This is a copy of the slides presented at the meeting but not formally written up for the volume.

Description: Epitaxial thin films of the multiferroic BiFeO3 have been grown by molecular beam epitaxy in an adsorption-controlled growth regime where substrate temperature and bismuth oxide over pressure establish phase and stoichiometry control. 30 nm thick BiFeO3 films have been deposited directly on (001) SrTiO3 and SrRuO3/(110) DyScO3, and on (0001) GaN containing a 1 nm thick TiO2 overlayer to enable the epitaxial transition between (0001) GaN and (0001) BiFeO3. Films grown on (001) SrTiO3 possess rocking curves identical to that of the underlying substrate, e.g., a full width at half maximum (FWHM) in ù of 25 arc sec in the best case. This is over 40 times narrower than the best published result for epitaxial BiFeO3 films deposited by any technique. On all of the above substrates, the BiFeO3 films exhibit rhombohedral symmetry. The in-plane epitaxial alignment observed for BiFeO3/TiO2/(0001) GaN differs by a 30° in-plane rotation from that observed in previous work for BiFeO3/SrTiO3/TiO2/(0001) GaN. Specifically, our (0001) BiFeO3/TiO2/(0001) GaN is oriented in-plane with [10-10]BiFeO3 [11-20]GaN, accompanied by a 180° in-plane rotational twin variant. The results of this work will be discussed in the context of the interfacial and crystallographic orientation dependence on the ferroelectric, antiferromagnetic, and dielectric properties of this multiferroic.