Electrical half-wave rectification at ferroelectric domain walls

Mobile intrinsic point defects for conductive neutral domain walls in LiNbO3

Conductive ferroelectric domain walls (DWs) hold great promise for neuromorphic nanoelectronics as they can contribute to realize multi-level diodes and nanoscale memristors. Point defects accumulating at DWs will change the local electrical transport properties. Hence, local, inter-switchable n- and p-type conductivity at DWs can be achieved through point defect population control. Here, we study the impact of point defects on the electronic structure at neutral domain walls in LiNbO3 by density functional theory (DFT). Segregation of Li and O vacancies was found to be energetically favourable at neutral DWs, implying that charge-compensating electrons or holes can give rise to n- or p-type conductivity. Changes in the electronic band gap and defect transition levels are discussed with respect to local property engineering, opening the pathway for reversible tuning between n- and p-type conduction at neutral ferroelectric DWs. Specifically, the high Curie temperature of LiNbO3 and the significant calculated mobility of O and Li vacancies suggest that thermal annealing and applied electric fields can be used experimentally to control point defect populations, and thus enable rewritable pn-junctions.

Reconfigurable Vertical Phototransistor with MoTe2 Homojunction for High-Speed Rectifier and Multivalued Logical Circuits

The most reported two-dimensional (2D) reconfigurable multivalued logic (RMVL) devices primarily involve a planar configuration and carrier transport, which limits the high-density circuit integration and high-speed logic operation. In this work, the vertical transistors with reconfigurable MoTe2 homojunction are developed for low-power, high-speed, multivalued logic circuits. Through top/bottom dual-gate modulation, the transistors can be configured into four modes: P-i-N, N-i-P, P-i-P, and N-i-N. The reconfigurable rectifying and photovoltaic behaviors are observed in P-i-N and N-i-P configurations, exhibiting ideal diode characteristics with a current rectification ratio over 105 and sign-reversible photovoltaic response with a photoswitching ratio up to 7.44 × 105. Taking advantage of the seamless homogeneous integration and short vertical channel architecture, the transistor can operate as an electrical switch with an ultrafast speed of 680 ns, surpassing the conventional p-n diode. The MoTe2 half-wave rectifier is then applied in high-frequency integrated circuits using both square wave and sinusoidal waveforms. By applying an electrical pulse with a 1/4 phase difference between two input signals, the RMVL circuit has been achieved. This work proposes a universal and reconfigurable vertical transistor, enabled by dual-gate electrostatic doping on top/bottom sides of MoTe2 homojunction, suggesting a high integration device scheme for high-speed RMVL circuits and systems.

Mechanical manipulation for ordered topological defects

Randomly distributed topological defects created during the spontaneous symmetry breaking are the fingerprints to trace the evolution of symmetry, range of interaction, and order parameters in condensed matter systems. However, the effective mean to manipulate topological defects into ordered form is elusive due to the topological protection. Here, we establish a strategy to effectively align the topological domain networks in hexagonal manganites through a mechanical approach. It is found that the nanoindentation strain gives rise to a threefold Magnus-type force distribution, leading to a sixfold symmetric domain pattern by driving the vortex and antivortex in opposite directions. On the basis of this rationale, sizeable mono-chirality topological stripe is readily achieved by expanding the nanoindentation to scratch, directly transferring the randomly distributed topological defects into an ordered form. This discovery provides a mechanical strategy to manipulate topological protected domains not only on ferroelectrics but also on ferromagnets/antiferromagnets and ferroelastics.

Quantitative Mapping of Chemical Defects at Charged Grain Boundaries in a Ferroelectric Oxide

Polar discontinuities, as well as compositional and structural changes at oxide interfaces can give rise to a large variety of electronic and ionic phenomena. In contrast to earlier work focused on domain walls and epitaxial systems, this work investigates the relation between polar discontinuities and the local chemistry at grain boundaries in polycrystalline ferroelectric ErMnO3 . Using orientation mapping and scanning probe microscopy (SPM) techniques, the polycrystalline material is demonstrated to develop charged grain boundaries with enhanced electronic conductance. By performing atom probe tomography (APT) measurements, an enrichment of erbium and a depletion of oxygen at all grain boundaries are found. The observed compositional changes translate into a charge that exceeds possible polarization-driven effects, demonstrating that structural phenomena rather than electrostatics determine the local chemical composition and related changes in the electronic transport behavior. The study shows that the charged grain boundaries behave distinctly different from charged domain walls, giving additional opportunities for property engineering at polar oxide interfaces.

