  Manipulation of magnons in artificial magnonic crystals (MCs) leads to
fascinating nonlinear wave phenomena such as the generation of gap solitons,
which has been mostly limited to one-dimensional systems. Here, we propose a
model system for the magnetization in two-dimensional MCs subjected to a
periodic external magnetic field, describing the dynamics of magnetic gap
solitons (MGSs) formed by nonlinear self-trapping. We show the formation,
stability, and dynamics for various two-dimensional gap modes, including gap
solitons and vortical ones. Their existence regions depend on the anisotropic
axis orientation of the ferromagnetic film. The Bloch oscillation and depinning
propagation of MGSs under constant spin-current injections are discovered and
characterized. We design a scheme of pulse current injection to achieve
distortionless propagation of MGSs. These findings show that the 2D magnonic
crystals can be viewed as a building block for MGSs-based storage and
transmission, where the propagation and localization are variously controlled
and reconfigurable.
