Instability analysis of spin torque oscillator with an in-plane magnetized free layer and a perpendicularly magnetized pinned layer

TL;DR

This paper develops a theoretical formula to determine the threshold current density for stable self-oscillation in a specific spin torque oscillator configuration, addressing limitations of linearized equations.

Contribution

It introduces a new energy-based theoretical approach to accurately predict the threshold current, improving upon the linearized Landau-Lifshitz-Gilbert equation.

Findings

Derived a formula matching numerical simulations

Identified limitations of linearized LLG equation

Discussed conditions for out-of-plane self-oscillation stability

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.