A phase-field model is developed to study local elastic coupling between magnetic and ferroelectric domains that show one-to-one pattern match. A multiferroic layered heterostructure of Co0.4Fe0.6/BaTiO3 is considered as an example. Dynamics of the local elastic coupling is investigated by simulating a time-dependent electric-field driven changes in local magnetization/polarization/strain distributions and by comparing the associated velocities of the magnetic and ferroelectric domain walls. It is found that the electric-field-driven dynamic magnetic domain evolution manifests itself as an alternating occurrence of local magnetization rotation and coupled motion of magnetic and ferroelectric domain walls with almost identical velocities.
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