Perturbation theory for propagating magnetic droplet solitons

Abstract

Droplet solitons are strongly nonlinear, inherently dynamic structures in the magnetization of ferromagnets, balancing dispersion (exchange energy) with focusing nonlinearity (strong perpendicular anisotropy). Large droplet solitons have the approximate form of a circular domain wall sustained by precession and, in contrast to single magnetic vortices, are predicted to propagate in an extended, homogeneous magnetic medium. In this work, multiscale perturbation theory is used to develop an analytical framework for investigating the impact of additional physical effects on the behaviour of a propagating droplet. After first developing soliton perturbation theory in the general context of Hamiltonian systems, a number of physical phenomena of current interest are investigated. These include droplet-droplet and droplet-boundary interactions, spatial magnetic field inhomogeneities, spin transfer torque induced forcing in a nanocontact device and damping. Their combined effects demonstrate the fundamental mechanisms for a previously observed droplet drift instability and under what conditions a slowly propagating droplet can be supported by the nanocontact, important considerations for applications. This framework emphasizes the particle-like dynamics of the droplet, providing analytically tractable and practical predictions for modern experimental configurations.

Chiral excitations of magnetic droplet solitons driven by their own inertia

“…For example, magnetic solitons exhibit inertial effects associated with their ability to store energy, for example by shape deformation [14][15]. In this picture, magnetic solitons can be treated as particles with an effective mass [3,14,[16][17][18], although direct control of their inertial effects and realizing massless soliton motions is a key element of success in this field [18,19].…”

“…Droplets are unique as they are inherently dynamical solitons. Due to their dynamical features and internal degrees of freedom, droplets can be considered dynamical particles carrying an effective mass [16,23], which they gain from the applied STT. This means that, in the absence of the STT, they lose their effective mass and dissipate.…”

Propagating Magnetic Droplet Solitons as Moveable Nanoscale Spin-Wave Sources with Tunable Direction of Emission

“…The motion of a dynamic particle-like droplet can also transform the energy stored in the precessional motion into the effective kinetic energy of the translational motion [36][37][38]. Similar to Newton's law ݀ܺ ሬሬሬሬሬ⃗ ‫ݐ݀/‬ = ܸ ሬ⃗ , the droplet continues to move with a constant velocity due to its inertia.…”

“…In addition, as its size decreases throughout the propagation, its velocity increases. Indeed, damping reduces the effective mass of the droplet rapidly by losing energy and, consequently, accelerates very quickly [36,38,47]. Finally, the droplet annihilates by exciting a SW burst.…”

Effect of Temperature on Magnetic Solitons Induced by Spin-Transfer Torque

“…Droplets have been experimentally created using the STT effect in nanocontacts to PMA films [17][18][19][20][21][22][23], and droplets are a particular case of STToscillators. Recently reported experiments have shown that the stability of these collective excitations is limited by the appearance of drift instabilities, which were attributed to the disorderlocal variations of the effective magnetic field [21,24]. Wills et al [25] identified theoretically an intrinsic deterministic linear instability and thermal fluctuations as additional instability mechanisms.…”