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Two-dimensional (2D) materials such as graphene and transition-metal dichalcogenides reveal the electronic phases that emerge when a bulk crystal is reduced to a monolayer 1 – 4 . Transition-metal oxide perovskites host a variety of correlated electronic phases 5 – 12 , so similar behaviour in monolayer materials based on transition-metal oxide perovskites would open the door to a rich spectrum of exotic 2D correlated phases that have not yet been explored. Here we report the fabrication of freestanding perovskite films with high crystalline quality almost down to a single unit cell. Using a recently developed method based on water-soluble Sr 3 Al 2 O 6 as the sacrificial buffer layer 13 , 14 we synthesize freestanding SrTiO 3 and BiFeO 3 ultrathin films by reactive molecular beam epitaxy and transfer them to diverse substrates, in particular crystalline silicon wafers and holey carbon films. We find that freestanding BiFeO 3 films exhibit unexpected and giant tetragonality and polarization when approaching the 2D limit. Our results demonstrate the absence of a critical thickness for stabilizing the crystalline order in the freestanding ultrathin oxide films. The ability to synthesize and transfer crystalline freestanding perovskite films without any thickness limitation onto any desired substrate creates opportunities for research into 2D correlated phases and interfacial phenomena that have not previously been technically possible. Ultrathin freestanding crystalline films of transition-metal oxide perovskites are fabricated and transferred to various substrates, proving their potential for exploring emergent 2D correlated phases.

Flexoelectricity is a universal electromechanical coupling effect whereby all dielectric materials polarise in response to strain gradients. In particular, nanoscale flexoelectricity promises exotic phenomena and functions, but reliable characterisation methods are required to unlock its potential. Here, we report anomalous mechanical control of quantum tunnelling that allows for characterising nanoscale flexoelectricity. By applying strain gradients with an atomic force microscope tip, we systematically polarise an ultrathin film of otherwise nonpolar SrTiO 3 , and simultaneously measure tunnel current across it. The measured tunnel current exhibits critical behaviour as a function of strain gradients, which manifests large modification of tunnel barrier profiles via flexoelectricity. Further analysis of this critical behaviour reveals significantly enhanced flexocoupling strength in ultrathin SrTiO 3 , compared to that in bulk, rendering flexoelectricity more potent at the nanoscale. Our study not only suggests possible applications exploiting dynamic mechanical control of quantum effect, but also paves the way to characterise nanoscale flexoelectricity. Flexoelectricity exists in every dielectric material exposed to a strain gradient and is enhanced at the nanoscale. However, precisely determining flexoelectric coupling parameters at the nanoscale is challenging, but has been overcome here by measuring the current across a tunnel junction.

The breaking of symmetry across an oxide heterostructure causes the electronic orbitals to be reconstructed at the interface into energy states that are different from their bulk counterparts1. The detailed nature of the orbital reconstruction critically affects the spatial confinement and the physical properties of the electrons occupying the interfacial orbitals2–4. Using an example of two-dimensional electron liquids forming at LaAlO3/SrTiO3 interfaces5,6 with different crystal symmetry, we show that the selective orbital occupation and spatial quantum confinement of electrons can be resolved with subnanometre resolution using inline electron holography. For the standard (001) interface, the charge density map obtained by inline electron holography shows that the two-dimensional electron liquid is confined to the interface with narrow spatial extension (~1.0 ± 0.3 nm in the half width). On the other hand, the two-dimensional electron liquid formed at the (111) interface shows a much broader spatial extension (~3.3 ± 0.3 nm) with the maximum density located ~2.4 nm away from the interface, in excellent agreement with density functional theory calculations.

Dielectrics have long been considered as unsuitable for pure electrical switches; under weak electric fields, they show extremely low conductivity, whereas under strong fields, they suffer from irreversible damage. Here, we show that flexoelectricity enables damage-free exposure of dielectrics to strong electric fields, leading to reversible switching between electrical states—insulating and conducting. Applying strain gradients with an atomic force microscope tip polarizes an ultrathin film of an archetypal dielectric SrTiO 3 via flexoelectricity, which in turn generates non-destructive, strong electrostatic fields. When the applied strain gradient exceeds a certain value, SrTiO 3 suddenly becomes highly conductive, yielding at least around a 10 8 -fold decrease in room-temperature resistivity. We explain this phenomenon, which we call the colossal flexoresistance, based on the abrupt increase in the tunneling conductance of ultrathin SrTiO 3 under strain gradients. Our work extends the scope of electrical control in solids, and inspires further exploration of dielectric responses to strong electromechanical fields. Manipulating the electric state of large band gap dielectrics without any damage is quite challenging. Here, the authors demonstrate by mechanically introducing strain gradients that large electric fields are generated via flexoelectric interactions, resulting in a reversible Zener breakdown in SrTiO 3 , changing the resistivity by 10 8 .

Two-level systems based on point defects in dielectric oxides offer promising entropy source for random number generators. The random telegraph noise (RTN) generated by the two-level systems is ideal for creating random bit-strings for advanced computing and cryptographic technologies. However, in classical oxide systems, RTN signals often suffer from instability due to undesired defect migration and metastable electronic states. Herein, we present a two-level quantum system based on SrRuO 3 /LaAlO 3 /Nb-doped SrTiO 3 heterostructure, which incorporates two different types of point defects, oxygen vacancies and antisite Ti defects. Temporal electron localization at antisite defects alters the energy levels of nearby oxygen vacancies through instantaneous Coulomb interaction, resulting in two-level current fluctuation across the interface. The RTN-like current signals exhibit high stability at room temperature. We utilize the stable two-level fluctuations to generate random bit-strings and confirm their applicability in practical stochastic machine learning algorithms for image super-resolution. This study provides a guideline for designing reliable entropy sources by exploiting the complementary interactions between cation and anion point defects in oxide-based electronic systems, essential for hardware-based random number generators. Random telegraph noise signals often suffer from low stability. Here, the authors demonstrate a two-level quantum system that incorporates two different types of point defects and produces highly stable random telegraph noise-like current signals.

