin pumping measurements. [ABSTRACT FROM AUTHOR]

Binary information encoded within the spin of carriers can be transferred into corresponding right- or left-handed circularly polarized photons emitted from an active semiconductor medium via carrier-photon angular momentum conversion. In order to attain maximized spin injection at out-of-plane magnetic remanence, a number of material systems have been explored as possible solid-state spin injectors. However, the circular polarization (Pc) of emitted light was still limited at 3-4% at remanence. Here, we demonstrate a sizable electroluminescence circular polarization from a III-V-based spin light-emitting diode at zero magnetic field with a perpendicular spin injector consisting of an ultrathin CoFeB ferromagnetic layer (1.2 nm) grown on a MgO tunnel barrier (2.5 nm). The maximum value of Pc measured at zero field is as large as 20% at 25 K and still 8% at 300 K. These types of ultrathin perpendicular spin injectors are of great interest (i) to realize the electrical switching of the magnetization of the injector layer owing to the advanced spin-transfer torque properties of the CoFeB layer and (ii) to be directly embedded in optical cavities for spin lasers due to their very low optical absorption loss. [ABSTRACT FROM AUTHOR]

Using first-principles calculations, we elucidate microscopic mechanisms of perpendicular magnetic anisotropy (PMA) in Fe/MgO magnetic tunnel junctions through evaluation of orbital and layer resolved contributions into the total anisotropy value. It is demonstrated that the origin of the large PMA values is far beyond simply considering the hybridization between Fe-3d and O-2p orbitals at the interface between the metal and the insulator. Onsite projected analysis shows that the anisotropy energy is not localized at the interface but it rather propagates into the bulk showing an attenuating oscillatory behavior which depends on orbital character of contributing states and interfacial conditions. Furthermore, it is found in most situations that states with dyz(xz) and dZ2 character tend always to maintain the PMA while those with dxy and dx2-y2 character tend to favor the in-plane anisotropy. It is also found that while MgO thickness has no influence on PMA, the calculated perpendicular magnetic anisotropy oscillates as a function of Fe thickness with a period of 2 ML and reaches a maximum value of 3.6 mJ/m2. [ABSTRACT FROM AUTHOR]

We report on first-principles calculations of spin-dependent properties in graphene induced by its interaction with a nearby magnetic insulator (europium oxide, EuO). The magnetic proximity effect results in spin polarization of graphene π orbitals by up to 24%, together with a large exchange-splitting band gap of about 36 meV. The position of the Dirac cone is further shown to depend strongly on the graphene-EuO interlayer. These findings point toward the possible engineering of spin gating by the proximity effect at a relatively high temperature, which stands as a hallmark for future all-spin information processing technologies. [ABSTRACT FROM AUTHOR]

Spin-orbit coupling (SOC) related to the minority interface resonance states (IRSs) of Fe(001) has been evidenced in full-epitaxial Fe(001)/MgO/Fe magnetic tunnel junctions (MTJs) from magnetotransport experiments correlated to theoretical ab initio calculations. We show that the SOC effect strongly depends on the symmetry composition of the 1RS, which has been skillfully engineered via the interfacial chemical structure in the Fe(001)/MgO stack. The SOC scattering is enhanced between the majority Δ1) and minority Δ5 band near the Fermi level when presenting a Δ5 symmetry dominant 1RS at the Fe/MgO interface. Our results validate the interplay between SOC and IRSs, which gives further understanding of the mechanisms responsible for the tunneling anisotropic magnetoresistance and the large perpendicular magnetic anisotropy at the Fe/MgO interface. [ABSTRACT FROM AUTHOR]

We demonstrate that a giant spin Hall effect (SHE) can be induced by introducing a small amount of Bi impurities in Cu. Our analysis, based on a new three-dimensional finite element treatment of spin transport, shows that the sign of the SHE induced by the Bi impurities is negative and its spin Hall (SH) angle amounts to --0.24. Such a negative large SH angle in CuBi alloys can be explained by applying the resonant scattering model proposed by Feri and Levy [Phys. Rev. Lett. 106, 157208 (2011)] to 6p impurities. [ABSTRACT FROM AUTHOR]

