  Magnonic crystals are prototype magnetic metamaterials designed for the
control of spin wave propagation. Conventional magnonic crystals are composed
of single domain elements. If magnetization textures, such as domain walls,
vortices and skyrmions, are included in the building blocks of magnonic
crystals, additional degrees of freedom over the control of the magnonic band
structure can be achieved. We theoretically investigate the influence of domain
walls on the spin wave propagation and the corresponding magnonic band
structure. It is found that the rotation of magnetization inside a domain wall
introduces a geometric vector potential for the spin wave excitation. The
corresponding Berry phase has quantized value $4 n_w \pi$, where $n_w$ is the
winding number of the domain wall. Due to the topological vector potential, the
magnonic band structure of magnonic crystals with domain walls as comprising
elements differs significantly from an identical magnonic crystal composed of
only magnetic domains. This difference can be utilized to realize dynamic
reconfiguration of magnonic band structure by a sole nucleation or annihilation
of domain walls in magnonic crystals.