Domain-wall nanoelectronics is considered to be a new paradigm for non-volatile memory and logic technologies in which domain walls, rather than domains, serve as an active element. Especially interesting are charged domain walls in ferroelectric structures, which have subnanometre thicknesses and exhibit non-trivial electronic and transport properties that are useful for various nanoelectronics applications 1 – 3 . The ability to deterministically create and manipulate charged domain walls is essential to realize their functional properties in electronic devices. Here we report a strategy for the controllable creation and manipulation of in-plane charged domain walls in BiFeO 3 ferroelectric films a few nanometres thick. By using an in situ biasing technique within a scanning transmission electron microscope, an unconventional layer-by-layer switching mechanism is detected in which ferroelectric domain growth occurs in the direction parallel to an applied electric field. Based on atomically resolved electron energy-loss spectroscopy, in situ charge mapping by in-line electron holography and theoretical calculations, we show that oxygen vacancies accumulating at the charged domain walls are responsible for the domain-wall stability and motion. Voltage control of the in-plane domain-wall position within a BiFeO 3 film gives rise to multiple non-volatile resistance states, thus demonstrating the key functional property of being a memristor a few unit cells thick. These results promote a better understanding of ferroelectric switching behaviour and provide a new strategy for creating unit-cell-scale devices. The direct observation of in-plane charged domain walls in BiFeO 3 ferroelectric films a few nanometres thick, their deterministic creation, manipulation and annihilation by applied voltage, as well the demonstration of their memristive functionality is reported.

In the version of this Letter originally published, in two instances in Fig. 1 the layers in the cross-sectional view of the (001) interface were incorrectly labelled: in Fig. 1b SrO+ should have read SrO0; in Fig. 1c LaO+, AlO2–, LaO+, TiO20, SrO+, TiO20 should have read LaO33–, Al3+, LaO33–, Ti4+, SrO34–, Ti4+. In Fig. 3c the upper-right equation read –σs = –e/2a2 but should have read –σs = e/2a2 and in Fig. 3f the lower-right equation read –σs = –e/2√3a2 but should have read σs = –e/2√3a2. These errors have now been corrected in the online version of the Letter.

Coupling between different degrees of freedom, that is, charge, spin, orbital and lattice, is responsible for emergent phenomena in complex oxide heterostrutures1,2. One example is the formation of a two-dimensional electron gas (2DEG) at the polar/non-polar LaAlO3/SrTiO3 (LAO/STO)3–7 interface. This is caused by the polar discontinuity and counteracts the electrostatic potential build-up across the LAO film3. The ferroelectric polarization at a ferroelectric/insulator interface can also give rise to a polar discontinuity8–10. Depending on the polarization orientation, either electrons or holes are transferred to the interface, to form either a 2DEG or two-dimensional hole gas (2DHG)11–13. While recent first-principles modelling predicts the formation of 2DEGs at the ferroelectric/insulator interfaces9,10,12–14, experimental evidence of a ferroelectrically induced interfacial 2DEG remains elusive. Here, we report the emergence of strongly anisotropic polarization-induced conductivity at a ferroelectric/insulator interface, which shows a strong dependence on the polarization orientation. By probing the local conductance and ferroelectric polarization over a cross-section of a BiFeO3–TbScO3 (BFO/TSO) (001) heterostructure, we demonstrate that this interface is conducting along the 109° domain stripes in BFO, whereas it is insulating in the direction perpendicular to these domain stripes. Electron energy-loss spectroscopy and theoretical modelling suggest that the anisotropy of the interfacial conduction is caused by an alternating polarization associated with the ferroelectric domains, producing either electron or hole doping of the BFO/TSO interface.

In the version of this Letter originally published, the right-hand arrow in Fig. 3b was incorrectly labelled; see correction note for details. Also, ref. 29 was incorrectly included in the reference list; it has now been removed.

Magnetic tunnel junctions (MTJs) are key components of spintronic devices, such as magnetic random-access memories. Normally, MTJs consist of two ferromagnetic (FM) electrodes separated by an insulating barrier layer. Their key functional property is tunneling magnetoresistance (TMR) that is a change in MTJ's resistance when magnetization of the two electrodes alters from parallel to antiparallel. Here, we demonstrate that TMR can occur in MTJs with a single FM electrode, provided that the counter electrode is an antiferromagnetic (AFM) metal that supports a spin-split band structure and/or a Néel spin current. Using RuO\\(_2\\) as a representative example of such antiferromagnet and CrO\\(_2\\) as a FM metal, we design all-rutile RuO\\(_2\\)/TiO\\(_2\\)/CrO\\(_2\\) MTJs to reveal a non-vanishing TMR. Our first-principles calculations predict that magnetization reversal in CrO\\(_2\\) significantly changes conductance of the MTJs stacked in the (110) or (001) planes. The predicted giant TMR effect of about 1000% in the (110) oriented MTJs stems from spin-dependent conduction channels in CrO\\(_2\\) (110) and RuO\\(_2\\) (110), whose matching alters with CrO\\(_2\\) magnetization orientation, while TMR in the (001) oriented MTJs originates from the Néel spin currents and different effective TiO\\(_2\\) barrier thickness for the two magnetic sublattices that can be engineered by the alternating deposition of TiO\\(_2\\) and CrO\\(_2\\) monolayers. Our results demonstrate a possibility of a sizable TMR in MTJs with a single FM electrode and offer a practical test for using the altermagnet RuO\\(_2\\) in functional spintronic devices.