Origin of the Critical Thickness in Improper Ferroelectric Thin Films

Improper ferroelectrics are expected to be more robust than conventional ferroelectrics against depolarizing field effects and to exhibit a much-desired absence of critical thickness. Recent studies, however, revealed the loss of ferroelectric response in epitaxial improper ferroelectric thin films. Here, we investigate improper ferroelectric hexagonal YMnO₃ thin films and find that the polarization suppression, and hence functionality, in the thinner films is due to oxygen off-stoichiometry. We demonstrate that oxygen vacancies form on the film surfaces to provide the necessary charge to screen the large internal electric field resulting from the positively charged YMnO₃ surface layers. Additionally, we show that by modifying the oxygen concentration of the films, the phase transition temperatures can be substantially tuned. We anticipate that our findings are also valid for other ferroelectric oxide films and emphasize the importance of controlling the oxygen content and cation oxidation states in ferroelectrics for their successful integration in nanoscale applications.

High-Power LiNbO3 Domain-Wall Nanodevices

Wide band gap semiconductors keep on pushing the limits of power electronic devices to higher switching speeds and higher operating temperatures, including diodes and transistors on low-cost Si substrates. Alternatively, erasable conducting walls created within ferroelectric single-crystal films integrated on the Si platform have emerged as a promising gateway to adaptive nanoelectronics in sufficient output power, where the repetitive creation of highly charged domain walls (DWs) is particularly important to increase the wall current density. Here, we observe large conduction of the head-to-head DW at an optimized inclination angle of 15° within a LiNbO₃ single crystal that is 3-4 orders of magnitude higher than that of the tail-to-tail DW. The wall conduction is diode-like with a linear current density of higher than 1 mA/μm and an on/off ratio of larger than 10⁶ under the application of a repetitive switching voltage pulse in time less than 10 ns and an endurance number of higher than 10⁵. The high-power diodes can not only perform direct data processing in high-density nonvolatile DW memories in fast operation speeds and low-energy consumption but also function as sensors in compact electromechanical systems, selectors in phase-change memory and resistive random-access memory, and half-wave/full-wave rectifiers in modern nanocircuits in dimensions approaching the thickness of the depletion layer below which the tradition p-n junction malfunctions.

Dynamic domain boundaries: chemical dopants carried by moving twin walls

Domain walls and specifically ferroelastic twin boundaries are depositaries and fast diffusion pathways for chemical dopants and intrinsic lattice defects. Ferroelastic domain patterns act as templates for chemical structures where the walls are the device and not the bulk. Several examples of such engineered domain boundaries are given. Moving twin boundaries are shown to carry with them the dopants, although the activation of this mechanism depends sensitively on the applied external force. If the force is too weak, the walls remain pinned while too strong forces break the walls free of the dopants and move them independently. Several experimental methods and approaches are discussed.

Domain Wall Dynamics in a Ferroelastic Spin Crossover Complex with Giant Magnetoelectric Coupling

Pinned and mobile ferroelastic domain walls are detected in response to mechanical stress in a Mn³⁺ complex with two-step thermal switching between the spin triplet and spin quintet forms. Single-crystal X-ray diffraction and resonant ultrasound spectroscopy on [Mn^III(3,5-diCl-sal₂(323))]BPh₄ reveal three distinct symmetry-breaking phase transitions in the polar space group series Cc → Pc → P1 → P1_(1/2). The transition mechanisms involve coupling between structural and spin state order parameters, and the three transitions are Landau tricritical, first order, and first order, respectively. The two first-order phase transitions also show changes in magnetic properties and spin state ordering in the Jahn–Teller-active Mn³⁺ complex. On the basis of the change in symmetry from that of the parent structure, Cc, the triclinic phases are also ferroelastic, which has been confirmed by resonant ultrasound spectroscopy. Measurements of magnetoelectric coupling revealed significant changes in electric polarization at both the Pc → P1 and P1 → P1_(1/2) transitions, with opposite signs. All these phases are polar, while P1 is also chiral. Remanent electric polarization was detected when applying a pulsed magnetic field of 60 T in the P1→ P1_(1/2) region of bistability at 90 K. Thus, we showcase here a rare example of multifunctionality in a spin crossover material where the strain and polarization tensors and structural and spin state order parameters are strongly coupled.

