Nanoscale lattice dynamics in hexagonal boron nitride moiré superlattices.

Twisted two-dimensional van der Waals (vdW) heterostructures have unlocked a new means for manipulating the properties of quantum materials. The resulting mesoscopic moiré superlattices are accessible to a wide variety of scanning probes. To date, spatially-resolved techniques have prioritized electronic structure visualization, with lattice response experiments only in their infancy. Here, we therefore investigate lattice dynamics in twisted layers of hexagonal boron nitride (hBN), formed by a minute twist angle between two hBN monolayers assembled on a graphite substrate. Nano-infrared (nano-IR) spectroscopy reveals systematic variations of the in-plane optical phonon frequencies amongst the triangular domains and domain walls in the hBN moiré superlattices. Our first-principles calculations unveil a local and stacking-dependent interaction with the underlying graphite, prompting symmetry-breaking between the otherwise identical neighboring moiré domains of twisted hBN.

Controlled creation and displacement of charged domain walls in ferroelectric thin films.

Charged domain walls in ferroelectric materials are of high interest due to their potential use in nanoelectronic devices. While previous approaches have utilized complex scanning probe techniques or frustrative poling here we show the creation of charged domain walls in ferroelectric thin films during simple polarization switching using either a conductive probe tip or patterned top electrodes. We demonstrate that ferroelectric switching is accompanied - without exception - by the appearance of charged domain walls and that these walls can be displaced and erased reliably. We ascertain from a combination of scanning probe microscopy, transmission electron microscopy and phase field simulations that creation of charged domain walls is a by-product of, and as such is always coupled to, ferroelectric switching. This is due to the (110) orientation of the tetragonal (Pb,Sr)TiO3 thin films and the crucial role played by the limited conduction of the LSMO bottom electrode layer used in this study. This work highlights that charged domain walls, far from being exotic, unstable structures, as might have been assumed previously, can be robust, stable easily-controlled features in ferroelectric thin films.

Velocity Control of 180° Domain Walls in Ferroelectric Thin Films by Electrode Modification.

The velocity of individual 180° domain walls in thin ferroelectric films of PbZr0.1Ti0.9O3 is strongly dependent on the thickness of the top Pt electrode made by electron-beam induced deposition (EBID). We show that when the thickness is varied in the range <100 nm the domain wall velocity is seen to change by 7 orders of magnitude. We attribute this huge range of velocities to the similarly large range of resistivities for the EBID Pt electrode as extrapolated from four-point probe measurements. The domain wall motion is governed by the supply of charges to the domain wall, determined by the top electrode resistivity, and which is described using a modified Stefan Problem model. This has significant implications for the feasibility of ferroelectric domain wall nanoelectronics, wherein the speed of operation will be limited by the maximum velocity of the propagating domain wall front. Furthermore, by introducing sections of either modified thickness or width along the length of a "line" electrode, the domain wall velocity can be changed at these locations, opening up possibilities for dynamic regimes.

Controlling domain wall motion in ferroelectric thin films.

Domain walls in ferroic materials have attracted significant interest in recent years, in particular because of the unique properties that can be found in their vicinity. However, to fully harness their potential as nanoscale functional entities, it is essential to achieve reliable and precise control of their nucleation, location, number and velocity. Here, using piezoresponse force microscopy, we show the control and manipulation of domain walls in ferroelectric thin films of Pb(Zr,Ti)O3 with Pt top electrodes. This high-level control presents an excellent opportunity to demonstrate the versatility and flexibility of ferroelectric domain walls. Their position can be controlled by the tuning of voltage pulses, and multiple domain walls can be nucleated and handled in a reproducible fashion. The system is accurately described by analogy to the classical Stefan problem, which has been used previously to describe many diverse systems and is here applied to electric circuits. This study is a step towards the realization of domain wall nanoelectronics utilizing ferroelectric thin films.

Polarization closure in PbZr((0.42))Ti((0.58))O(3) nanodots.

Domain states in PbZr((0.42))Ti((0.58))O(3) single-crystal ferroelectric nanodots, formed on cooling through the Curie temperature, were imaged by transmission electron microscopy. In the majority of cases, 90° stripe domains were found to form into four distinct "bundles" or quadrants. Detailed analysis of the dipole orientations in the system was undertaken, using both dark-field imaging and an assumption that charged domain walls were energetically unfavorable in comparison to uncharged walls. On this basis, we conclude that the dipoles in these nanodots are arranged such that the resultant polarizations, associated with the four quadrant domain bundles, form into a closed loop. This "polarization closure" pattern is reminiscent of the flux-closure already commonly observed in soft ferromagnetic microdots but to date unseen in analogous ferroelectric dots.

Mesoscale flux-closure domain formation in single-crystal BaTiO3.

Over 60 years ago, Charles Kittel predicted that quadrant domains should spontaneously form in small ferromagnetic platelets. He expected that the direction of magnetization within each quadrant should lie parallel to the platelet surface, minimizing demagnetizing fields,and that magnetic moments should be configured into an overall closed loop, or flux-closure arrangement. Although now a ubiquitous observation in ferromagnets, obvious flux-closure patterns have been somewhat elusive in ferroelectric materials. This is despite the analogous behaviour between these two ferroic subgroups and the recent prediction of dipole closure states by atomistic simulations research. Here we show Piezoresponse Force Microscopy images of mesoscopic dipole closure patterns in free-standing, single-crystal lamellae of BaTiO(3). Formation of these patterns is a dynamical process resulting from system relaxation after the BaTiO(3) has been poled with a uniform electric field. The flux-closure states are composed of shape conserving 90° stripe domains which minimize disclination stresses.

Domain bundle boundaries in single crystal BaTiO3 lamellae: searching for naturally forming dipole flux-closure/quadrupole chains.

Naturally occurring boundaries between bundles of 90° stripe domains, which form in BaTiO(3) lamellae on cooling through the Curie Temperature, have been characterized using both piezoresponse force microscopy (PFM) and scanning transmission electron microscopy (STEM). Detailed interpretation of the dipole configurations present at these boundaries (using data taken from PFM) shows that in the vast majority of cases they are composed of simple zigzag 180° domain walls. Topological information from STEM shows that occasionally domain bundle boundaries can support chains of dipole flux closure and quadrupole nanostructures, but these kinds of boundaries are comparatively rare; when such chains do exist, it is notable that singularities at the cores of the dipole structures are avoided. The symmetry of the boundary shows that diads and centers of inversion exist at positions where core singularities should have been expected.