Domain walls as new 2D functional materials

Ferroelectric domain walls offer the exciting prospect of truly nanoscale reconfigurable circuits owing to their small thickness, typically ~1-5 nm, their inherently mobile nature and the functional properties they exhibit. 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. In this work we demonstrate an ability that allows extensive control of individual and multiple 180° domain walls in PbZr0.1Ti0.9O3 thin films. Instrumental in this implementation are the unique properties of the Pt top electrode deposited by electron-beam induced breakdown of a precursor gas. Additionally this work is accurately described through the framework of an analogy to the classical Stefan problem which has previously been used to describe many diverse systems but is here applied to electric circuits.

Furthermore advances towards readout of domain wall position, via a ‘read-restore’ technique will be presented. This method involves measurement of partial switching currents due to domain wall perturbations from an initial position through sub-switching voltage pulses.

Finally, understanding the interaction of domain walls with defects is crucial to tailoring their properties. Domain wall pinning/depinning has a significant impact on bulk materials properties. For future devices based on individual domain walls and their motion, defects could potentially kill or create functionality. Dr McGilly will show that local nanoscale defect regions can be used to modify imprint and domain wall motion. This adds an additional dimension to the domain-wall-control toolbox.

Among the many interesting features of ferroic domain walls, one that has attracted recent interest is their photovoltaic response, triggered by the observation of above-bandgap photovoltages proportional to the number of domain walls in BiFeO₃ films.  However, ferroelectrics are known to also be able to display above-bandgap photovoltages even when in a mono-domain state, owing to the so-called ‘bulk photovoltaic effect’. Isolating the physics of the bulk photovoltaic effect is, however, complicated because the roles of shift currents, depolarisation fields, domain walls and even photochemistry are generally entangled. 

In an effort to better understand the bulk photovoltaic effect, we have studied the photovoltaic properties of antiferroelectric thin films of PbZrO₃ grown on transparent conductive substrates. We find the effect to be independent of depolarisation fields or domains, and depend only on internal symmetry (shift current theory) and on conductivity: the bulk photovoltaic effect is ‘switched on’ only when the antiferroelectric is switched into the polar state, and remains stable even in the absence of external bias thanks to the photorefractive pinning of the polar state. This allows antiferroelectrics to functionally mimic the photovoltaic behaviour of ferroelectrics, thus becoming a second family of materials where the bulk photovoltaic effect is possible.

Quantitatively, the photovoltage is the product of the (intrinsic) shift current times the (extrinsic) resistivity of the film, which explains the large dispersion of photovoltages reported for the same material. This also means that high resistivity films can display giant photovoltages only limited by the breakdown strength of the film; in the particular case of our antiferroelectric films, photovoltages in excess of 100 V can be achieved in the vertical direction. When divided by thickness, the resulting photoelectric fields are >5MV/cm, the largest ever reported for any material. 

In ferroelectric materials, domain walls separate regions with different polarisation orientation, and can present novel functional properties quite different from those of the parent phase. The extreme localisation of such properties at these intrinsically nanoscale features makes them potentially useful as active components in future miniaturised electronic devices. 

Particularly exciting has been the discovery of domain-wall-specific electrical conduction in many ferroelectric families. Here, I will present our scanned probe microscopy observations of such conduction in Pb(Zr,Ti)O3 (PZT), highlighting the key role of oxygen vacancies and surface adsorbates, whose distribution can be modulated to reversibly control domain wall transport. We also map out the effects of the surface adsorbates on polarisation switching and domain wall velocities under different conditions of relative humidity. Using a ‘pump-probe’ approach, we explore the earliest stages of domain switching, demonstrating unexpectedly long lifetimes for the subcritical nucleus formed under ultrashort high voltage pulses.

In the same ferroelectric samples, we also find an unusual piezoelectric shear response, forbidden by symmetry in the parent phase, which could be technologically important for ferroelectric based surface acoustic wave devices.

Variability of the electronic properties of 2D materials and ferroelectrics (FE) offers a wealth of fundamentally important physical phenomena and exciting technological opportunities for the hybrid 2D-FE heterostructures comprised of these materials. Among particularly promising aspects of these heterostructures is a coupling between the electrically-switchable polarisation and electronic transport, which allows realisation of advanced devices with enhanced functional characteristics. This talk will focus on recent advances in realisation of these electronic devices. Specifically, we employ polarisation reversal to modulate (1) the in-plane transport of the interfacial conducting channel in the ferroelectric field effect transistor (FE-FET) devices, and (2) the perpendicular-to-plane tunnelling conductance across the ferroelectric barrier in the ferroelectric tunnel junction (FTJ) devices. We show that interface engineering in the 2D-FE systems provides a possibility of successfully addressing the most serious challenges relevant to device performance, such as ON/OFF ratio, lifetime, operation endurance and reliability.

Topological spin structures that emerge due to the Dzyaloshinskii-Moriya interaction (DMI), such as chiral domain walls and skyrmions possess a high stability and are of key importance for magnetic memories and logic devices.

