Magnetization uniformity and threshold current of out-of-plane precession in spin-torque oscillator with synthetic ferrimagnet free layer under perpendicular magnetic field: Micromagnetic simulation study

A spin-torque oscillator (STO) is a microwave oscillator based on a magnetoresistive (MR) element [1], [2], and has been investigated for applications such as information storages, communications, and computing units. For these applications, large output signal and stable oscillation are necessary. So far, it has been reported that the large output signal can be obtained by out-of-plane precession (OPP) of free layer in an STO based on a magnetic tunnel junction (MTJ) and having an in-plane pinned layer [3]–[6]. This is because in OPP change of angle between the magnetizations of free and pinned layers is large and the relative angle change is converted into the output signal through the large MR effect of the MTJ. To further improve the output power and the stability of the OPP, we have recently fabricated an STO based on an in-plane MTJ with a synthetic ferrimagnet (SyF) free layer (SyF-STO). We have chosen the SyF free layer because improvement of the output power and the stability has been reported for in-plane oscillation [7]–[9]. We have investigated whether the OPP is possible in the SyF-STO. As a result, by the OPP of the free layer we have obtained large output power of the order of $1 \mu \mathrm {W}$ in perpendicular field [10]. (In Ref. [10] we reported the maximum output power of $3.7 \mu \mathrm {W}$. This value includes an error in estimation, and the correct value is $0.93 \mu \mathrm {W}$.) In this study, to clarify the reason for the large output power obtained in the SyF-STO, we compare the SyF-STO with an STO with a single free layer (SFL-STO) by micromagnetic simulation. Figure 1 shows schematics of these STOs. The SyF-STO has two free layers which are antiferromagnetically coupled (AFC) by the interlayer coupling. The pinned layers are also AFC. An external field $H_{z}$ and a current $I$ are applied in the perpendicular direction. The spin-transfer torque acts on the free layer 2 and the pinned layer 1. To the bottom pinned layer, a $- x -$direction magnetic field is applied, modeling an exchange bias field. In the simulation, we use the parameters corresponding to the sample in the experiment. The parameters for the SFL-STO are the same as the SyF-STO except that the SFL-STO has a single free layer. Figure 2(a) shows oscillation powers of each STO as a function of $H_{z}$ for $I=8.5$ mA, which are obtained from the $y -$components of the spatially-averaged magnetizations. The oscillation power is estimated by time average of square of the $y -$component of normalized magnetization. For $H_{z}\ge 5$ kOe, both STOs exhibit the large oscillation powers due to the OPP. In the SyF-STO, the magnetizations of the two free layers are synchronized and their in-plane components are in opposite directions. The oscillation power is larger for the SyF-STO. In the parameter range of the OPP, the oscillation frequencies of both STOs show essentially the same dependence on $H_{z}$, that is, the oscillation frequencies increase, showing a step. By investigating the waveforms of the magnetizations, we find that this step originates from coupled magnetization oscillation of the free and pinned layers due to magnetic dipolar field and the spintransfer torque. This dependence of the oscillation freqeuncy on $H_{z}$ well reproduces that observed in the experiment [10]. Such steps of oscillation frequency have been reported for SFL-STOs with OPP [1], [7], [11]. To clarify the reason of the difference of the oscillation power, we compare amplitudes of the spatially-averaged magnetizations of the free layers. Figure 2(b) shows time averages of the amplitudes. Since the magnetization is normalized, the amplitude is closer to 1 when the magnetization is spatially uniform. It is found that the amplitude for the SyF-STO is kept near 0.9 for the OPP, while that for the SFL-STO decreases to about 0.75 at around $H_{z}=5$ kOe. This difference means that the free layer magnetization of the SyF-STO is uniform compared with the SFL-STO. Inset in Fig. 2(b) shows magnetization configurations of the free layers of the SyF- and SFL- STOs for $H_{z}=5$ kOe. The $y -$component is shown by the color scale at a moment when the in-plane components of the spatially-averaged magnetizations are in the $x -$direction. In the SyF-STO, although local fluctuations can be seen, their magnitudes are relatively small. On the other hand, in the SFL-STO, the free layer is divided into two regions in which the in-plane components of the magnetizations are almost in opposite directions. This non-uniform magnetization pattern reduces stray field outside the free layer, and stabilizes magnetic field distribution. From this result we think that the almost uniform magnetization precession in the SyF-STO is because the SyF free layer reduces the stray field and thus the magnetic field distribution can be stabilized even by the uniform magnetizations. The uniform OPP of free layer magnetizations leads to the larger output power, which is a possible explanation for the large output power observed in the experiment [10]. Finally, in Fig. 2(c) we compare threshold current for the OPP, and find that the threshold current is smaller for the SyF free layer. It can be thought that this lower threshold current enables the OPP by a bias voltage lower than a voltage at which the dielectric breakdown of the MTJ occurs.