Theoretically, the so-called zigzag edge of graphenes provides localized electrons due to the presence of flat energy bands near the Fermi level. Spin interaction makes the localized spins strongly polarized, yielding ferromagnetism. However, in most experimental studies, ferromagnetism has been observed in uncontrollable and complicated carbon-based systems. Here, we fabricate graphenes with honeycomblike arrays of hexagonal nanopores, which have a large ensemble of hydrogen-terminated and low-defect pore edges that are prepared by a nonlithographic method (nanoporous alumina templates). We observe large-magnitude ferromagnetism derived from electron spins localizing at the zigzag nanopore edges. This promises to be a realization of graphene magnets and novel spintronic devices. [ABSTRACT FROM AUTHOR]

The charge and spin diffusion equations, taking into account spin-flip and spin-transfer torque, were numerically solved using a finite element method in complex noncollinear geometry with strongly inhomogeneous current flow. As an illustration, spin-dependent transport through a nonmagnetic nanoconstriction, separating two magnetic layers was investigated. Unexpected results such as vortices of spin-currents in the vicinity of the nanoconstriction were obtained. The angular variations of magnetoresistance and spin-transfer torque are strongly influenced by the structure geometry. [ABSTRACT FROM AUTHOR]

We present theoretical studies of the intrinsic spin-orbit torque (SOT) in a single-domain ferromagnetic layer with Rashba spin-orbit coupling (SOC) using the nonequilibrium Green's function formalism for a tight-binding Hamiltonian. We find that, in the case of a small electric field, the intrinsic SOT to first order in SOC has only the field-like torque symmetry and can be interpreted as the longitudinal spin current induced by the charge current and Rashba field. We analyze the results in terms of the material-related parameters of the electronic structure, such as the band filling, bandwidth, exchange splitting, and the Rashba SOC strength. On the basis of these numerical and analytical results, we discuss the magnitude and sign of SOT. Our results suggest that the different sign of SOT in identical ferromagnets with different supporting layers, e.g., Co/Pt and Co/Ta, can be attributed to electrostatic doping of the ferromagnetic layer by the support. [ABSTRACT FROM AUTHOR]

We present measurements of the spin Hall effect (SHE) in AuW and AuTa alloys for a large range of W or Ta concentrations by combining experiments on lateral spin valves and ferromagnetic-resonance/spin-pumping techniques. The main result is the identification of a large enhancement of the spin Hall angle (SHA) by the side-jump mechanism on Ta impurities, with a SHA as high as +0.5 (i.e., 50%) for about 10% of Ta. In contrast, the SHA in AuW does not exceed +0.15 and can be explained by intrinsic SHE of the alloy without significant extrinsic contribution from skew or side-jump scattering by W impurities. The AuTa alloys, as they combine a very large SHA with a moderate resistivity (smaller than 85μΩcm), are promising for spintronic devices exploiting the SHE. [ABSTRACT FROM AUTHOR]

Magnetoresistive and magnetoresonance measurements carried out on patterned perpendicular magnetic tunnel junction pillars and full-sheet films reveal magnetic inhomogeneities of FeCoB free layer grown on MgO and coated with Ta. At low FeCoB thicknesses, the layer behaves as an ensemble of weakly coupled grains resulting in a decrease of the free-layer thermal stability. In contrast, for thicker layers, the grains become more strongly coupled but strong magnetic inhomogeneities remain, yielding the emergence and further increase of a second-order magnetic anisotropy term (~K2effcos4θ), eventually resulting in an easy-cone anisotropy. We show that the static and dynamic magnetic properties of such a free layer can be successfully described by a granular model with three thickness-dependent parameters: mean perpendicular anisotropy of the grains, grain-to-grain anisotropy distribution, and intergrain exchangelike coupling strength. Easy-cone anisotropy may help reduce the stochasticity of the spin transfer torque switching. However, it arises at intermediate values of the intergrain exchange coupling where the spin transfer torque (STT) switching efficiency is degraded, as shown by multimacrospin modeling. This is due to the excitation of exchange modes contributing weakly to the STT switching process while dissipating part of the STT energy. [ABSTRACT FROM AUTHOR]

