Inverse transition of labyrinthine domain patterns in ferroelectric thin films.

Phase separation is a cooperative process, the kinetics of which underpin the orderly morphogenesis of domain patterns on mesoscopic scales1,2. Systems of highly degenerate frozen states may exhibit the rare and counterintuitive inverse-symmetry-breaking phenomenon3. Proposed a century ago4, inverse transitions have been found experimentally in disparate materials, ranging from polymeric and colloidal compounds to high-transition-temperature superconductors, proteins, ultrathin magnetic films, liquid crystals and metallic alloys5,6, with the notable exception of ferroelectric oxides, despite extensive theoretical and experimental work on the latter. Here we show that following a subcritical quench, the non-equilibrium self-assembly of ferroelectric domains in ultrathin films of Pb(Zr0.4Ti0.6)O3 results in a maze, or labyrinthine pattern, featuring meandering stripe domains. Furthermore, upon increasing the temperature, this highly degenerate labyrinthine phase undergoes an inverse transition whereby it transforms into the less-symmetric parallel-stripe domain structure, before the onset of paraelectricity at higher temperatures. We find that this phase sequence can be ascribed to an enhanced entropic contribution of domain walls, and that domain straightening and coarsening is predominantly driven by the relaxation and diffusion of topological defects. Computational modelling and experimental observation of the inverse dipolar transition in BiFeO3 suggest the universality of the phenomenon in ferroelectric oxides. The multitude of self-patterned states and the various topological defects that they embody may be used beyond current domain and domain-wall-based7 technologies by enabling fundamentally new design principles and topologically enhanced functionalities within ferroelectric films.

Real-space imaging of non-collinear antiferromagnetic order with a single-spin magnetometer.

Although ferromagnets have many applications, their large magnetization and the resulting energy cost for switching magnetic moments bring into question their suitability for reliable low-power spintronic devices. Non-collinear antiferromagnetic systems do not suffer from this problem, and often have extra functionalities: non-collinear spin order may break space-inversion symmetry and thus allow electric-field control of magnetism, or may produce emergent spin-orbit effects that enable efficient spin-charge interconversion. To harness these traits for next-generation spintronics, the nanoscale control and imaging capabilities that are now routine for ferromagnets must be developed for antiferromagnetic systems. Here, using a non-invasive, scanning single-spin magnetometer based on a nitrogen-vacancy defect in diamond, we demonstrate real-space visualization of non-collinear antiferromagnetic order in a magnetic thin film at room temperature. We image the spin cycloid of a multiferroic bismuth ferrite (BiFeO3) thin film and extract a period of about 70 nanometres, consistent with values determined by macroscopic diffraction. In addition, we take advantage of the magnetoelectric coupling present in BiFeO3 to manipulate the cycloid propagation direction by an electric field. Besides highlighting the potential of nitrogen-vacancy magnetometry for imaging complex antiferromagnetic orders at the nanoscale, these results demonstrate how BiFeO3 can be used in the design of reconfigurable nanoscale spin textures.

Author Correction: Electric and antiferromagnetic chiral textures at multiferroic domain walls.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Electric and antiferromagnetic chiral textures at multiferroic domain walls.

Chirality, a foundational concept throughout science, may arise at ferromagnetic domain walls1 and in related objects such as skyrmions2. However, chiral textures should also exist in other types of ferroic materials, such as antiferromagnets, for which theory predicts that they should move faster for lower power3, and ferroelectrics, where they should be extremely small and possess unusual topologies4,5. Here, we report the concomitant observation of antiferromagnetic and electric chiral textures at domain walls in the room-temperature ferroelectric antiferromagnet BiFeO3. Combining reciprocal and real-space characterization techniques, we reveal the presence of periodic chiral antiferromagnetic objects along the domain walls as well as a priori energetically unfavourable chiral ferroelectric domain walls. We discuss the mechanisms underlying their formation and their relevance for electrically controlled topological oxide electronics and spintronics.

Multi-stimuli manipulation of antiferromagnetic domains assessed by second-harmonic imaging.

Among the variety of magnetic textures available in nature, antiferromagnetism is one of the most 'discrete' because of the exact cancellation of its staggered internal magnetization. It is therefore very challenging to probe. However, its insensitivity to external magnetic perturbations, together with the intrinsic sub-picosecond dynamics, make it very appealing for tomorrow's information technologies. Thus, it is essential to understand the microscopic mechanisms governing antiferromagnetic domains to achieve accurate manipulation and control. Using optical second-harmonic generation, a unique and laboratory-available tool, we succeeded in imaging with sub-micrometre resolution both electric and antiferromagnetic orders in the model multiferroic BiFeO3. We show here that antiferromagnetic domains can be manipulated with low power consumption, using sub-coercive electric fields and sub-picosecond light pulses. Interestingly, we also show that antiferromagnetic and ferroelectric domains can behave independently, thus revealing that magneto-electric coupling can lead to various arrangements of the two orders.

