  Magnetoelectric coupling in multiferroic heterostructures can produce large
lateral modulations of magnetic anisotropy enabling the imprinting of
ferroelectric domains into ferromagnetic films. Exchange and magnetostatic
interactions within ferromagnetic films oppose the formation of such domains.
Using micromagnetic simulations and a 1-D model, we demonstrate that competing
energies lead to the breakdown of domain pattern transfer below a critical
domain width. Moreover, rotation of the magnetic field results in abrupt
transitions between two scaling regimes with different magnetic anisotropy.
