  We use spin polarized low energy electron microscopy to investigate domain
pattern transfer in a multiferroic heterostructure consisting of a
$(111)$-oriented BaTiO$_{\mathrm{3}}$ substrate and an epitaxial Ni film. After
in-situ thin film deposition and annealing through the ferroelectric phase
transition, interfacial strain transfer from ferroelastic domains in the
substrate and inverse magnetostriction in the magnetic thin film introduce a
uniaxial in-plane magnetic anisotropy that rotates by $60^{\circ}$ between
alternating stripe regions. We show that two types of magnetic domain wall can
be initialized in principle. Combining experimental results with micromagnetic
simulations we show that a competition between the exchange and magnetostatic
energies in these domain walls have a strong influence on the magnetic domain
configuration.
