Spin Torque Oscillators with Thermal Noise: A Constant Energy Orbit Approach

TL;DR

This paper models the dynamics of biaxial macrospins under thermal noise and spin transfer torque, identifying conditions for stable precession states and testing macrospin assumptions in spin-torque oscillators.

Contribution

It introduces an energy averaging approach to analyze tilt effects on macrospin dynamics and predicts stable precession states, advancing understanding of spin-torque oscillator behavior.

Findings

Stable out-of-plane precession states identified.

Conditions for stability derived and testable experimentally.

Macrospin model applicability assessed with internal magnetic degrees of freedom.

Abstract

We consider a biaxial macrospin with an easy and hard axis, and study its dynamical evolution under the combined effects of thermal noise and spin transfer torque. The spin-torque is associated with both a perpendicularly magnetized polarizer and an in-plane magnetized reference layer, leading to an effective tilt between the easy and spin polarization axes. Using techniques based on energy averaging over the relevant dynamical trajectories, we analyze the effects of tilt on the dynamics and derive the conditions for the occurrence of stable out-of-plane precessionary states. The presence of these states and their predicted stability boundaries can be tested in experiments on orthogonal spin-transfer devices, and may also serve as a test of the applicability of the macrospin model to real devices, which have internal magnetic degrees of freedom.