Electric-field control of magnetic order above room temperature.

Controlling magnetism by means of electric fields is a key issue for the future development of low-power spintronics. Progress has been made in the electrical control of magnetic anisotropy, domain structure, spin polarization or critical temperatures. However, the ability to turn on and off robust ferromagnetism at room temperature and above has remained elusive. Here we use ferroelectricity in BaTiO3 crystals to tune the sharp metamagnetic transition temperature of epitaxially grown FeRh films and electrically drive a transition between antiferromagnetic and ferromagnetic order with only a few volts, just above room temperature. The detailed analysis of the data in the light of first-principles calculations indicate that the phenomenon is mediated by both strain and field effects from the BaTiO3. Our results correspond to a magnetoelectric coupling larger than previous reports by at least one order of magnitude and open new perspectives for the use of ferroelectrics in magnetic storage and spintronics.

Giant tunnel electroresistance for non-destructive readout of ferroelectric states.

Ferroelectrics possess a polarization that is spontaneous, stable and electrically switchable, and submicrometre-thick ferroelectric films are currently used as non-volatile memory elements with destructive capacitive readout. Memories based on tunnel junctions with ultrathin ferroelectric barriers would enable non-destructive resistive readout. However, the achievement of room-temperature polarization stability and switching at very low thickness is challenging. Here we use piezoresponse force microscopy at room temperature to show robust ferroelectricity down to 1 nm in highly strained BaTiO(3) films; we also use room-temperature conductive-tip atomic force microscopy to demonstrate resistive readout of the polarization state through its influence on the tunnel current. The resulting electroresistance effect scales exponentially with ferroelectric film thickness, reaching approximately 75,000% at 3 nm. Our approach exploits the otherwise undesirable leakage current-dominated by tunnelling at these very low thicknesses-to read the polarization state without destroying it. We demonstrate scalability down to 70 nm, corresponding to potential densities of >16 Gbit inch(-2). These results pave the way towards ferroelectric memories with simplified architectures, higher densities and faster operation, and should inspire further exploration of the interplay between quantum tunnelling and ferroelectricity at the nanoscale.

Crafting the magnonic and spintronic response of BiFeO3 films by epitaxial strain.

Multiferroics are compounds that show ferroelectricity and magnetism. BiFeO3, by far the most studied, has outstanding ferroelectric properties, a cycloidal magnetic order in the bulk, and many unexpected virtues such as conductive domain walls or a low bandgap of interest for photovoltaics. Although this flurry of properties makes BiFeO3 a paradigmatic multifunctional material, most are related to its ferroelectric character, and its other ferroic property--antiferromagnetism--has not been investigated extensively, especially in thin films. Here we bring insight into the rich spin physics of BiFeO3 in a detailed study of the static and dynamic magnetic response of strain-engineered films. Using Mössbauer and Raman spectroscopies combined with Landau-Ginzburg theory and effective Hamiltonian calculations, we show that the bulk-like cycloidal spin modulation that exists at low compressive strain is driven towards pseudo-collinear antiferromagnetism at high strain, both tensile and compressive. For moderate tensile strain we also predict and observe indications of a new cycloid. Accordingly, we find that the magnonic response is entirely modified, with low-energy magnon modes being suppressed as strain increases. Finally, we reveal that strain progressively drives the average spin angle from in-plane to out-of-plane, a property we use to tune the exchange bias and giant-magnetoresistive response of spin valves.

Interface-induced room-temperature multiferroicity in BaTiO3.

Multiferroic materials possess two or more ferroic orders but have not been exploited in devices owing to the scarcity of room-temperature examples. Those that are ferromagnetic and ferroelectric have potential applications in multi-state data storage if the ferroic orders switch independently, or in electric-field controlled spintronics if the magnetoelectric coupling is strong. Future applications could also exploit toroidal moments and optical effects that arise from the simultaneous breaking of time-reversal and space-inversion symmetries. Here, we use soft X-ray resonant magnetic scattering and piezoresponse force microscopy to reveal that, at the interface with Fe or Co, ultrathin films of the archetypal ferroelectric BaTiO3 simultaneously possess a magnetization and a polarization that are both spontaneous and hysteretic at room temperature. Ab initio calculations of realistic interface structures provide insight into the origin of the induced moments and bring support to this new approach for creating room-temperature multiferroics.