Atomic-Scale Visualization of Polar Domain Boundaries in Ferroelectric In2Se3 at the Monolayer Limit

Domain boundaries in ferroelectric materials exhibit rich and diverse physical properties distinct from their parent materials and have been proposed for broad applications in nanoelectronics and quantum information technology. Due to their complexity and diversity, the internal atomic and electronic structure of domain boundaries that governs the electronic properties remains far from being elucidated. By using scanning tunneling microscopy and spectroscopy (STM/S) combined with density functional theory (DFT) calculations, we directly visualize the atomic structure of polar domain boundaries in two-dimensional (2D) ferroelectric β'-In₂Se₃ down to the monolayer limit. We observe a double-barrier energy potential with a width of about 3 nm across the 60° tail-to-tail domain boundaries in monolayer β'-In₂Se₃. The results will deepen our understanding of domain boundaries in 2D ferroelectric materials and stimulate innovative applications of these materials.

Charged Ferroelectric Domain Walls for Deterministic ac Signal Control at the Nanoscale

The direct current (dc) conductivity and emergent functionalities at ferroelectric domain walls are closely linked to the local polarization charges. Depending on the charge state, the walls can exhibit unusual dc conduction ranging from insulating to metallic-like, which is leveraged in domain-wall-based memory, multilevel data storage, and synaptic devices. In contrast to the functional dc behaviors at charged walls, their response to alternating currents (ac) remains to be resolved. Here, we reveal ac characteristics at positively and negatively charged walls in ErMnO₃, distinctly different from the response of the surrounding domains. By combining voltage-dependent spectroscopic measurements on macroscopic and local scales, we demonstrate a pronounced nonlinear response at the electrode-wall junction, which correlates with the domain-wall charge state. The dependence on the ac drive voltage enables reversible switching between uni- and bipolar output signals, providing conceptually new opportunities for the application of charged walls as functional nanoelements in ac circuitry.

An Electrocatalytic Reaction As a Basis for Chemical Computing in Water Droplets

Aqueous droplets covered with amphiphilic Janus Au/Fe₃O₄ nanoparticles and suspended in an organic phase serve as building blocks of droplet-based electronic circuitry. The electrocatalytic activity of these nanoparticles in a hydrogen evolution reaction (HER) underlies the droplet's ability to rectify currents with typical rectification ratios of ∼10. In effect, individual droplets act as low-frequency half-wave rectifiers, whereas several appropriately wired droplets enable full-wave rectification. When the HER-supporting droplets are combined with salt-containing "resistor" ones, the resulting ensembles can act as AND or OR gates or as inverters.

Engineering Individual Oxygen Vacancies: Domain-Wall Conductivity and Controllable Topological Solitons

Nanoscale devices that utilize oxygen vacancies in two-dimensional metal-oxide structures garner much attention due to conductive, magnetic, and even superconductive functionalities they exhibit. Ferroelectric domain walls have been a prominent recent example because they serve as a hub for topological defects and hence are attractive for next-generation data technologies. However, owing to the light weight of oxygen atoms and localized effects of their vacancies, the atomic-scale electrical and mechanical influence of individual oxygen vacancies has remained elusive. Here, stable individual oxygen vacancies were engineered in situ at domain walls of seminal titanate perovskite ferroics. The atomic-scale electric-field, charge, dipole-moment, and strain distribution around these vacancies were characterized by combining advanced transmission electron microscopy and first-principle methodologies. The engineered vacancies were used to form quasi-linear quadrupole topological defects. Significant intraband states were found in the unit cell of the engineered vacancies, proposing a meaningful domain-wall conductivity for miniaturized data-storage applications. Reduction of the Ti ion as well as enhanced charging and electric-field concentration were demonstrated near the vacancy. A 3-5% tensile strain was observed at the immediate surrounding unit cells of the vacancies. Engineering individual oxygen vacancies and topological solitons thus offers a platform for predetermining both atomic-scale and global functional properties of device miniaturization in metal oxides.

