Intrinsic spin orbit torque in a single domain nanomagnet

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 non-equilibrium Green's function formalism for a model Hamiltonian. We find that, to the first order in SOC, the intrinsic SOT 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 band filling, band width, exchange splitting, as well as the Rashba SOC strength. On the basis of these numerical and analytical results, we discuss the magnitude and sign of SOT. Our results show that the different sign of SOT in identical ferromagnetic layers with different supporting layers, e.g. Co/Pt and Co/Ta, could be attributed to electrostatic doping of the ferromagnetic layer by the support.Comment: 10 pages, 2 figure

Voltage induced control and magnetoresistance of noncollinear frustrated magnets

Noncollinear frustrated magnets are proposed as a new class of spintronic materials with high magnetoresistance which can be controlled with relatively small applied voltages. It is demonstrated that their magnetic configuration strongly depends on position of the Fermi energy and applied voltage. The voltage induced control of noncollinear frustrated materials (VCFM) can be seen as a way to intrinsic control of colossal magnetoresistance (CMR) and is the bulk material counterpart of spin transfer torque concept used to control giant magnetoresistance in layered spin-valve structures.Comment: 4 pages, 4 figure

Analytical description of ballistic spin currents and torques in magnetic tunnel junctions

In this work we demonstrate explicit analytical expressions for both charge and spin currents which constitute the 2x2 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.Comment: 10 pages, 6 figure

Impurity-induced tuning of quantum well states in spin-dependent resonant tunneling

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 (QWS) which depends on the impurity potential, impurity position and the symmetry of the QWS.Comment: 4 pages, 4 figures, submitted to Phys. Rev. Let

Voltage Dependence of Spin Transfer Torque in Magnetic Tunnel Junctions

Theoretical investigations of spin transfer torque in magnetic tunnel junctions using the tight-binding model in the framework of non-equilibrium Green functions formalism are presented. We show that the behavior of the spin transfer torque as a function of applied voltage can vary over a wide range depending on the band parameters of the ferromagnetic electrodes and the insulator that comprise the magnetic tunnel junction. The behavior of both the parallel and perpendicular components of the spin torque is addressed. This behavior is explained in terms of the spin and charge current dependence and on the interplay between evanescent states in the insulator and the Fermi surfaces of ferromagnetic electrodes comprising the junction. The origin of the perpendicular (field-like) component of spin transfer torque at zero bias, i.e. exchange coupling through the barrier between ferromagnetic electrodes is discussed.Comment: 5 pages,4 figure

Spin-polarized current-induced torque in magnetic tunnel junctions

We present tight-binding calculations of the spin torque in noncollinear magnetic tunnel junctions based on the nonequilibrium Green functions approach. We have calculated the spin torque via the effective local magnetic moment approach and the divergence of the spin current. We show that both methods are equivalent, i.e., the absorption of the spin current at the interface is equivalent to the exchange interaction between the electron spins and the local magnetization. The transverse components of the spin torque parallel and perpendicular to the interface oscillate with different phase and decay in the ferromagnetic layer FM as a function of the distance from the interface. The period of oscillations is inversely proportional to the difference between the Fermi momentum of the majority and minority electrons. The phase difference between the two transverse components of the spin torque is due to the precession of the electron spins around the exchange field in the FM layer. In the absence of applied bias and for a relatively thin barrier, the component of the spin torque perpendicular to the interface is nonzero due to the exchange coupling between the FM layers across the barrier.Journal of Applied Physics 99(8), 08G501. (2006)0021-897

Spin-orbit torque-assisted switching in magnetic insulator thin films with perpendicular magnetic anisotropy

As an in-plane charge current flows in a heavy metal film with spin-orbit coupling, it produces a torque on and thereby switches the magnetization in a neighbouring ferromagnetic metal film. Such spin-orbit torque (SOT)-induced switching has been studied extensively in recent years and has shown higher efficiency than switching using conventional spin-transfer torque. Here we report the SOT-assisted switching in heavy metal/magnetic insulator systems. The experiments used a Pt/BaFe12O19 bilayer where the BaFe12O19 layer exhibits perpendicular magnetic anisotropy. As a charge current is passed through the Pt film, it produces a SOT that can control the up and down states of the remnant magnetization in the BaFe12O19 film when the film is magnetized by an in-plane magnetic field. It can reduce or increase the switching field of the BaFe12O19 film by as much as about 500 Oe when the film is switched with an out-of-plane field

First-principles quantum transport modeling of spin-transfer and spin-orbit torques in magnetic multilayers

We review a unified approach for computing: (i) spin-transfer torque in magnetic trilayers like spin-valves and magnetic tunnel junction, where injected charge current flows perpendicularly to interfaces; and (ii) spin-orbit torque in magnetic bilayers of the type ferromagnet/spin-orbit-coupled-material, where injected charge current flows parallel to the interface. Our approach requires to construct the torque operator for a given Hamiltonian of the device and the steady-state nonequilibrium density matrix, where the latter is expressed in terms of the nonequilibrium Green's functions and split into three contributions. Tracing these contributions with the torque operator automatically yields field-like and damping-like components of spin-transfer torque or spin-orbit torque vector, which is particularly advantageous for spin-orbit torque where the direction of these components depends on the unknown-in-advance orientation of the current-driven nonequilibrium spin density in the presence of spin-orbit coupling. We provide illustrative examples by computing spin-transfer torque in a one-dimensional toy model of a magnetic tunnel junction and realistic Co/Cu/Co spin-valve, both of which are described by first-principles Hamiltonians obtained from noncollinear density functional theory calculations; as well as spin-orbit torque in a ferromagnetic layer described by a tight-binding Hamiltonian which includes spin-orbit proximity effect within ferromagnetic monolayers assumed to be generated by the adjacent monolayer transition metal dichalcogenide.Comment: 22 pages, 9 figures, PDFLaTeX; prepared for Springer Handbook of Materials Modeling, Volume 2 Applications: Current and Emerging Material

Semiconductor Spintronics

Spintronics refers commonly to phenomena in which the spin of electrons in a solid state environment plays the determining role. In a more narrow sense spintronics is an emerging research field of electronics: spintronics devices are based on a spin control of electronics, or on an electrical and optical control of spin or magnetism. This review presents selected themes of semiconductor spintronics, introducing important concepts in spin transport, spin injection, Silsbee-Johnson spin-charge coupling, and spindependent tunneling, as well as spin relaxation and spin dynamics. The most fundamental spin-dependent nteraction in nonmagnetic semiconductors is spin-orbit coupling. Depending on the crystal symmetries of the material, as well as on the structural properties of semiconductor based heterostructures, the spin-orbit coupling takes on different functional forms, giving a nice playground of effective spin-orbit Hamiltonians. The effective Hamiltonians for the most relevant classes of materials and heterostructures are derived here from realistic electronic band structure descriptions. Most semiconductor device systems are still theoretical concepts, waiting for experimental demonstrations. A review of selected proposed, and a few demonstrated devices is presented, with detailed description of two important classes: magnetic resonant tunnel structures and bipolar magnetic diodes and transistors. In most cases the presentation is of tutorial style, introducing the essential theoretical formalism at an accessible level, with case-study-like illustrations of actual experimental results, as well as with brief reviews of relevant recent achievements in the field.Comment: tutorial review; 342 pages, 132 figure