The complex interplay of spin, charge, orbital and lattice degrees of freedom provides a plethora of exotic phases and physical phenomena. In recent years, complex spin topologies have emerged as a consequence of the electronic band structure and the interplay between spin and spin-orbit coupling in materials. Here we produce complex topologies of electrical polarization--namely, nanometre-scale vortex-antivortex (that is, clockwise-anticlockwise) arrays that are reminiscent of rotational spin topologies--by making use of the competition between charge, orbital and lattice degrees of freedom in superlattices of alternating lead titanate and strontium titanate layers. Atomic-scale mapping of the polar atomic displacements by scanning transmission electron microscopy reveals the presence of long-range ordered vortex-antivortex arrays that exhibit nearly continuous polarization rotation. Phase-field modelling confirms that the vortex array is the low-energy state for a range of superlattice periods. Within this range, the large gradient energy from the vortex structure is counterbalanced by the corresponding large reduction in overall electrostatic energy (which would otherwise arise from polar discontinuities at the lead titanate/strontium titanate interfaces) and the elastic energy associated with epitaxial constraints and domain formation. These observations have implications for the creation of new states of matter (such as dipolar skyrmions, hedgehog states) and associated phenomena in ferroic materials, such as electrically controllable chirality.

A new development in small-angle neutron scattering with polarization analysis allows us to directly extract the average spatial distributions of magnetic moments and their correlations with threedimensional directional sensitivity in any magnetic field. Applied to a collection of spherical magnetite nanoparticles 9.0 nm in diameter, this enhanced method reveals uniformly canted, magnetically active shells in a nominally saturating field of 1.2 T. The shell thickness depends on temperature, and it disappears altogether when the external field is removed, confirming that these canted nanoparticle shells are magnetic, rather than structural, in origin.

Single-crystalline thin films of complex oxides show a rich variety of functional properties such as ferroelectricity, piezoelectricity, ferro and antiferromagnetism and so on that have the potential for completely new electronic applications. Direct synthesis of such oxides on silicon remains challenging because of the fundamental crystal chemistry and mechanical incompatibility of dissimilar interfaces. Here we report integration of thin (down to one unit cell) single crystalline, complex oxide films onto silicon substrates, by epitaxial transfer at room temperature. In a field-effect transistor using a transferred lead zirconate titanate layer as the gate insulator, we demonstrate direct reversible control of the semiconductor channel charge with polarization state. These results represent the realization of long pursued but yet to be demonstrated single-crystal functional oxides on-demand on silicon.

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Domains and domain walls are critical in determining the response of ferroelectrics, and the ability to controllably create, annihilate, or move domains is essential to enable a range of next-generation devices. Whereas electric-field control has been demonstrated for ferroelectric 180° domain walls, similar control of ferroelastic domains has not been achieved. Here, using controlled composition and strain gradients, we demonstrate deterministic control of ferroelastic domains that are rendered highly mobile in a controlled and reversible manner. Through a combination of thin-film growth, transmission-electron-microscopy-based nanobeam diffraction and nanoscale band-excitation switching spectroscopy, we show that strain gradients in compositionally graded PbZr1-xTixO3 heterostructures stabilize needle-like ferroelastic domains that terminate inside the film. These needle-like domains are highly labile in the out-of-plane direction under applied electric fields, producing a locally enhanced piezoresponse. This work demonstrates the efficacy of novel modes of epitaxy in providing new modalities of domain engineering and potential for as-yet-unrealized nanoscale functional devices.

Leveraging competition between energetically degenerate states to achieve large field-driven responses is a hallmark of functional materials, but routes to such competition are limited. Here, a new route to such effects involving domain-structure competition is demonstrated, which arises from strain-induced spontaneous partitioning of PbTiO thin films into nearly energetically degenerate, hierarchical domain architectures of coexisting c/a and a /a domain structures. Using band-excitation piezoresponse force microscopy, this study manipulates and acoustically detects a facile interconversion of different ferroelastic variants via a two-step, three-state ferroelastic switching process (out-of-plane polarized c → in-plane polarized a → out-of-plane polarized c state), which is concomitant with large nonvolatile electromechanical strains (≈1.25%) and tunability of the local piezoresponse and elastic modulus (>23%). It is further demonstrated that deterministic, nonvolatile writing/erasure of large-area patterns of this electromechanical response is possible, thus showing a new pathway to improved function and properties.

Ferroelectric domain walls are of great interest as elementary building blocks for future electronic devices due to their intrinsic few-nanometre width, multifunctional properties and field-controlled topology. To realize the electronic functions, domain walls are required to be electrically conducting and addressable non-destructively. However, these properties have been elusive because conducting walls have to be electrically charged, which makes them unstable and uncommon in ferroelectric materials. Here we reveal that spontaneous and recorded domain walls in thin films of lead zirconate and bismuth ferrite exhibit large conductance at microwave frequencies despite being insulating at d.c. We explain this effect by morphological roughening of the walls and local charges induced by disorder with the overall charge neutrality. a.c. conduction is immune to large contact resistance enabling completely non-destructive walls read-out. This demonstrates a technological potential for harnessing a.c. conduction for oxide electronics and other materials with poor d.c. conduction, particularly at the nanoscale.

Ferroelectrics, with their spontaneous switchable electric polarization and strong coupling between their electrical, mechanical, thermal, and optical responses, provide functionalities crucial for a diverse range of applications. Over the past decade, there has been significant progress in epitaxial strain engineering of oxide ferroelectric thin films to control and enhance the nature of ferroelectric order, alter ferroelectric susceptibilities, and to create new modes of response which can be harnessed for various applications. This review aims to cover some of the most important discoveries in strain engineering over the past decade and highlight some of the new and emerging approaches for strain control of ferroelectrics. We discuss how these new approaches to strain engineering provide promising routes to control and decouple ferroelectric susceptibilities and create new modes of response not possible in the confines of conventional strain engineering. To conclude, we will provide an overview and prospectus of these new and interesting modalities of strain engineering helping to accelerate their widespread development and implementation in future functional devices.