Impact of Device Variability and Circuit Phase Shift in Synchronized Spin Torque Oscillators
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0998-J02-06
Impact of Device Variability and Circuit Phase Shift in Synchronized Spin Torque Oscillators Johan Persson, Yan Zhou, and Johan Akerman Microelectronics and Applied Physics, Information and Communication Technology, Electrum 229, Stockholm, 16440, Sweden
ABSTRACT Current-induced magnetization dynamics in a system composed of two electrically coupled spin torque oscillators (STOs) is examined. The dynamics of the STOs is modeled by the LandauñLifshitzñGilbert equations modified with a Slonczewski spin-transfer torque term. To study the impact of realistic process variations on STO synchronization we let the two STOs have different in-plane anisotropy fields (Hk). The simulation also provides for a time delay τ. We construct a phase diagram of the STO synchronization as a function of Hk and direct current (Idc) at different τ. The phase diagram turns out to be quite rich with different types of synchronized precession modes. While the synchronized state is originally very sensitive to STO process variations and can only sustain up to 4% Hk variation, the addition of a small time delay dramatically improves its robustness and allows as much as 145% Hk variation in the entire out-of-plane precession regime. It is also shown that the two STOs can not only be locked in frequency, but also in phase at a given τ and the phase difference between the two STOs can be tuned by varying the dc current.
INTRODUCTION The investigations of current-induced magnetization excitation in magnetic nanopillars have received tremendous attention since the spin-transfer phenomenon was predicted in the original theoretical studies of Berger and Slonczewski in late 1990s [1-3]. It has first been shown that a spin-polarized direct current through a ferromagnetic layer will exert a torque on the magnetic moment and can flip its direction when the spin polarized current exceeds a certain critical value [3]. Several theoretical models have been developed to describe physical mechanisms of the spin transfer and current-driven switching phenomena [4]. Apart from this, spin-polarized current induced magnetic switching has already been experimentally demonstrated in recent years [5-7]. The spin transfer device can reduce the write current and the size of magnetic random access memory (MRAM) and hence may enable the implementation of high-density, low-power MRAM [8]. More recently, it has been experimentally demonstrated that, under certain conditions of applied field and current density, a spin-polarized dc current can cause a transition to steady precessional modes with typical frequencies in the GHz range [9ñ11]. This phenomenon is of great importance from the point of view of possible applications in microwave generation [12]. However, the microwave power emitted
from a single spin torque oscillator (STO) is at present typically less than a millionth of a milliwatt [13,14]. To increase the output to a useful level of the order of micro- or milliwatts, a device could consist of an array of phase coherent STOs. Kaka et al. [13] and M
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