Magnetization switching by microwaves synchronized in the vicinity of precession frequency

Abstract

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...

Magnetization switching by current and microwaves

“…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.…”

Three-dimensional magnetic recording using ferromagnetic resonance

“…46) Different from MAS discussed in Sect. 3, it does not require a dc magnetic field, and the rotation direction of the microwave field plays a key role in determining the final state.…”

Magnetization switching by microwaves initially rotating in opposite direction to precession

“…This model originated from the recent observation of magnetization switching solely by microwaves in micromagnetic simulation, 25) as well as the experimental observation of the synchronization between the target ferromagnet and an STO. 16) As pointed out in Ref., 24) the term proportional to (dm z /dt)t in Eq. (8) characterizing the difference between the precession frequency and the microwave frequency is also necessary for switching.…”

“…23) We recently proposed another type of resonant switching, in which the microwave frequency is always slightly different from the precession frequency. 24) Macrospin and/or micromagnetic simulations confirmed switching of the magnetization by microwaves with a time-dependent frequency. [20][21][22][23][24][25] These works, however, assume that the microwaves always rotate in the same direction as those of the magnetization precession.…”

“…16) Several theoretical models have been proposed to show magnetization switching by microwaves with a timedependent frequency. [20][21][22][23][24] The previous theories are based on a resonant switching model, 20) the variation method, 21,22) and the autoresonance model. 23) We recently proposed another type of resonant switching, in which the microwave frequency is always slightly different from the precession frequency.…”