Scaling effect of spin-torque nano-oscillators

The areal density of commercial hard disk drives (HDD) is increasing rapidly, which requires the development of new HDD read sensor. For nanoscale magnetic recording sensing, a novel spin-torque oscillator (STO)-based read head sensor has been proposed as a promising candidate.^1–3 When a spin-polarized current is injected into a magnetic layer, depending on the direction and intensity of the charge, the local magnetization is switched to the opposite direction or is driven into a permanent precession along the effective field. The precession frequency is tunable by the external magnetic field or applied current. The STO-based read head sensor senses the presence of an external magnetic field by detecting the variation of the precession frequency. Compared to the conventional magnetoresistive (MR) read head, which is functioning based on the giant magnetoresistive (GMR) effect or tunneling magnetoresistance (TMR) effect, the STO read head has two key benefits, including the signal-to-noise ratio (SNR)¹ and data-transfer rate.³ Calculations have shown that high SNRs can be obtained in devices smaller than 30 × 30 nm² by using a delay detection method.¹ For conventional MR sensors, the data-transfer rate is limited by the ferromagnetic energy relaxation rate, since the bias field is applied along the hard-axis of the free layer. For STO-based magnetic field sensors, the bias field is along the easy-axis. Numerical simulations have demonstrated that the data-transfer rate can be above 5 Gbit/s.³ 

As the STO device is scaled down to smaller than 40 nm, the linewidth of the output signal increases because of large phase noise induced by thermal effects. Therefore, understanding the magnetization dynamics and the relation between the linewidth and device size is crucial. When the STO dimension is shrunk to less than 30 nm, the linewidth is estimated to be around 200 MHz.² Micromagnetic simulations demonstrated that, for STOs smaller than 40 nm, reducing the device size lowers the oscillation-onset voltage. Furthermore, the stable oscillation region of the free layer is reduced due to the expansion of the unstable oscillation region of the reference layer in the oscillation phase diagram.⁴ In their paper, however, the authors did not mention the linewidth variation as the device dimension decreased. The linewidth and signal-to-noise ratio of a linear oscillator have been calculated analytically as a function of the device size with the approximation that the oscillation is far beyond the oscillation threshold.¹ The result shows that the linewidth increases from about 2 to 20 MHz as the device size is reduced from 100 to 20 nm. In this work, we report the numerical simulation results of the frequency, linewidth, and the corresponding magnetization dynamics of the STO as the size is decreased from 40 to 10 nm. In our simulations, we only consider free layer oscillations, while neglecting the impact of the reference layer.

The simulations are performed by the Object Oriented MicroMagnetic Framework (OOMMF).⁵ It is based on the Landau-Lifshitz-Gilbert (LLG) equation with a spin-transfer torque term.^6,7 Thermal effects are considered in the simulation at T = 300 K. Cuboids with dimensions of 40 × 40 × 2, 20 × 20 × 2, and 10 × 10 × 2 nm³, which are defined as devices A, B, and C, respectively, are modeled as the free layer. For devices A and B, a mesh size of 2 × 2 × 1 nm³ is used. For device C, the mesh size is set to 1 × 1 × 1 nm³ due to the small device size. For simulation, a damping constant α = 0.015, a saturation magnetization M_s = 1074 emu/cm³, an exchange stiffness constant A = 1.8 × 10⁻⁶ erg/cm, and a crystalline anisotropy constant K = 2 × 10⁴ erg/cm³ are applied. Simulation parameters are chosen to match our experimental results at larger device size. To mimic the frequency difference between the binary states 0 and 1, we assume that the magnetic fields from the recording media of states 0 and 1 are ±500 Oe. To avoid magnetization switching at ±500 Oe, an in-plane bias magnetic field of 700 Oe is applied. Therefore, the total external fields of states 0 and 1 are 1200 Oe and 200 Oe, respectively.