Observation of Electric-Field-Induced Structural Dislocations in a Ferroelectric Oxide

Dislocations are 1D topological defects with emergent electronic properties. Their low dimensionality and unique properties make them excellent candidates for innovative device concepts, ranging from dislocation-based neuromorphic memory to light emission from diodes. To date, dislocations are created in materials during synthesis via strain fields or flash sintering or retrospectively via deformation, for example, (nano)-indentation, limiting the technological possibilities. In this work, we demonstrate the creation of dislocations in the ferroelectric semiconductor Er(Mn,Ti)O₃ with nanoscale spatial precision using electric fields. By combining high-resolution imaging techniques and density functional theory calculations, direct images of the dislocations are collected, and their impact on the local electric transport behavior is studied. Our approach enables local property control via dislocations without the need for external macroscopic strain fields, expanding the application opportunities into the realm of electric-field-driven phenomena.

Multiferroic heterostructures for spintronics

For next-generation technology, magnetic systems are of interest due to the natural ability to store information and, through spin transport, propagate this information for logic functions. Controlling the magnetization state through currents has proven energy inefficient. Multiferroic thin-film heterostructures, combining ferroelectric and ferromagnetic orders, hold promise for energy efficient electronics. The electric field control of magnetic order is expected to reduce energy dissipation by 2–3 orders of magnitude relative to the current state-of-the-art. The coupling between electrical and magnetic orders in multiferroic and magnetoelectric thin-film heterostructures relies on interfacial coupling though magnetic exchange or mechanical strain and the correlation between domains in adjacent functional ferroic layers. We review the recent developments in electrical control of magnetism through artificial magnetoelectric heterostructures, domain imprint, emergent physics and device paradigms for magnetoelectric logic, neuromorphic devices, and hybrid magnetoelectric/spin-current-based applications. Finally, we conclude with a discussion of experiments that probe the crucial dynamics of the magnetoelectric switching and optical tuning of ferroelectric states towards all-optical control of magnetoelectric switching events.

Conductivity control via minimally invasive anti-Frenkel defects in a functional oxide

Utilizing quantum effects in complex oxides, such as magnetism, multiferroicity and superconductivity, requires atomic-level control of the material's structure and composition. In contrast, the continuous conductivity changes that enable artificial oxide-based synapses and multiconfigurational devices are driven by redox reactions and domain reconfigurations, which entail long-range ionic migration and changes in stoichiometry or structure. Although both concepts hold great technological potential, combined applications seem difficult due to the mutually exclusive requirements. Here we demonstrate a route to overcome this limitation by controlling the conductivity in the functional oxide hexagonal Er(Mn,Ti)O₃ by using conductive atomic force microscopy to generate electric-field induced anti-Frenkel defects, that is, charge-neutral interstitial-vacancy pairs. These defects are generated with nanoscale spatial precision to locally enhance the electronic hopping conductivity by orders of magnitude without disturbing the ferroelectric order. We explain the non-volatile effects using density functional theory and discuss its universality, suggesting an alternative dimension to functional oxides and the development of multifunctional devices for next-generation nanotechnology.

Ferroelectric Domain Wall Memristor

A domain wall-enabled memristor is created, in thin film lithium niobate capacitors, which shows up to twelve orders of magnitude variation in resistance. Such dramatic changes are caused by the injection of strongly inclined conducting ferroelectric domain walls, which provide conduits for current flow between electrodes. Varying the magnitude of the applied electric-field pulse, used to induce switching, alters the extent to which polarization reversal occurs; this systematically changes the density of the injected conducting domain walls in the ferroelectric layer and hence the resistivity of the capacitor structure as a whole. Hundreds of distinct conductance states can be produced, with current maxima achieved around the coercive voltage, where domain wall density is greatest, and minima associated with the almost fully switched ferroelectric (few domain walls). Significantly, this "domain wall memristor" demonstrates a plasticity effect: when a succession of voltage pulses of constant magnitude is applied, the resistance changes. Resistance plasticity opens the way for the domain wall memristor to be considered for artificial synapse applications in neuromorphic circuits.

Defect-Enhanced Polarization Switching in the Improper Ferroelectric LuFeO3

Results of switching behavior of the improper ferroelectric LuFeO₃ are presented. Using a model set of films prepared under controlled chemical and growth-rate conditions, it is shown that defects can reduce the quasi-static switching voltage by up to 40% in qualitative agreement with first-principles calculations. Switching studies show that the coercive field has a stronger frequency dispersion for the improper ferroelectrics compared to a proper ferroelectric such as PbTiO₃ . It is concluded that the primary structural order parameter controls the switching dynamics of such improper ferroelectrics.

