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Ferroelectric domain supercrystals

Ferroelectric materials exhibit complex domain structures that can be controlled by tailoring their electrical or mechanical boundary conditions. X-ray diffraction experiments show that in artificially layered superlattices composed of ultrathin metallic and ferroelectric layers, the three-dimensional ordering of ferroelectric domains leads to a domain supercrystal .

Over the last two decades, ferroelectric domains and domain walls have proven to be a fascinating playground for exploring novel ways of creating functional materials and devices [1]. Individual domain walls, where the local symmetry is different from the bulk, can host properties that are radically different from those of the host material. Ferroelectric domain walls can be orders of magnitude more conducting than the domains they separate, offering the prospect of transient or reconfigurable electronics where individual conducting elements are created and destroyed by the application of an electric field. Additionally, domain walls in heterostructures of ultrathin ferroelectrics exhibit highly inhomogeneous patterns of rotating dipoles that are not possible in bulk materials. The dynamics of these domain walls can lead to extremely large permittivities and even to so-called negative capacitance behaviour [2].

Much of the research on such domain patterns has focused on superlattices consisting of alternating ultrathin ferroelectric and dielectric layers, where the dielectric layers introduce a discontinuity in the ferroelectric polarisation. This induces the formation of dense, periodic nanodomain structures that minimise the electrostatic energy of the

system and are especially well-suited for characterisation using diffraction techniques [3,4]. However, the formation of such domain patterns in the presence of free carriers has been much less well explored.

Domain formation in superlattices consisting of ferroelectric PbTiO3 and metallic SrRuO3 layers deposited on DyScO3 substrates was investigated using a combination of synchrotron X-ray diffraction (XRD) experiments at beamlines ID01 and BM02, piezoresponse force microscopy (PFM), scanning transmission electron microscopy (STEM) and phase-field modelling. In superlattices with relatively thick PbTiO3 layers, a domain structure that doubles the superlattice periodicity along the out-of-plane direction appears (Figure 62), with sharp diffraction peaks indicating that this new phase is highly ordered in all three directions and is coherent across the entire thickness of the superlattice.

Combining the information from XRD, PFM and STEM reveals a highly ordered domain supercrystal structure, shown in Figures 63a and 63b, in excellent agreement with phase field simulations. The supercrystal structure appears in order to minimise both the electrostatic and the elastic energy. The tensile misfit strain imposed by the substrate favours a structure with alternating in-plane and out-of- plane polarisations, while the electrostatic energy cost due to the poor screening at the ferroelectric-metal interfaces favours the formation of in-plane and out-of-plane flux- closure domains with no net polarisation [5]. This domain structure is characterised by periodic deformations, with alternating expansions and contractions of the lattice that couple through the whole superlattice, creating three- dimensional ordering.

Fig. 62: X-ray diffraction signatures of the supercrystal phase. Reciprocal space maps in the (a) QY-QZ and (b,c) QX-QY planes around the 002pc Bragg peak of a PbTiO3/SrRuO3 superlattice, with sharp satellite

peaks due to the 3D ordered domain structure. d) Reciprocal space map in the QX-QY plane

around the 103pc Bragg peak showing satellites that arise due to a complex tilt pattern.

Figure adapted from principal publication with permission from Springer Nature.