We present a theory of the anisotropy of tunneling magnetoresistance (ATMR) phenomenon in magnetic tunnel junctions (MTJs) attributed to Rashba spin-orbit interaction in the insulating barrier. ATMR represents the difference of tunnel magnetoresistance (TMR) amplitude measured with in-plane and out-of-plane magnetic configurations. It is demonstrated that within the spin-polarized free-electron model the change of conductance associated with the ATMR is exactly twice the change of conductance measured at full saturation (i.e., in parallel configuration of magnetizations) between in-plane and out-of-plane configuration, i.e., the tunneling anisotropic magnetoresistance (TAMR). Both ATMR and TAMR are closely related to the TMR amplitude and spin-orbit constant. The predicted ATMR phenomenon is confirmed experimentally, showing a few percent value in the case of the widely studied CoFeB/MgO/CoFeB based MTJ. [ABSTRACT FROM AUTHOR]

A complete set of the generalized drift-diffusion equations for a coupled charge and spin dynamics in ferromagnets in the presence of extrinsic spin-orbit coupling is derived from the quantum kinetic approach, covering major transport phenomena, such as the spin and anomalous Hall effects, spin swapping, spin precession, and relaxation processes. We argue that the spin swapping effect in ferromagnets is enhanced due to spin polarization, while the overall spin texture induced by the interplay of spin-orbital and spin precession effects displays a complex spatial dependence that can be exploited to generate torques and nucleate or propagate domain walls in centrosymmetric geometries without the use of external polarizers, as opposed to the conventional understanding of spin-orbit mediated torques.

The Dzyaloshinskii-Moriya interaction (DMI) has been recently recognized to play a crucial role in allowing fast domain wall dynamics driven by spin-orbit torques and the generation of magnetic Skyrmions. Here, we unveil the main features and microscopic mechanisms of DMI in Co/Pt bilayers via first principles calculations. We find that the large DMI of the bilayers has a dominant contribution from the spins of the interfacial Co layer. This DMI between the interfacical Co spins extends very weakly away from the interface and is associated with a spin-orbit coupling in the adjacent atomic layer of Pt. Furthermore, no direct correlation is found between DMI and proximity induced magnetism in Pt. These results clarify the underlying mechanisms of DMI at interfaces between ferromagnetic and heavy metals and should help optimizing material combinations for domain wall and Skyrmion-based devices.

Double-barrier heterostructures are model systems for the study of electron tunneling and discrete energy levels in a quantum well (QW). Until now resonant tunneling phenomena in metallic QWs have been observed for limited thicknesses (1-2 nm) under which electron phase coherence is conserved. In the present study we show evidence of QW resonance states in Fe QWs up to 12 nm thick and at room temperature in fully epitaxial double MgAlO_{x} barrier magnetic tunnel junctions. The electron phase coherence displayed in this QW is of unprecedented quality because of a homogenous interface phase shift due to the small lattice mismatch at the Fe-MgAlO_{x} interface. The physical understanding of the critical role of interface strain on QW phase coherence will greatly promote the development of spin-dependent quantum resonant tunneling applications.

We predict an anomalous bias dependence of the spin transfer torque parallel to the interface, Tparallel, in magnetic tunnel junctions, which can be selectively tuned by the exchange splitting. It may exhibit a sign reversal without a corresponding sign reversal of the bias or even a quadratic bias dependence. We demonstrate that the underlying mechanism is the interplay of spin currents for the ferromagnetic (antiferromagnetic) configurations, which vary linearly (quadratically) with bias, respectively, due to the symmetric (asymmetric) nature of the barrier. The spin transfer torque perpendicular to interface exhibits a quadratic bias dependence.

We report exact model calculations of the spin-dependent tunneling in double magnetic tunnel junctions in the presence of impurities in the well. We show that the impurity can tune selectively the spin channels giving rise to a wide variety of interesting and novel transport phenomena. The tunneling magnetoresistance, the spin polarization, and the local current can be dramatically enhanced or suppressed by impurities. The underlying mechanism is the impurity-induced shift of the quantum well states (QWSs), which depends on the impurity potential, impurity position, and the symmetry of the QWS., (Copyright 2004 The American Physical Society)