“…The appearance of domains is caused by the imperfect screening of the spontaneous polarization due to the finite intrinsic screening length at the metal-ferroelectric interface, and it is expected even for structurally perfect interfaces [5,45,46]. However, experimentally, the presence of domains was usually inferred indirectly from studies of polarization dynamics [47], film tetragonality [48], macroscopic piezoresponse [49,50], or second-harmonic generation [51]. Recently, depolarization-induced polarization arrangements [52] and periodic flux-closure structures [27] have been observed directly in electroded PbTiO 3 films using transmission electron microscopy (TEM), but a systematic study of these domains, their scaling with ferroelectric thickness, and their effect on the macroscopic properties is still lacking.…”