Autoresonant switching of the magnetization in single-domain nanoparticles: Two-level theory

Klughertz, Guillaume; Frièdland, L.; Hervieux, Paul-Antoine; Manfredi, Giovanni

doi:10.1103/physrevb.91.104433

Cited by 22 publications

(37 citation statements)

References 36 publications

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“…These conclusions are consistent with Ref. 18) The other approach for switching is to restrict ν to f (E) and neglect the damping. 19) In this case, the magnetization is always in the resonance state.…”

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confidence: 91%

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Magnetization switching by microwaves synchronized in the vicinity of precession frequency

Taniguchi

2015

Appl. Phys. Express

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We propose a theoretical framework of a magnetization switching induced solely by a microwave. The microwave frequency is always close to but slightly different from the oscillation frequency of the magnetization. By efficiently absorbing energy from the microwave, the magnetization climbs up the energy landscape to synchronize the precession with the microwave. We introduced a dimensionless parameter ǫ determining the difference between the microwave frequency and the instant oscillation frequency of the magnetization. We analytically derived the condition of ǫ to switch the magnetization, and confirmed its validity by the comparison with numerical simulations.Microwave-assisted magnetization reversal 1-10) is a fascinating subject in magnetism for practical applications such as high-density recording. An oscillating field generated by microwaves excites a small-amplitude oscillation of the magnetization in the ferromagnet and significantly reduces the switching field to, typically, half of the uniaxial anisotropy field for an optimized microwave frequency. However, zero-field switching has not been reported experimentally; this is an outstanding problem in this field. A proposal of a theoretical possibility for switching induced solely by microwaves, as well as a deep understanding of its physical picture, will be an important guideline for further development in this field.In previous works on microwave-assisted magnetization reversal, 1-10) the microwave source is isolated from the ferromagnet. Recently, however, an alternative system has been investigated both experimentally and numerically 11,12) in which a spin torque oscillator (STO) is used as the microwave source. An oscillating dipole field emitted from the STO acts as microwaves on the ferromagnet and induces switching. Simultaneously, the dipole field from the ferromagnet changes the oscillation angle, as well as the oscillation frequency, in the STO. Therefore, in this situation, the microwave frequency from the STO depends on the magnetization direction in the ferromagnet. This motivated us to investigate the possibility of switching the magnetization solely by microwaves, the frequency of which depends on the magnetization direction itself. The purpose of this letter is to propose a theoretical framework for the switching process. Figure 1 schematically shows the energy landscape of a ferromagnet. The magnetization direction from the stable state is characterized by the energy E. When the magnetization arrives at the position at which the energy is E, the magnetic field excites precession of the magnetization on the constant energy curve with an oscillation frequency f (E). The FMR frequency, f FMR , corresponds to f (E) at the minimum energy state. Let us assume that the microwave frequency ν is close to but slightly different from the instant precession frequency f (E); i.e., ν = f (E) − ∆f with |∆f /f | ≪ 1. Because the instantaneous oscillation frequency f (E) changes with time during the magnetization dynamics, the microwave frequency ν shou...

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confidence: 91%

“…For example, let us consider autoresonance model 18) in which the microwave frequency of this model is ν = f 0 − at with constants f 0 and a. Because ν − f (E) should be negative for switching, as mentioned above, the constant a should be positive.…”

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confidence: 99%

Magnetization switching by microwaves synchronized in the vicinity of precession frequency

Taniguchi

2015

Appl. Phys. Express

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“…In such system, the microwave frequency becomes time dependent because the microwave originates from the dynamic coupling between the free layer and the STO through the dipole interaction. The magnetization dynamics by microwaves having time-dependent frequency is an attractive topic in the field of microwaveassisted magnetization reversal [24,[31][32][33][34][35][36]. For simplicity however, we focus on a constant frequency only in this paper.…”

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confidence: 99%

Magnetization switching by current and microwaves

2016

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We propose a theoretical model of magnetization switching in a ferromagnetic multilayer by both electric current and microwaves. The electric current gives a spin transfer torque on the magnetization, while the microwaves induce a precession of the magnetization around the initial state. Based on numerical simulation of the Landau-Lifshitz-Gilbert (LLG) equation, it is found that the switching current is significantly reduced compared with the switching caused solely by the spin transfer torque when the microwave frequency is in a certain range. We develop a theory of switching from the LLG equation averaged over a constant energy curve. It was found that the switching current should be classified into four regions, depending on the values of the microwave frequency. Based on the analysis, we derive an analytical formula of the optimized frequency minimizing the switching current, which is smaller than the ferromagnetic resonance frequency. We also derive an analytical formula of the minimized switching current. Both the optimized frequency and the minimized switching current decrease with increasing the amplitude of the microwave field. The results will be useful to achieve high thermal stability and low switching current in spin torque systems simultaneously.

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“…Since the autoresonance threshold is a weakly nonlinear phenomenon [20], our next goal is to discuss the slow, weakly nonlinear evolution in the problem and we use Whitham's averaged Lagrangian approach [22] for achieving this goal. This approach is designed to describe wave systems with slow parameters.…”

Section: The Threshold Phenomenonmentioning

confidence: 99%

“…In recent years, autoresonance ideas were also implemented in magnetics. Examples are autoresonant waves in magnetic materials [17,18], the switching of magnetization of single domain point-like nanoparticles [19,20], and most recently the autoresonant excitation of large amplitude standing magnetization waves in long ferromagnetic nanowires by using rotating driving fields with short wavelength spatial modulations [21]. This recent approach required two resonant stages, where in the first stage one excites a rotating, but uniform magnetization of the wire, while later, in the second resonant stage, the system develops a spatially modified standing wave profile.…”

Section: Introductionmentioning

confidence: 99%

Narrow autoresonant magnetization structures in finite-length ferromagnetic nanoparticles

Shagalov

Frièdland

2019

Phys. Rev. E

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The autoresonant approach to excitation and control of large amplitude uniformly precessing magnetization structures in finite length easy axis ferromagnetic nanoparticles is suggested and analyzed within the Landau-Lifshitz-Gilbert model. These structures are excited by using a spatially uniform, oscillating, chirped frequency magnetic field, while the localization is imposed via boundary conditions. The excitation requires the amplitude of the driving oscillations to exceed a threshold. The dissipation effect on the threshold is also discussed. The autoresonant driving effectively compensates the effect of dissipation, but lowers the maximum amplitude of the excited structures. Fully nonlinear localized autoresonant solutions are illustrated in simulations and described via an analog of a quasi-particle in an effective potential. The precession frequency of these solutions is continuously locked to that of the drive, while the spatial magnetization profile approaches the soliton limit when the length of the nanoparticle and the amplitude of the excited solution increase.I.

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Autoresonant switching of the magnetization in single-domain nanoparticles: Two-level theory

Cited by 22 publications

References 36 publications

Magnetization switching by microwaves synchronized in the vicinity of precession frequency

Magnetization switching by microwaves synchronized in the vicinity of precession frequency

Magnetization switching by current and microwaves

Narrow autoresonant magnetization structures in finite-length ferromagnetic nanoparticles

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