Abstract
We study the theoretical conditions to excite a stable self-oscillation in a spin-torque oscillator with an in-plane magnetized free layer and a perpendicularly magnetized pinned layer in the presence of magnetic field pointing in an arbitrary direction. The linearized Landau-Lifshitz-Gilbert (LLG) equation is found to be inapplicable to evaluate the threshold between the stable and self-oscillation states because the critical current density estimated from the linearized equation is considerably larger than that found in the numerical simulation. We derive a theoretical formula of the threshold current density by focusing on the energy gain of the magnetization from the spin torque during a time shorter than a precession period. A good agreement between the derived formula and the numerical simulation is obtained. The condition to stabilize the out-of-plane self-oscillation above the threshold is also discussed.
- Received 29 February 2016
- Revised 7 April 2016
DOI:https://doi.org/10.1103/PhysRevB.93.174401
©2016 American Physical Society