  A domain wall in a ferromagnetic system will move under the action of an
external magnetic field. Ultrathin Co layers sandwiched between Pt have been
shown to be a suitable experimental realization of a weakly disordered 2D
medium in which to study the dynamics of 1D interfaces (magnetic domain walls).
The behavior of these systems is encapsulated in the velocity-field response
v(H) of the domain walls. In a recent paper [P.J. Metaxas et al., Phys. Rev.
Lett. 104, 237206 (2010)] we studied the effect of ferromagnetic coupling
between two such ultrathin layers, each exhibiting different v(H)
characteristics. The main result was the existence of bound states over
finite-width field ranges, wherein walls in the two layers moved together at
the same speed. Here, we discuss in detail the theory of domain wall dynamics
in coupled systems. In particular, we show that a bound creep state is expected
for vanishing H and we give the analytical, parameter free expression for its
velocity which agrees well with experimental results.