Domains and domain walls in multiferroics

Multiferroics are materials combining several ferroic orders, such as ferroelectricity, ferro- (or antiferro-) magnetism, ferroelasticity and ferrotoroidicity. They are of interest both from a fundamental perspective, as they have multiple (coupled) non-linear functional responses providing a veritable myriad of correlated phenomena, and because of the opportunity to apply these functionalities for new device applications. One application is, for instance, in non-volatile memory, which has led to special attention being devoted to ferroelectric and magnetic multiferroics. The vision is to combine the low writing power of ferroelectric information with the easy, non-volatile reading of magnetic information to give a “best of both worlds” computer memory. For this to be realised, the two ferroic orders need to be intimately linked via the magnetoelectric effect. The magnetoelectric coupling – the way polarization and magnetization interact – is manifested by the formation and interactions of domains and domain walls, and so to understand how to engineer future devices one must first understand the interactions of domains and domain walls. In this article, we provide a short introduction to the domain formation in ferroelectrics and ferromagnets, as well as different microscopy techniques that enable the visualization of such domains. We then review the recent research on multiferroic domains and domain walls, including their manipulation and intriguing properties, such as enhanced conductivity and anomalous magnetic order. Finally, we discuss future perspectives concerning the field of multiferroic domain walls and emergent topological structures such as ferroelectric vortices and skyrmions.

Unexpected Giant Microwave Conductivity in a Nominally Silent BiFeO3 Domain Wall

Nanoelectronic devices based on ferroelectric domain walls (DWs), such as memories, transistors, and rectifiers, have been demonstrated in recent years. Practical high-speed electronics, on the other hand, usually demand operation frequencies in the gigahertz (GHz) regime, where the effect of dipolar oscillation is important. Herein, an unexpected giant GHz conductivity on the order of 10³ S m^-1 is observed in certain BiFeO₃ DWs, which is about 100 000 times greater than the carrier-induced direct current (dc) conductivity of the same walls. Surprisingly, the nominal configuration of the DWs precludes the alternating current (ac) conduction under an excitation electric field perpendicular to the surface. Theoretical analysis shows that the inclined DWs are stressed asymmetrically near the film surface, whereas the vertical walls in a control sample are not. The resultant imbalanced polarization profile can then couple to the out-of-plane microwave fields and induce power dissipation, which is confirmed by the phase-field modeling. Since the contributions from mobile-carrier conduction and bound-charge oscillation to the ac conductivity are equivalent in a microwave circuit, the research on local structural dynamics may open a new avenue to implement DW nano-devices for radio-frequency applications.

Hexagonal manganites: Strong coupling of ferroelectricity and magnetic orders

Hexagonal manganites belong to an exciting class of materials exhibiting strong interactions between a highly frustrated magnetic system, the ferroelectric polarization, and the lattice. The existence and mutual interaction of different magnetic ions (Mn and rare earth) results in complex magnetic phase diagrams and novel physical phenomena. A summary and discussion of the various properties, underlying physical mechanisms, the role of the rare earth ions, and the complex interactions in multiferroic hexagonal manganites are presented in this review.

An Electronically Driven Improper Ferroelectric: Tungsten Bronzes as Microstructural Analogs for the Hexagonal Manganites

Since the observation that the properties of ferroic domain walls (DWs) can differ significantly from the bulk materials in which they are formed, it has been realized that domain wall engineering offers exciting new opportunities for nanoelectronics and nanodevice architectures. Here, a novel improper ferroelectric, CsNbW₂ O₉ , with the hexagonal tungsten bronze structure, is reported. Powder neutron diffraction and symmetry mode analysis indicate that the improper transition (T_C = 1100 K) involves unit cell tripling, reminiscent of the hexagonal rare earth manganites. However, in contrast to the manganites, the symmetry breaking in CsNbW₂ O₉ is electronically driven (i.e., purely displacive) via the second-order Jahn-Teller effect in contrast to the geometrically driven tilt mechanism of the manganites. Nevertheless CsNbW₂ O₉ displays the same kinds of domain microstructure as those found in the manganites, such as the characteristic six-domain "cloverleaf" vertices and DW sections with polar discontinuities. The discovery of a completely new material system, with domain patterns already known to generate interesting functionality in the manganites, is important for the emerging field of DW nanoelectronics.

