Crossover between fast and slow excitation of magnetization by spin torque

Abstract

A crossover between two mechanisms destabilizing the magnetization in equilibrium by the spin transfer effect is found in a ferromagnetic multilayer consisting of an in-plane magnetized free layer and a perpendicularly magnetized pinned layer, where an in-plane magnetic field is applied, and electric current flows from the pinned to the free layer. A fast transition from the in-plane to the out-of-plane state occurs in the low-field region, whereas a slow transition with small-amplitude oscillation becomes dominant in the high-field region. On the other hand, only the fast transition mechanism appears for the opposite current direction. PACS numbers:Excitation of magnetization dynamics such as switching and self-oscillation in a ferromagnetic/nonmagnetic multilayer by the spin transfer effect 1,2 has been studied extensively for application in practical devices such as magnetic memory and microwave generators 3-15 . It has been recognized that there is a threshold value of the electric current necessary to destabilize the magnetization in equilibrium and excite any type of magnetization dynamics by the spin torque effect. Evaluation of the threshold current is important because it determines the performance of spin torque devices, for example, power consumption. To this end, a deep understanding of the physical mechanism of magnetization instability due to the spin torque is necessary.In this letter, the physical mechanism destabilizing the magnetization in a ferromagnetic multilayer consisting of an in-plane magnetized free layer and a perpendicularly magnetized pinned layer is studied theoretically. We find that this system shows a crossover between two mechanisms destabilizing the magnetization in equilibrium, depending on the magnitude of an in-plane applied magnetic field. A fast transition, on the order of nanoseconds, from an in-plane stable state to an out-ofplane state is dominant in the low-field region, whereas a slow transition in a time range exceeding 100 ns with a small-amplitude oscillation principally determines the instability threshold in the high-field region. This crossover appears only when the electric current flows perpendicular to the plane from the pinned layer to the free layer. When the current direction is reversed, the instability threshold is determined solely by the fast transition. Figure 1 schematically shows the system under consideration. The z-axis is perpendicular to the film-plane, and an in-plane magnetic field is applied along the x-axis. The unit vectors pointing in the magnetization directions of the free and pinned layers are denoted by m and p, respectively. The magnetization of the pinned layer points in the positive z-direction, p = +e z . The magnetization dynamics in the free layer is described by the LLG equation, where γ and α are the gyromagnetic ratio and Gilbert damping constant, respectively. The magnetic field consists of an applied field H appl and demagnetization field along the z-direction. Throughout this letter, the magnetic field is considered to poin...

Spin torque oscillator for microwave assisted magnetization reversal

“…Therefore, the threshold current for a positive current is given by min[j th− , j c ], whereas that for a negative current is j th+ . A similar result is obtained for a different system 22 . We also introduce another characteristic current necessary to move the magnetization parallel to the z direction given by…”

An analytical computation of magnetic field generated from a cylinder ferromagnet

“…A potential structure of a spin torque oscillator for MAMR is a ferromagnetic multilayer consisting of an in-plane magnetized free layer and a perpendicularly magnetized pinned layer [21,59,60,61,62,63,64,65], which is schematically shown in Fig. 4(a).…”

“…where η, J, and d are the spin polarization, electric current density, and thickness of the free layer, respectively, whereas and e = |e| are the reduced Planck constant and elementary charge, respectively. The spin torque asymmetry [65] is neglected, for simplicity. The spin transfer torque by a positive (negative) current moves the magnetization to the negative (positive) z direction.…”

Out-of-Plane Auto-Oscillation in Spin Hall Oscillator With Additional Polarizer

“…In other words, p should be tilted in the yz plane to maximize the efficiency of the spin injection having the finite z-component of the spin polarization. This is an important difference from GMR or MTJ, where the ycomponent of the polarizer is unnecessary to excite an out-ofplane auto-oscillation [23][24][25][26][27][28][29][30][31][32]. We note that the tilted magnetic anisotropy has been investigated by making use of a higherorder anisotropy or an interlayer exchange coupling between two ferromagnets [34,35].…”

“…Due to the restriction, the spin Hall effect, for example, cannot excite an out-of-plane autooscillation of a magnetization in a ferromagnet in the absence of an external magnetic field [16], which is a problematic issue in current magnetics. This is a disadvantage of the spin Hall geometry to giant magnetoresistive (GMR) system and magnetic tunnel junctions (MTJs), where the torque direction can be changed by controlling the magnetization direction in the pinned layer [17][18][19][20][21][22], and the out-of-plane auto-oscillation of the in-plane magnetized system has already been reported both experimentally and theoretically [23][24][25][26][27][28][29][30][31][32].…”