  Nonlocal compensation of magnetic damping by spin injection has been
theoretically shown to establish dynamic, noncollinear magnetization states
that carry spin currents over micrometer distances. Such states can be
generically referred to as dissipative exchange flows (DEFs) because spatially
diffusing spin currents are established by the mutual exchange torque exerted
by neighboring spins. Analytical studies to date have been limited to the weak
spin injection assumption whereby the equation of motion for the magnetization
is mapped to hydrodynamic equations describing spin flow and then linearized.
Here, we analytically and numerically study easy-plane ferromagnetic channels
subject to spin injection of arbitrary strength at one extremum under a unified
hydrodynamic framework. We find that DEFs generally exhibit a nonlinear profile
along the channel accompanied by a nonlinear frequency tuneability. At large
injection strengths, we fully characterize a novel magnetization state we call
a contact-soliton DEF (CS-DEF) composed of a stationary soliton at the
injection site, which smoothly transitions into a DEF and exhibits a negative
frequency tuneability. The transition between a DEF and a CS-DEF occurs at the
maximum precessional frequency and coincides with the Landau criterion: a
subsonic to supersonic flow transition. Leveraging the hydraulic-electrical
analogy, the current-voltage characteristics of a nonlinear DEF circuit are
presented. Micromagnetic simulations of nanowires that include
magnetocrystalline anisotropy and non-local dipole fields are in qualitative
agreement with the analytical results. The magnetization states found here
along with their characteristic profile and spectral features provide
quantitative guidelines to pursue an experimental demonstration of DEFs in
ferromagnetic materials and establishes a unified description for long-distance
spin transport.
