Attraction, merger, reflection, and annihilation in magnetic droplet soliton scattering

Abstract

The interaction behavior of solitons are defining characteristics of these nonlinear, coherent structures. Due to recent experimental observations, thin ferromagnetic films offer a promising medium in which to study the scattering properties of two-dimensional magnetic droplet solitons, particlelike, precessing dipoles. Here, a rich set of two-droplet interaction behaviors are classified through micromagnetic simulations. Repulsive and attractive interaction dynamics are generically determined by the relative phase and speeds of the two droplets and can be classified into four types: (1) merger into a breather bound state, (2) counterpropagation trapped along the axis of symmetry, (3) reflection, and (4) violent droplet annihilation into spin wave radiation and a breather. Utilizing a nonlinear method of images, it is demonstrated that these dynamics describe repulsive/attractive scattering of a single droplet off of a magnetic boundary with pinned/free spin boundary conditions, respectively. These results explain the mechanism by which propagating and stationary droplets can be stabilized in a confined ferromagnet.Solitary waves or solitons are particle-like wave packets that arise in a wide range of physical contexts from a balance between dispersive spreading and nonlinear focusing. One of the key phenomena that differentiates nonlinear coherent structures such as solitons from their linear counterparts is what happens when such structures interact. Soliton solutions of equations with very special mathematical structure (integrability) have been shown to interact elastically [1] and can be attractive or repulsive [2]. In more general systems, soliton interactions can be significantly more complex, exhibiting fusion, fission, annihilation, or spiraling [3,4]. A relative phase between the solitons plays a dominant role in determining the resulting interaction behaviors. An additional interaction feature, 90• scattering, has been predicted for twodimensional (2D) magnetic solitons [5,6] and solitons in field theories [7,8]. The recent experimental observation of a magnetic droplet soliton in a spatially extended film [9] provides the impetus for our deeper study of magnetic soliton interactions. Here, we show that the interaction of a pair of 2D magnetic droplet solitons (from here on in, droplets) exhibits rich behavior, principally dependent on the droplets' relative phase.Previous studies of soliton interaction in 2D ferromagnetic materials have concentrated primarily on vortices, topological structures that exhibit restricted dynamics [10]. Unless the ferromagnet is confined [11], conservation of overall topological charge pins the magnetic "center of mass" in place, e.g. a single vortex core, limiting motion to rotating collections [5,12] or linear motion of vortex pairs with net zero topological charge. Perpendicular scattering of two interacting vortex pairs has been theoretically demonstrated [6]. It appears that 90• scattering has a more universal character [8], not requiring a topological charge, and p...

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