Thermal activation barriers for creation and annihilation of magnetic droplet solitons in the presence of spin transfer torque

Abstract

Droplet solitons are magnetization fluctuations that preserve their shape as they precess with uniform frequency ω=0. They satisfy a delicate balance between anisotropy and exchange interactions, and decay in the presence of dissipation. To prevent this, a spin polarized current σ can be applied via a nanocontact of radius ρ*. The magnitude of the current can be increased to induce switching between uniform precession at the ferromagnetic resonance frequency (ω=1), and a stable precession at a frequency larger than the Zeeman frequency (ω=0, in zero applied field). In the absence of dissipation, conservative solitons of frequency ω0 are described by a function Θ(ρ;ω0), where Θ is the angle of the magnetization with the easy axis and ρ is the distance to the center of the nanocontact1. We introduce an effective energy ξ that quantifies the work done (against damping and spin torque) to create a fluctuation of arbitrary shape Θ(ρ). We show that, for specific values of σ, some conservative soliton solutions are saddles of ξ. This allows us to calculate activation barriers Δξ between uniform precession at the ferromagnetic resonance and stable solitons. We present results of Δξ as a function of σ for a variety of nanocontact radii ρ* and spin-torque anisotropy parameters ν. We present micromagnetic simulations with a modified Spin-Transfer-Torque extension in OOMMF which uses the effective energy ξ introduced here. In this way, the difference of energies between transition states and metastable configurations can be used to estimate annihilation rates of droplet solitons.