Stochastic ejection of nanocontact droplet solitons via drift instability

Abstract

The magnetic droplet soliton is a large amplitude, coherently precessing wave state that exists in ferromagnetic thin films with perpendicular magnetic anisotropy. To effectively sustain a droplet, magnetic damping can be locally compensated in a nanocontact region that imparts spin-transfer torque; this has been successfully deployed in experiment to directly image the droplet and probe its dynamics electrically. However, theory predicts and experiments indicate the existence of a drift instability whereby the droplet is ejected from the spin-transfer-torque-active region and subsequently decays, an effect that may be enhanced or possibly induced by thermal fluctuations.Using soliton perturbation theory and large deviation theory, this work determines the soliton ejection rate and the most likely path an ejected soliton tracks in the presence of thermal fields.These results lead to an effective lower bound on the stability of magnetic droplet solitons in spintransfer torque nanocontact devices operating at finite temperature and point to ways in which droplets can be made more robust.

Thermal Activation Barriers for Creation and Annihilation of Magnetic Droplet Solitons in the Presence of Spin Transfer Torque

“…In this paper we have studied the thermal stability of magnetic droplet solitons which are linearly stable against the drift instability 25,27 . Taking advantage of the rotational symmetry, we transform the problem to a reference frame that rotates with the droplet soliton, thereby simplifying the problem.…”

“…As noted in the introduction, even in the region of the current/field phase diagram where the droplet soliton is linearly stable to the drift instability, thermal activation over a barrier can still eject the droplet soliton from the nanocontact region. Numerical estimates of this thermally-induced ejection have been provided in 27 , where two mechanisms for thermally activated droplet soliton annihilation were considered: "noiseinduced damping", which corresponds to the droplet soliton decay mechanism considered in this paper, and ejection via drift instability. Because our analysis mostly considers dif-ferent regions of the parameters space from those addressed in 27 , a direct comparison between our results and theirs is not possible at the present time.…”

“…In a subsequent paper, Wills, Iacocca and Hoefer 26 (see also 27 ) found that droplet solitons are linearly unstable at large bias currents, being subject to a drift instability in which the droplet soliton center drifts outside of the nanocontact region. (This had been noticed a year earlier in micromagnetic simulations by Lendinez et al 28 .)…”

“…In recent work, Moore and Hoefer 27 computed decay of magnetic droplet solitons in the linearly stable region through a different mechanism, namely thermally activated ejection of the intact droplet soliton from the nanocontact region. In the region of parameter space in which the droplet soliton is linearly stable against drift, the decay mechanism studied here competes with the ejection mechanism, and which one dominates droplet soliton decay will depend on the experimental parameters.…”

Magnetic Droplet Mode in a Vertical Nanocontact-Based Spin Hall Nano-Oscillator at Oblique Fields

“…4(j-k)] are the largest at small fields, with the largest F W HM of 11 MHz observed at H = 800 Oe. The linewidth broadening at small fields is likely associated with the phase noise due to the inhomogeneous distribution of the ef-fective field (including the local variations of magnetic anisotropy and current-induced Oersted fields) coupled with the droplet drift instabilities [38][39][40][43][44][45]. We now address the thermal effects on the spectral coherence of the generated microwave signals, and their relation to the dynamical mode structure of VNC-SHNO.…”