In purely c-axis oriented PbZr$_{0.2}$Ti$_{0.8}$O$_3$ ferroelectric thin films, a lateral piezoresponse force microscopy signal is observed at the position of 180{deg}domain walls, where the out-of-plane oriented polarization is reversed. Using elect
ric force microscopy measurements we exclude electrostatic effects as the origin of this signal. Moreover, our mechanical simulations of the tip/cantilever system show that the small tilt of the surface at the domain wall below the tip does not satisfactorily explain the observed signal either. We thus attribute this lateral piezoresponse at domain walls to their sideways motion (shear) under the applied electric field. From simple elastic considerations and the conservation of volume of the unit cell, we would expect a similar lateral signal more generally in other ferroelectric materials, and for all types of domain walls in which the out-of-plane component of the polarization is reversed through the domain wall. We show that in BiFeO$_3$ thin films, with 180, 109 and 71{deg}domain walls, this is indeed the case.
Ferroelectric switching in BiFeO$_3$ multiferroic thin films with intrinsic ``stripe-like and ``bubble-like polydomain configurations was studied by piezoresponse force microscopy. Using the local electric field applied by a scanning probe microscope
tip, we observe reversal of both out-of-plane and in-plane components of the polarization, with the final domain state depending on the tip sweeping direction. In ``bubble-like samples, complete control of the polarization is achieved, with in-plane polarization change mediated and stabilized by out-of-plane polarization reversal. In ``stripe-like samples the intrinsic domain structure influences polarization switching and in-plane reversal may occur without out-of-plane change. The observed switching behaviour can be well correlated with the radial and vertical components of the highly inhomogeneous electric field applied by the tip.
In studies using piezoresponse force microscopy, we observe a non-zero lateral piezoresponse at 180$^circ$ domain walls in out-of-plane polarized, c-axis-oriented tetragonal ferroelectric Pb(Zr$_{0.2}$Ti$_{0.8}$)O$_3$ epitaxial thin films. We attribu
te these observations to a shear strain effect linked to the sign change of the $d_{33}$ piezoelectric coefficient through the domain wall, in agreement with theoretical predictions. We show that in monoclinically distorted tetragonal BiFeO$_3$ films, this effect is superimposed on the lateral piezoresponse due to actual in-plane polarization, and has to be taken into account in order to correctly interpret the ferroelectric domain configuration.
We have combined neutron scattering and piezoresponse force microscopy to study the relation between the exchange bias observed in CoFeB/BiFeO3 heterostructures and the multiferroic domain structure of the BiFeO3 films. We show that the exchange fiel
d scales with the inverse of the ferroelectric and antiferromagnetic domain size, as expected from Malozemoffs model of exchange bias extended to multiferroics. Accordingly, polarized neutron reflectometry reveals the presence of uncompensated spins in the BiFeO3 film at the interface with the CoFeB. In view of these results we discuss possible strategies to switch the magnetization of a ferromagnet by an electric field using BiFeO3.
We have analyzed the morphology of ferroelectric domains in very thin films of multiferroic BiFeO3. Unlike the more common stripe domains observed in thicker films BiFeO3 or in other ferroics, the domains tend not to be straight, but irregular in sha
pe, with significant domain wall roughening leading to a fractal dimensionality. Also contrary to what is usually observed in other ferroics, the domain size appears not to scale as the square root of the film thickness. A model is proposed in which the observed domain size as a function of film thickness can be directly linked to the fractal dimension of the domains.
