Dynamics of metastable contact soliton dissipative exchange flows in one-dimensional ferromagnetic channels

Dissipative exchange flows (DEFs) are large-amplitude boundary value solutions of ferromagnetic channels. In their low injection limit, DEFs reduce to spin superfluids. However, in the strong injection limit, nonlinearities dominate close to the injection site and a soliton is formed smoothly connecting to a spin superfluid in the remainder of the channel; this solution has been termed a contact soliton dissipative exchange flow (CS-DEF). Here, we numerically investigate CS-DEF solutions in a moderate injection regime and a finite injection width. We find a solution where two metastable solitons coexist in the injection region. This solution is metastable in the sense that any perturbation to the system will eject one of the solitons out of the injection region. Moreover, soliton dynamics can be excited when two injection regions are separated by a certain distance. We find that the ensuing spin superfluid between the solitons induces a steady-state dynamics in which metastable solitons are continually ejected and nucleated. Furthermore, depending on the relative signs of the spin injections, the soliton dynamics possess a particular handedness and frequency related to the spin transfer torque delivered by the spin superfluid. Our results provide insights into the spin current transport, where the interaction between spin superfluids and solitons suggests a mechanism for detaching contact-solitons from the injection boundary. Although this study focuses on the ``nonlocal'' interaction between solitons, it may lead to the investigation of new mechanisms for inserting solitons in a DEF, e.g., for discrete motion and transport of information over long distances.