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

Vertical current induced domain wall motion in MgO-based magnetic tunnel junction with low current densities

Shifting electrically a magnetic domain wall (DW) by the spin transfer mechanism is one of the future ways foreseen for the switching of spintronic memories or registers. The classical geometries where the current is injected in the plane of the magnetic layers suffer from a poor efficiency of the intrinsic torques acting on the DWs. A way to circumvent this problem is to use vertical current injection. In that case, theoretical calculations attribute the microscopic origin of DW displacements to the out-of-plane (field-like) spin transfer torque. Here we report experiments in which we controllably displace a DW in the planar electrode of a magnetic tunnel junction by vertical current injection. Our measurements confirm the major role of the out-of-plane spin torque for DW motion, and allow to quantify this term precisely. The involved current densities are about 100 times smaller than the one commonly observed with in-plane currents. Step by step resistance switching of the magnetic tunnel junction opens a new way for the realization of spintronic memristive devices

Time-resolved detection of spin-transfer-driven ferromagnetic resonance and spin torque measurement in magnetic tunnel junctions

Several experimental techniques have been introduced in recent years in attempts to measure spin transfer torque in magnetic tunnel junctions (MTJs). The dependence of spin torque on bias is important for understanding fundamental spin physics in magnetic devices and for applications. However, previous techniques have provided only indirect measures of the torque and their results to date for the bias dependence are qualitatively and quantitatively inconsistent. Here we demonstrate that spin torque in MTJs can be measured directly by using time-domain techniques to detect resonant magnetic precession in response to an oscillating spin torque. The technique is accurate in the high-bias regime relevant for applications, and because it detects directly small-angle linear-response magnetic dynamics caused by spin torque it is relatively immune to artifacts affecting competing techniques. At high bias we find that the spin torque vector differs markedly from the simple lowest-order Taylor series approximations commonly assumed.Comment: 29 pages, 5 figures including supplementary materia

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