To identify the precession frequency at states 0 and 1 and increase the signal-to-noise ratio, it is necessary to find out the oscillation spectra with the minimum linewidth. Fig. 1 shows the frequency and corresponding linewidth variation of devices A, B, and C with increasing current density. Since the energy barrier is proportional to the free layer volume and the anisotropy E_b = V × H_K, the thermal effect plays a major role in small devices due to their low energy barriers. As can be seen from Fig. 1, the overall linewidth of small devices is larger than that of large devices. Moreover, the frequency and linewidth results become noisier as the device size is shrunk. For device A, the frequency variation can be divided into two parts. When the current density is below 5.5 × 10⁸ A/m², the frequency variation is tiny. This is due to the fact that the magnetization is undergoing small angle oscillations, for which the thermally excited ferromagnetic resonance noise is dominant, and the frequency is expected to remain constant. Above 5.5 × 10⁸ A/m², the steep frequency drop is characteristic of in-plane magnetization oscillation, which is induced by an increase of the precession cone angle. The two regions of frequency variation correspond to different linewidth trends. At low current density, we observe a linewidth reduction down to 0.7 GHz, which is due to the compensation of the damping torque by the spin transfer torque. At high current density, the linewidth starts to increase with increasing current density due to the nonlinearity of the STO. In this case, a small fluctuation in amplitude can contribute to the phase noise. The frequency and linewidth behaviors of device A are in good qualitative agreement with those of STOs that are about 100 nm.⁸ 

For devices smaller than 40 nm, the frequency and linewidth variations are different. Unlike device A, the frequency reduction of device B is uniform over the whole current region, and we observe no obvious boundary. The linewidth remains almost constant at low current density. For device C, both frequency and linewidth are flat with some large fluctuations. A possible reason is that as the device size is smaller, the magnetization precession becomes unstable due to large thermal fluctuations. Besides the different frequency and linewidth trends, the threshold current density also decreases as the size is shrunk. From a linear extrapolation of the linewidth at zero current, we obtain threshold current densities for devices A, B, and C of 5.34 × 10¹⁰ A/m², 4 × 10¹⁰ A/m², and 6.27 × 10⁹ A/m², respectively. They are smaller than the normal threshold current density of a 100-nm-sized STO, which is usually on the order of 10¹¹ A/m². Our simulation results agree qualitatively with previous results.⁴ It implies that the spin-transfer torque (STT) effect is large in small devices even if the STT amplitude for each unit area is the same. The only difference is that even without the effect of the reference layer, the decreasing size of the free layer still leads to magnetization instability due to the energy barrier effect.

Since the linewidth increases with decreasing device size, it is important to find out whether small STOs can work for magnetic read sensors. Fig. 2 shows the power spectral density of devices A, B, and C at the magnetic fields of 200 and 1200 Oe, which represent the media field of state 1 and 0. The current density is set at the point which the minimum linewidth is obtained above the threshold current. For devices A and B, the frequency at 200 and 1200 Oe can be distinguished due to the relatively small linewidth. However, for device C, the power spectra are overlapped at the peak edge due to the large thermal noise and small energy barrier. This study suggests that small STOs with sizes down to 20 nm may apply to the hard disk drive.

To understand the magnetization dynamics in detail, we plot the corresponding magnetization vector trajectories for devices A, B, and C at external fields of 200 and 1200 Oe applied along the x-axis. In Fig. 3(a), the magnetization vector of device A spins around the external field. At the field of 200 Oe, the damping torque is relatively small. Due to the shape anisotropy, the magnetization vector trajectory is in “clam-shell” shape with some tiny fluctuations. As the device size is decreased to 20 nm, the fluctuations become larger as shown in Fig. 2(b). The magnetization vector trajectory turns from the stable oscillation state to the unstable state. In Fig. 3(c), as the device size continues decreasing to 10 nm, the magnetization vector trajectory is noisier and even has visible distortion from the “clam-shell” shape. The unstable oscillation state is not only reflected in the fluctuations along the z-axis, but also in the asymmetric trajectories along the field direction. At the magnetic field of 1200 Oe, the magnetization precession of device A is less affected by thermal noise. As shown in Fig. 3(d), the magnetization spins around the field direction smoothly. On the contrary, devices B and C are in stable oscillation with small fluctuations. The magnetization dynamics result also agrees with the linewidth data shown in Fig. 2, where the linewidth of device B and C is still larger than 1 GHz at 1200 Oe.

In conclusion, the frequency, linewidth, and oscillation behavior of STOs with the device size from 40 to 10 nm have been investigated by micromagnetic simulations. Reducing the device size induces unstable oscillation behavior, which is revealed in the linewidth variation and magnetization vector trajectories. Our results show possible applications of 20-nm-square STOs for magnetic read sensors.

This work was supported by Seagate Technology. We acknowledge Dr. Wonjoon Jung, Dr. Jae-Young Yi, Dr. Eric W. Singleton, and Dr. Mark Kief for useful discussions and suggestions.