Static and dynamic magnetic solitons play a critical role in applied nanomagnetism. Magnetic droplets, a type of non-topological dissipative soliton, can be nucleated and sustained in nanocontact spin-torque oscillators with perpendicular magnetic anisotropy free layers. Here, we perform a detailed experimental determination of the full droplet nucleation boundary in the current–field plane for a wide range of nanocontact sizes and demonstrate its excellent agreement with an analytical expression originating from a stability analysis. Our results reconcile recent contradicting reports of the field dependence of the droplet nucleation. Furthermore, our analytical model both highlights the relation between the fixed layer material and the droplet nucleation current magnitude, and provides an accurate method to experimentally determine the spin transfer torque asymmetry of each device.

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...

Droplet solitons are coherently precessing solitary waves that have been recently realized in thin ferromagnets with perpendicular anisotropy.In the strongly nonlinear regime, droplets can be well approximated by a slowly precessing, circular domain wall with a hyperbolic tangent form. Utilizing this representation, this work develops a general droplet modulation theory and applies it to study the long range effects of the magnetostatic field and a nanocontact spin torque oscillator (NC-STO) where spin polarized currents act as a gain source to counteract magnetic damping. An analysis of the dynamical equations for the droplet's center, frequency and phase demonstrates a negative processional frequency shift due to long range dipolar interactions, dependent on film thickness. Further analysis also demonstrates the onset of a saddle-node bifurcation at the minimum sustaining current for the NC-STO. The basin of attraction associated with the stable node demonstrates that spin torque enacts a restoring force to excursions of the droplet from the nanocontact center, observed previously in numerical simulations. Large excursions lead to the droplet's eventual decay into spin waves

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.

Magnetic dissipative droplets are localized, strongly nonlinear dynamical modes excited in nanocontact spin valves with perpendicular magnetic anisotropy. These modes find potential application in nanoscale structures for magnetic storage and computation, but dissipative droplet studies have so far been limited to extended thin films. Here, numerical and asymptotic analyses are used to demonstrate the existence and properties of novel solitons in confined structures. As a nanowire's width is decreased with a nanocontact of fixed size at its center, the observed modes undergo transitions from a fully localized two-dimensional droplet into a two-dimensional droplet edge mode and then a pulsating one-dimensional droplet. These solitons are interpreted as dissipative versions of classical, conservative solitons, allowing for an analytical description of the modes and the mechanisms of bifurcation. The presented results open up new possibilities for the study of low-dimensional solitons and droplet applications in nanostructures.