Nonlinear dynamics of spin transfer nano-oscillators

Abstract

The evolution equation of a ferromagnetic spin system described by Heisenberg nearest-neighbour interaction is given by Landau–Lifshitz–Gilbert (LLG) equation, which is a fascinating nonlinear dynamical system. For a nanomagnetic trilayer structure (spin valve or pillar) an additional torque term due to spin-polarized current has been suggested by Slonczewski, which gives rise to a rich variety of dynamics in the free layer. Under appropriate conditions the spin-polarized current gives a time-varying resistance to the magnetic structure thereby inducing magnetization oscillations of frequency which lies in the microwave region. Such a device is called a spin transfer nanooscillator (STNO). However, this interesting nanoscale level source of microwaves lacks efficiency due to its low emitting power typically of the order of nWs. To overcome this difficulty, one has to consider the collective dynamics of synchronized arrays/networks of STNOs as suggested by Fert and coworkers so that the power can be enhanced N 2 times that of a single STNO. We show that this goal can be achieved by applying a common microwave magnetic field to an array of STNOs. In order to make the system technically more feasible to practical level integration with CMOS circuits, we establish suitable electrical connections between the oscillators. Although the electrical connection makes the system more complex, the applied microwave magnetic field drives the system to synchronization in large regions of parameter space.