Capacitance effect on the oscillation and switching characteristics of spin torque oscillators
© Zeng et al.; licensee Springer. 2014
Received: 2 July 2014
Accepted: 7 October 2014
Published: 3 November 2014
We have studied the capacitance effect on the oscillation characteristics and the switching characteristics of the spin torque oscillators (STOs). We found that when the external field is applied, the STO oscillation frequency exhibits various dependences on the capacitance for injected current ranging from 8 to 20 mA. The switching characteristic is featured with the emerging of the canted region; the canted region increases with the capacitance. When the external field is absent, the STO free-layer switching time exhibits different dependences on the capacitance for different injected current. These results help to establish the foundation for capacitance-involved STO modeling.
KeywordsCapacitance effect Oscillation frequency Canted region Switching time
The conventional way of changing the magnetization of a thin film is usually realized through applying an external magnetic field. In recent years, it has been found both theoretically [1–3] and experimentally [4, 5] that a spin-polarized current which carries more spin up or spin down electrons can also change the magnetization when passing through the thin film. This effect helps to generate steady precession of the free-layer magnetization in a spin valve structure by an injected spin-polarized current, which results in a periodic variation of the device resistance and forms spin-torque oscillators (STOs) [6–12]. The advantages of the STO are its capability of generating microwave with ultra-wide bandwidth (from 100 MHz to 60 GHz) and its easy modulation at very high frequency. Its potential application as microwave generator has received unprecedented attention. Among the many unrevealed problems remained in the STO area, much research effort focuses on the STO authentic modeling. However, the capacitance effect is not considered at all in most previous studies [13–15]. Capacitance effect [13–15] being introduced by intrinsic sources (parasitic capacitance due to the interaction between the multilayer thin films in STOs) and extrinsic sources (lead capacitance due to the connection between the external IC and STOs) is inevitable during the preparation process of spin-torque oscillators (typically GMR multilayers). Therefore, in order to accurately reflect the characteristics of prepared spin-torque oscillator devices, it is highly essential to explore the capacitance effect on oscillation characteristics and switching characteristics. Meanwhile, this research not only helps to establish the foundation for capacitance-involved STO modeling but also helps to reveal the origin of capacitance effect in nanodevices. Since our findings could be applied in the modeling of authentic STO, which is highly beneficial for supporting and guiding the fabrication process in nanotechnology and nanoscience industry.
In this paper, a circuit model where a capacitor connected in parallel with a STO is proposed. The marcospin model is adopted to explore how the magnetodynamics of the STO is influenced by the capacitor. The oscillation characteristics and the switching characteristics are both fully studied.
where μ0 is the magnetic vacuum permeability, η is the spin transfer efficiency, M S is the free-layer saturation magnetization, and Vf is the volume of the free layer. In this study, the free layer is composed of a typical CoFeB thin film with a circular shape with a dimension of 250 nm and thickness of 3 nm. The b J term in metallic spin valve structures is small. We define |β| = 10% in this study. Other parameter values are presented as follows : |γ| = 1.86 × 1011 Hz/T, η = 0.35, M S = 1,270 kA/m, α = 0.008, Happ =0.05 T, H d = 4πMs = 1.27 T, H k = 0.02 T, R P = 15.8 Ω, R AP = 23.4 Ω, and e = 1.6021764e-19.
The magnetic dynamics can then be numerically solved using (1) and (7).
where Htheta and Hphi stand for the effective field in a spherical coordinate system, Istheta and Isphi stand for the current injected into the STO in a spherical coordinate system.
where Iamper stands for the total current injected into the STO and the capacitor, Cap stands for the value of capacitance. By solving Equations (8), (9), and (10) using runge-kutta method , the time-varying θ, and Iamper are identified, where the magnetic dynamics are then obtained.
Results and discussion
A. Oscillation characteristics with external field
B. Switching characteristics with external field
C. Switching characteristics without external field
where a J (c) represents the in-plane spin torque components with capacitance considered and acrit(c) represents the critical spin torque which intrigues the switching with capacitance considered. The reason the STO exhibits different dependences on the capacitance for different injected current is because when Idc is relatively small (7 mA), the switching time is very slow since the in-plane spin torque component a J (c) (500 Oe in this case) has just exceed the value of the critical spin torque which intrigues the switching with capacitance considered acrit(c) (450 Oe in this case). However, when Idc is relatively large (30 mA), the switching time is very fast since the in-plane spin torque component a J (c) has increased to level of 10,000 Oe, which far exceed acrit(c). Thus the switching time in Figure 7b is much smaller than the switching time in Figure 7a. On the other hand, when Idc is relatively small (7 mA), the influence of capacitance on a J (c) is smaller than the influence of capacitance on acrit(c). When Idc is relatively large (30 mA), the influence of capacitance on a J (c) is larger than the influence of capacitance on acrit(c). When Idc is relatively small (7 mA), the switching time is mainly determined by acrit(c). However, the acrit(c) value is negatively correlated with the capacitance (calculation not presented here). Thus, for capacitance in the range of 0.01 to 1 pF, the acrit(c) value gradually decreases. For capacitance in the range of 1 to 100 pF, the acrit(c) value gradually increases. This explains the switching time tendency in Figure 7a. When Idc is relatively large (30 mA), the switching time is mainly determined by a J (c). Since the a J (c) is very large and not influenced by the capacitance, the switching time only changes slightly (7.7%) as the capacitance increases.
In summary, we have shown that with the external field applied, the STO oscillation frequency demonstrates a general negative correlation with the capacitance for injected current ranges from 8 to 12 mA while a general positive correlation with capacitance for injected current 20 mA. Canted regions are revealed for injected current higher than critical value. The free-layer magnetization switches from parallel state to canted state instead of from parallel state to anti-parallel state. When the external field is absent, the STO free-layer magnetization switching time exhibits two stages of variation with the capacitance for both small injected current value (7 mA) and large injected current value (30 mA). However, the variation trends are opposite for small injected current value (decrease in first stage and increase in second stage) and large injected current value (increase in first stage and decrease in second stage).
This work was supported in part by the Seed Funding Program for Basic Research and Small Project Funding Program from the University of Hong Kong, ITF Tier 3 funding (ITS/104/13), ITF Tier 3 funding (ITS/171/13), RGC-GRF grant (HKU 704911P), and University Grants Committee of Hong Kong (Contract No. AoE/P-04/08).
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