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

The interaction behaviors 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, particle-like, 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.

Figure 1

Droplet interactions. (a) Breathing droplet at two times. (b) In-phase merger and counterpropagation. (c) Out-of-phase reflection. (d)–(g) Droplet merger (e), annihilation to magnons (f), spontaneous breather formation (g). Inset to (g): Spatial minimum of $m_z$ as a function of time for (d)–(g); vertical dashed lines denote times in (d)–(g).

Figure 2

Head-on collision properties. (a) Cross-over phase for varying initial $\omega$, $V$. (b)–(d) Postcollision properties for initial $\omega =0.4$, $V=0.6$. Scattered droplet energy (b), frequency (c), and speed (d).

Figure 3

Method of images depicting head-on collision of droplet with a free spin boundary (vertical line). Two counterpropagating edge droplets are created.