Thickness-dependent polarization of strained BiFeO3 films with constant tetragonality.

We measure the ferroelectric polarization of BiFeO3 films down to 3.6 nm using low energy electron and photoelectron emission microscopy. The measured polarization decays strongly below a critical thickness of 5-7 nm predicted by continuous medium theory whereas the tetragonal distortion does not change. We resolve this apparent contradiction using first-principles-based effective Hamiltonian calculations. In ultrathin films, the energetics of near open circuit electrical boundary conditions, i.e., an unscreened depolarizing field, drive the system through a phase transition from single out-of-plane polarization to nanoscale stripe domains. It gives rise to an average polarization close to zero as measured by the electron microscopy while maintaining the relatively large tetragonal distortion imposed by the nonzero polarization state of each individual domain.

Multiferroic phase transition near room temperature in BiFeO3 films.

In multiferroic BiFeO(3) thin films grown on highly mismatched LaAlO(3) substrates, we reveal the coexistence of two differently distorted polymorphs that leads to striking features in the temperature dependence of the structural and multiferroic properties. Notably, the highly distorted phase quasiconcomitantly presents an abrupt structural change, transforms from a standard to a nonconventional ferroelectric, and transitions from antiferromagnetic to paramagnetic at 360±20 K. These coupled ferroic transitions just above room temperature hold promises of giant piezoelectric, magnetoelectric, and piezomagnetic responses, with potential in many applications fields.

Bridging multiferroic phase transitions by epitaxial strain in BiFeO3.

We report the influence of epitaxial strain on the multiferroic phase transitions of BiFeO3 films. Using advanced characterization techniques and calculations we show that while the magnetic Néel temperature hardly varies, the ferroelectric Curie temperature TC decreases dramatically with strain. This is in contrast with the behavior of standard ferroelectrics where strain enhances the polar cation shifts and thus TC. We argue that this is caused by an interplay of polar and oxygen tilting instabilities and that strain can drive both transitions close together to yield increased magnetoelectric responses.

A versatile nanotechnology to connect individual nano-objects for the fabrication of hybrid single-electron devices.

We report on the high yield connection of single nano-objects as small as a few nanometres in diameter to separately elaborated metallic electrodes, using a 'table-top' nanotechnology. Single-electron transport measurements validate that transport occurs through a single nano-object. The vertical geometry of the device natively allows an independent choice of materials for each electrode and the nano-object. In addition ferromagnetic materials can be used without encountering oxidation problems. The possibility of elaborating such hybrid nanodevices opens new routes for the democratization of spintronic studies in low dimensions.

Antiferromagnetic textures in BiFeO3 controlled by strain and electric field.

Antiferromagnetic thin films are currently generating considerable excitement for low dissipation magnonics and spintronics. However, while tuneable antiferromagnetic textures form the backbone of functional devices, they are virtually unknown at the submicron scale. Here we image a wide variety of antiferromagnetic spin textures in multiferroic BiFeO3 thin films that can be tuned by strain and manipulated by electric fields through room-temperature magnetoelectric coupling. Using piezoresponse force microscopy and scanning NV magnetometry in self-organized ferroelectric patterns of BiFeO3, we reveal how strain stabilizes different types of non-collinear antiferromagnetic states (bulk-like and exotic spin cycloids) as well as collinear antiferromagnetic textures. Beyond these local-scale observations, resonant elastic X-ray scattering confirms the existence of both types of spin cycloids. Finally, we show that electric-field control of the ferroelectric landscape induces transitions either between collinear and non-collinear states or between different cycloids, offering perspectives for the design of reconfigurable antiferromagnetic spin textures on demand.

Mapping the spatial distribution of charge carriers in LaAlO3/SrTiO3 heterostructures.

At the interface between complex insulating oxides, novel phases with interesting properties may occur, such as the metallic state reported in the LaAlO(3)/SrTiO(3) system . Although this state has been predicted and reported to be confined at the interface, some studies indicate a much broader spatial extension, thereby questioning its origin. Here, we provide for the first time a direct determination of the carrier density profile of this system through resistance profile mappings collected in cross-section LaAlO(3)/SrTiO(3) samples with a conducting-tip atomic force microscope (CT-AFM). We find that, depending on specific growth protocols, the spatial extension of the high-mobility electron gas can be varied from hundreds of micrometres into SrTiO(3) to a few nanometres next to the LaAlO(3)/SrTiO(3) interface. Our results emphasize the potential of CT-AFM as a novel tool to characterize complex oxide interfaces and provide us with a definitive and conclusive way to reconcile the body of experimental data in this system.