Ferroelectric polarization in multiferroics

Multiferroic materials, showing ordering of both electrical and magnetic degrees of freedom, are promising candidates enabling the design of novel electronic devices. Various mechanisms ranging from geometrically or spin-driven improper ferroelectricity via lone-pairs, charge-order or -transfer support multiferroicity in single-phase or composite compounds. The search for materials showing these effects constitutes one of the most important research fields in solid-state physics during the last years, but scientific interest even traces back to the middle of the past century. Especially, a potentially strong coupling between spin and electric dipoles captured the interest to control via an electric field the magnetization or via a magnetic field the electric polarization. This would imply a promising route for novel electronics. Here, we provide a review about the dielectric and ferroelectric properties of various multiferroic systems ranging from type I multiferroics, in which magnetic and ferroelectric order develop almost independently of each other, to type II multiferroics, which exhibit strong coupling of magnetic and ferroelectric ordering. We thoroughly discuss the dielectric signatures of the ferroelectric polarization for BiFeO3, Fe3O4, DyMnO3 and an organic charge-transfer salt as well as show electric-field poling studies for the hexagonal manganites and a spin-spiral system LiCuVO4.

Functional Ferroic Domain Walls for Nanoelectronics

A prominent challenge towards novel nanoelectronic technologies is to understand and control materials functionalities down to the smallest scale. Topological defects in ordered solid-state (multi-)ferroic materials, e.g., domain walls, are a promising gateway towards alternative sustainable technologies. In this article, we review advances in the field of domain walls in ferroic materials with a focus on ferroelectric and multiferroic systems and recent developments in prototype nanoelectronic devices.

Structures and electronic properties of domain walls in BiFeO3 thin films

Domain walls (DWs) in ferroelectrics are atomically sharp and can be created, erased, and reconfigured within the same physical volume of ferroelectric matrix by external electric fields. They possess a myriad of novel properties and functionalities that are absent in the bulk of the domains, and thus could become an essential element in next-generation nanodevices based on ferroelectrics. The knowledge about the structure and properties of ferroelectric DWs not only advances the fundamental understanding of ferroelectrics, but also provides guidance for the design of ferroelectric-based devices. In this article, we provide a review of structures and properties of DWs in one of the most widely studied ferroelectric systems, BiFeO₃ thin films. We correlate their conductivity and photovoltaic properties to the atomic-scale structure and dynamic behaviors of DWs.

Observation of Uncompensated Bound Charges at Improper Ferroelectric Domain Walls

Low-temperature electrostatic force microscopy (EFM) is used to probe unconventional domain walls in the improper ferroelectric semiconductor Er_0.99Ca_0.01MnO₃ down to cryogenic temperatures. The low-temperature EFM maps reveal pronounced electric far fields generated by partially uncompensated domain-wall bound charges. Positively and negatively charged walls display qualitatively different fields as a function of temperature, which we explain based on different screening mechanisms and the corresponding relaxation time of the mobile carriers. Our results demonstrate domain walls in improper ferroelectrics as a unique example of natural interfaces that are stable against the emergence of electrically uncompensated bound charges. The outstanding robustness of improper ferroelectric domain walls in conjunction with their electronic versatility brings us an important step closer to the development of durable and ultrasmall electronic components for next-generation nanotechnology.

Large Carrier Mobilities in ErMnO3 Conducting Domain Walls Revealed by Quantitative Hall-Effect Measurements

Kelvin probe force microscopy (KPFM) has been used to directly and quantitatively measure Hall voltages, developed at conducting tail-to-tail domain walls in ErMnO₃ single crystals, when current is driven in the presence of an approximately perpendicular magnetic field. Measurements across a number of walls, taken using two different atomic force microscope platforms, consistently suggest that the active p-type carriers have unusually large room temperature mobilities of the order of hundreds of square centimeters per volt second. Associated carrier densities were estimated to be of the order of 10¹³ cm^-3. Such mobilities, at room temperature, are high in comparison with both bulk oxide conductors and LaAlO₃-SrTiO₃ sheet conductors. High carrier mobilities are encouraging for the future of domain-wall nanoelectronics and, significantly, also suggest the feasibility of meaningful investigations into dimensional confinement effects in these novel domain-wall systems.