Macrospin description of the perpendicular polarizer-planar free-layer spin-torque oscillator

Ebels, U.; Houssameddine, D.; Firastrau, I.; Gusakova, D.; Thirion, C.; Diény, B.; Buda-Prejbeanu, L. D.

doi:10.1103/physrevb.78.024436

Cited by 86 publications

(80 citation statements)

References 53 publications

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“…Positive current corresponds to electron flow from the free to the pinned layer. The values of the parameters Note that the parameter λ has often been assumed to be zero in previous works [9][10][11]13,17 , including our recent work 16 , for simplicity. However, this parameter plays a key role, as described in the following discussion.…”

Section: Pacs Numbersmentioning

confidence: 99%

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Crossover between fast and slow excitation of magnetization by spin torque

Taniguchi¹

2016

Appl. Phys. Express

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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...

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Section: Pacs Numbersmentioning

confidence: 99%

“…torque-induced magnetization dynamics, is called linear analysis of the LLG equation 9,17,21 . In this approach, the spin torque is assumed to cancel the damping torque when the current magnitude equals that of the threshold current.…”

Section: Pacs Numbersmentioning

confidence: 99%

Crossover between fast and slow excitation of magnetization by spin torque

Taniguchi¹

2016

Appl. Phys. Express

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“…In particular, a spin-torque oscillator consisting of an in-plane magnetized free layer and a perpendicularly magnetized pinned layer has been an attractive research subject in the field of magnetism. [11][12][13][14][15][16][17][18][19][20][21]. In this type of spin-torque oscillator, the spin torque forces the magnetization of the free layer into out of plane, and excites a large amplitude oscillation around the perpendicular axis.…”

Section: Introductionmentioning

confidence: 99%

“…In order to observe the oscillation experimentally through magnetoresistance effect, however, the symmetry breaking should occur since the change of the relative angle between the magnetizations of the free and pinned layers in time is necessary. The linear analysis in the presence of an in-plane anisotropy [16] or the perturbation approach to the system additionally having an in-plane magnetized reference layer [19] have been made to develop practical theory.…”

Section: Introductionmentioning

confidence: 99%

Instability analysis of spin-torque oscillator with an in-plane magnetized free layer and a perpendicularly magnetized pinned layer

Taniguchi

2016

Phys. Rev. B

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We study the theoretical conditions to excite a stable self-oscillation in a spin-torque oscillator with an in-plane magnetized free layer and a perpendicularly magnetized pinned layer in the presence of magnetic field pointing in an arbitrary direction. The linearized Landau-Lifshitz-Gilbert (LLG) equation is found to be inapplicable to evaluate the threshold between the stable and self-oscillation states because the critical current density estimated from the linearized equation is considerably larger than that found in the numerical simulation. We derive a theoretical formula of the threshold current density by focusing on the energy gain of the magnetization from the spin torque during a time shorter than a precession period. A good agreement between the derived formula and the numerical simulation is obtained. The condition to stabilize the out-of-plane self-oscillation above the threshold is also discussed.

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“…A spin-torque oscillator (STO) [1][2][3][4][5][6] with an in-plane (IP) magnetized free layer and an out-ofplane (OP) magnetized polarizer [7][8][9][10][11][12][13][14][15] has been attracting a great deal of attention as microwave field generators 12,[16][17][18][19][20] and high-speed field sensors. [21][22][23][24][25][26] The schematic of the STO is illustrated in Fig.…”

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confidence: 99%

Critical current density of a spin-torque oscillator with an in-plane magnetized free layer and an out-of-plane magnetized polarizer

Matsumoto

Imamura

2016

AIP Advances

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Spin-torque induced magnetization dynamics in a spin-torque oscillator with an inplane (IP) magnetized free layer and an out-of-plane (OP) magnetized polarizer under IP shape-anisotropy field (H k ) and applied IP magnetic field (H a ) was theoretically studied based on the macrospin model. The rigorous analytical expression of the critical current density (J c1 ) for the OP precession was obtained. The obtained expression successfully reproduces the experimentally obtained H a -dependence of J c1 reported in [D. Houssameddine et al., Nat. Mater. 6, 447 (2007)].

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Macrospin description of the perpendicular polarizer-planar free-layer spin-torque oscillator

Cited by 86 publications

References 53 publications

Crossover between fast and slow excitation of magnetization by spin torque

Crossover between fast and slow excitation of magnetization by spin torque

Instability analysis of spin-torque oscillator with an in-plane magnetized free layer and a perpendicularly magnetized pinned layer

Critical current density of a spin-torque oscillator with an in-plane magnetized free layer and an out-of-plane magnetized polarizer

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