Spin torque driven dynamics of a coupled two layer structure: interplay between conservative and dissipative coupling

In this manuscript the general concepts of spin wave theory are adapted to the dynamics of a self-polarized system based on two layers coupled via interlayer exchange (conservative coupling) and mutual spin torque (dissipative coupling). An analytical description of the non-linear dynamics is proposed and validated through numerical simulations. In contrast to the single layer model, the phase equation of the coupled system has a contribution coming from the dissipative part of the LLGS equation. It is shown that this is a major contribution to the frequency mandatory to describe well the most basic features of the dynamics of coupled systems. Using the proposed model a specific feature of coupled dynamics is addressed: the redshift to blueshift transition observed in the frequency current dependence of this kind of exchange coupled systems upon increasing the applied field. It is found that the blueshift regime can only occur in a region of field where the two linear eigenmodes contribute equally to the steady state mode (i.e. high mode hybridization). Finally, a general perturbed Hamiltonian equation for the coupled system is proposed.Comment: 16 pages, 7 figue

Respective influence of in-plane and out-of-plane spin-transfer torques in magnetization switching of perpendicular magnetic tunnel junctions

The relative contributions of in-plane (damping-like) and out-of-plane (field-like) spin-transfer-torques in the magnetization switching of out-of-plane magnetized magnetic tunnel junctions (pMTJ) has been theoretically analyzed using the transformed Landau-Lifshitz (LL) 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 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 perpendicular MTJ pillars 36 nm in diameter, which exhibit macrospin-like behavior. The physical nonequivalence of Landau and Gilbert dissipation terms in presence of STT-induced dynamics is also discussed

Modulating spin transfer torque switching dynamics with two orthogonal spin-polarizers by varying the cell aspect ratio

We study in-plane magnetic tunnel junctions with additional perpendicular polarizer for subnanosecond-current-induced switching memories. The spin-transfer-torque switching dynamics was studied as a function of the cell aspect ratio both experimentally and by numerical simulations using the macrospin model. We show that the anisotropy field plays a significant role in the dynamics, along with the relative amplitude of the two spin-torque contributions. This was confirmed by micromagnetic simulations. Real-time measurements of the reversal were performed with samples of low and high aspect ratio. For low aspect ratios, a precessional motion of the magnetization was observed and the effect of temperature on the precession coherence was studied. For high aspect ratios, we observed magnetization reversals in less than 1 ns for high enough current densities, the final state being controlled by the current direction in the magnetic tunnel junction cell.Comment: 6 pages, 7 figure

Fast computation of magnetostatic fields by Non-uniform Fast Fourier Transforms

The bottleneck of micromagnetic simulations is the computation of the long-ranged magnetostatic fields. This can be tackled on regular N-node grids with Fast Fourier Transforms in time N logN, whereas the geometrically more versatile finite element methods (FEM) are bounded to N^4/3 in the best case. We report the implementation of a Non-uniform Fast Fourier Transform algorithm which brings a N logN convergence to FEM, with no loss of accuracy in the results

Current induced domain wall dynamics in the presence of spin orbit torques

Current induced domain wall (DW) motion in perpendicularly magnetized nanostripes in the presence of spin orbit torques is studied. We show using micromagnetic simulations that the direction of the current induced DW motion and the associated DW velocity depend on the relative values of the field like torque (FLT) and the Slonczewski like torques (SLT). The results are well explained by a collective coordinate model which is used to draw a phase diagram of the DW dynamics as a function of the FLT and the SLT. We show that a large increase in the DW velocity can be reached by a proper tuning of both torques.Comment: 9 pages, 3 figure

Dimensionality cross-over in magnetism: from domain walls (2D) to vortices (1D)

Dimensionality cross-over is a classical topic in physics. Surprisingly it has not been searched in micromagnetism, which deals with objects such as domain walls (2D) and vortices (1D). We predict by simulation a second-order transition between these two objects, with the wall length as the Landau parameter. This was conrmed experimentally based on micron-sized ux-closure dots

Domain wall tilting in the presence of the Dzyaloshinskii-Moriya interaction in out-of-plane magnetized magnetic nanotracks

We show that the Dzyaloshinskii-Moriya interaction (DMI) can lead to a tilting of the domain wall (DW) surface in perpendicularly magnetized magnetic nanotracks when DW dynamics is driven by an easy axis magnetic field or a spin polarized current. The DW tilting affects the DW dynamics for large DMI and the tilting relaxation time can be very large as it scales with the square of the track width. The results are well explained by an analytical model based on a Lagrangian approach where the DMI and the DW tilting are included. We propose a simple way to estimate the DMI in a magnetic multilayers by measuring the dependence of the DW tilt angle on a transverse static magnetic field. Our results shed light on the current induced DW tilting observed recently in Co/Ni multilayers with inversion asymmetry, and further support the presence of DMI in these systems.Comment: 12 pages, 3 figures, 1 Supplementary Material