Synchronization and chaos in spin torque oscillator with two free layers

The magnetization dynamics in a spin torque oscillator (STO) consisting of two in-plane magnetized free layers is studied by solving the Landau-Lifshitz-Gilbert equation and evaluating the Lyapunov exponent numerically. The phase diagrams of the oscillation frequencies of the magnetizations and magnetoresistance and the maximum Lyapunov exponent are obtained from the numerical simulations. The phase synchronization is found in the low current region, whereas the magnetizations oscillate with different frequencies in the middle current region. On the other hand, positive Lyapunov exponents found in the high current region indicate the existence of chaos in the STO.