Large elasto-optic effect and reversible electrochromism in multiferroic BiFeO3.

The control of optical fields is usually achieved through the electro-optic or acousto-optic effect in single-crystal ferroelectric or polar compounds such as LiNbO3 or quartz. In recent years, tremendous progress has been made in ferroelectric oxide thin film technology-a field which is now a strong driving force in areas such as electronics, spintronics and photovoltaics. Here, we apply epitaxial strain engineering to tune the optical response of BiFeO3 thin films, and find a very large variation of the optical index with strain, corresponding to an effective elasto-optic coefficient larger than that of quartz. We observe a concomitant strain-driven variation in light absorption--reminiscent of piezochromism--which we show can be manipulated by an electric field. This constitutes an electrochromic effect that is reversible, remanent and not driven by defects. These findings broaden the potential of multiferroics towards photonics and thin film acousto-optic devices, and suggest exciting device opportunities arising from the coupling of ferroic, piezoelectric and optical responses.

Tunnel electroresistance through organic ferroelectrics.

Organic electronics is emerging for large-area applications such as photovoltaic cells, rollable displays or electronic paper. Its future development and integration will require a simple, low-power organic memory, that can be written, erased and readout electrically. Here we demonstrate a non-volatile memory in which the ferroelectric polarisation state of an organic tunnel barrier encodes the stored information and sets the readout tunnel current. We use high-sensitivity piezoresponse force microscopy to show that films as thin as one or two layers of ferroelectric poly(vinylidene fluoride) remain switchable with low voltages. Submicron junctions based on these films display tunnel electroresistance reaching 1,000% at room temperature that is driven by ferroelectric switching and explained by electrostatic effects in a direct tunnelling regime. Our findings provide a path to develop low-cost, large-scale arrays of organic ferroelectric tunnel junctions on silicon or flexible substrates.

Control of ferroelectricity and magnetism in multi-ferroic BiFeO3 by epitaxial strain.

Recently, strain engineering has been shown to be a powerful and flexible means of tailoring the properties of ABO3 perovskite thin films. The effect of epitaxial strain on the structure of the perovskite unit cell can induce a host of interesting effects, these arising from either polar cation shifts or rotation of the oxygen octahedra, or both. In the multi-ferroic perovskite bismuth ferrite (BiFeO3-BFO), both degrees of freedom exist, and thus a complex behaviour may be expected as one plays with epitaxial strain. In this paper, we review our results on the role of strain on the ferroic transition temperatures and ferroic order parameters. We find that, while the Néel temperature is almost unchanged by strain, the ferroelectric Curie temperature strongly decreases as strain increases in both the tensile and compressive ranges. Also unexpected is the very weak influence of strain on the ferroelectric polarization value. Using effective Hamiltonian calculations, we show that these peculiar behaviours arise from the competition between antiferrodistortive and polar instabilities. Finally, we present results on the magnetic order: while the cycloidal spin modulation present in the bulk survives in weakly strained films, it is destroyed at large strain and replaced by pseudo-collinear antiferromagnetic ordering. We discuss the origin of this effect and give perspectives for devices based on strain-engineered BiFeO3.

Strain dependence of polarization and piezoelectric response in epitaxial BiFeO3 thin films.

Epitaxial strain has recently emerged as a powerful means to engineer the properties of ferroelectric thin films, for instance to enhance the ferroelectric Curie temperature (T(C)) in BaTiO(3). However, in multiferroic BiFeO(3) thin films an unanticipated strain-driven decrease of T(C) was reported and ascribed to the peculiar competition between polar and antiferrodistortive instabilities. Here, we report a systematic characterization of the room-temperature ferroelectric and piezoelectric properties for strain levels ranging between -2.5% and +1%. We find that polarization and the piezoelectric coefficient increase by about 20% and 250%, respectively, in this strain range. These trends are well reproduced by first-principles-based techniques.

Ferroelectric control of spin polarization.

A current drawback of spintronics is the large power that is usually required for magnetic writing, in contrast with nanoelectronics, which relies on "zero-current," gate-controlled operations. Efforts have been made to control the spin-relaxation rate, the Curie temperature, or the magnetic anisotropy with a gate voltage, but these effects are usually small and volatile. We used ferroelectric tunnel junctions with ferromagnetic electrodes to demonstrate local, large, and nonvolatile control of carrier spin polarization by electrically switching ferroelectric polarization. Our results represent a giant type of interfacial magnetoelectric coupling and suggest a low-power approach for spin-based information control.