Spin orbit effect address two key challenges in spintronics devices based on domain walls: (i) chiral exchange coupling such as the DMI increase domain wall robustness and stability and (ii) spin-orbit torques lead to ultra-efficient domain wall manipulation.

Professor Klaui and colleagues have investigated in detail the dynamics of domain walls and find that in addition to conventional spin transfer torque, also spin orbit torques play a key role. By comparing the wall motion with current-induced magnetization switching in our systems, it can be deduced that the spin-orbit torques independently of the DMI and we find that the motion observed Ta(5nm)/Co20Fe60B20(1nm)/MgO(2nm) can be attributed to a DMI that is opposite to such stacks with a magnetic CoFe layer pointing to the B at the interface that governs the sign of the DMI.

For skyrmions Professor Klaui demonstrates for the first time that we can move a train of skyrmions in a “racetrack”-type device due to spin-orbit torques reliably and find skyrmion lattices at room temperature in confined geometries. Single skyrmion dynamics is imaged using x-ray holography and from the trajectories a large mass is deduced that directly results from the topology of the skyrmion.

The mobility of ferroelastic twin walls in perovskites under application of external stress is generally well understood and conforms to expectations from considerations of wall thickness, number density and interactions with defects. Different mechanisms, such as back and forth motion of needle tips and migration of ledges along the length of the walls occupy different regions of parameter space according to the relaxation times and stress levels involved. However, these appear to become jammed if two separate ferroelastic instabilities become coupled. In systems which are ferroelectric, the response to external strain again depends on a contrast in shear strain across 90° twin walls but the diversity of domain types increases, to include both static and dynamic polar nano-regions. The influence of these is seen in elastic softening in the stability field of the para phase. Magnetic domain walls similarly can combine gradients in the magnetic order parameter with gradients in strain to give walls which behave like other ferroelastic twin walls in some cases. In other cases, elastic stiffening indicates that the normal strain relaxation mechanism does not occur. The strength and dynamics of these effects are seen in changes of elastic constants and an elastic loss which can be observed by Resonant Ultrasound Spectroscopy in a wide variety of ferroic and multiferroic materials such as LaAlO₃, LaCoO₃, EuTiO₃, PbFe_0.5Nb_0.5O₃, PbFe_0.5Ta_0.5O₃ and KMnF₃.

The development of spherical aberration correctors for electromagnetic lenses established a major improvement in the new generation of electron microscopes. The growing desire to control materials at an atomic level requires capabilities to image and analyse material at this scale. This talk will give a brief introduction to the state of the art electron microscopy, and its application to two different oxide materials.

Using aberration-corrected scanning transmission electron microscopy (STEM), we analysed in detail the domain structure of Co/PbTiO₃/(La,Sr)MnO₃ ferroelectric tunnel junctions. Annular Bright Field (ABF) imaging was used to directly visualise both cations (Pb,Ti) and oxygen position, measuring the relative displacement and dipole distribution unit cell by unit cell. The dipole maps of different PbTiO₃ thin films revealed a clear influence on the equilibrium domain pattern.

PbSc_0.5Ta_0.5O₃ is an ergodic relaxor, forming polar nano regions that fluctuate in polarisation. Under appropriate imaging conditions a tweed/domain structure is visible using transmission electron microscopy, which is seen to switch repeatedly at room temperature. The domains become smaller on heating as the Curie temperature is approached, while they enlarge and slow down upon cooling, switching over seconds or being completely static at liquid nitrogen temperature.

In this talk Professor Scott will present examples in which domains and domain walls in multiferroics are best described via fluid mechanics and not conventional hysteresis behaviour.  The systems examined include wrinkling and the onset of capillary waves along the leading edge in ferroelectric lead germanate  Pb5Ge3O11 (Ph.D. thesis of Alexei Gruverman, Ekaterinburg 1990); folding of ferroelastic domains in PbFe(1/2)Nb(1/2)O3/PZT and PbFe(1/2)Ta(1/2)O3/PZT; and vortex arrays in PZT (Ramesh et al., Nature 2015).

These phenomena are viscosity-driven saddle points, with velocity and/or field thresholds (e.g., 150 kV/cm in lead germanate).  The result is often nm-wide ferroelectric rectilinear domains nestled inside larger (100-nm) ferroelastic domains; the latter have highly curved walls, violating the Landau-Lifshitz-Kittel Laws, but compatible with the "walls within walls" model of Janovec and Privratska. This model also suggests that ferroic domains that exhibit folding will not exhibit skyrmion-like vortex arrays; folding requires relatively low domain viscosity whereas vortex arrays are favored by higher viscosity.

The simplest model that exhibits folding bifurcations in two dimensions is

dy/dt = a - dy - by2

dx/dt = cx.

These approximate the Standard Linear Model (Kelvin-Voigt plus Maxwell elements) in stress-strain mechanics, although for real metals, the exponent by2 is more typically by5 (1943 Osgood Model).