  Magnetization dynamics in thin film ferromagnets can be studied using a
dispersive hydrodynamic formulation. The equations describing the
magnetodynamics map to a compressible fluid with broken Galilean invariance
parametrized by the longitudinal spin density and a magnetic analog of the
fluid velocity that define spin-density waves. A direct consequence of these
equations is the determination of a magnetic Mach number. Micromagnetic
simulations reveal nucleation of nonlinear structures from an impenetrable
object realized by an applied magnetic field spot or a defect. In this work,
micromagnetic simulations demonstrate vortex-antivortex pair nucleation from an
obstacle. Their interaction establishes either ordered or irregular
vortex-antivortex complexes. Furthermore, when the magnetic Mach number exceeds
unity (supersonic flow), a Mach cone and periodic wavefronts are observed,
which can be well-described by solutions of the steady, linearized equations.
These results are reminiscent of theoretical and experimental observations in
Bose-Einstein condensates, and further supports the analogy between the
magnetodynamics of a thin film ferromagnet and compressible fluids. The
nucleation of nonlinear structures and vortex-antivortex complexes using this
approach enables the study of their interactions and effects on the stability
of spin-density waves.
