The secondary nature of polarization in improper ferroelectrics promotes functional properties beyond those of conventional ferroelectrics. In technologically relevant ultrathin films, however, the improper ferroelectric behavior remains largely unexplored. Here, we probe the emergence of the coupled improper polarization and primary distortive order parameter in thin films of hexagonal YMnO₃. Combining state-of-the-art in situ characterization techniques separately addressing the improper ferroelectric state and its distortive driving force, we reveal a pronounced thickness dependence of the improper polarization, which we show to originate from the strong modification of the primary order at epitaxial interfaces. Nanoscale confinement effects on the primary order parameter reduce the temperature of the phase transition, which we exploit to visualize its order-disorder character with atomic resolution. Our results advance the understanding of the evolution of improper ferroelectricity within the confinement of ultrathin films, which is essential for their successful implementation in nanoscale applications.

Forthcoming low-energy consumption oxide electronics rely on the deterministic control of ferroelectric and multiferroic domain states at the nanoscale. In this review, we address the recent progress in the field of investigation of ferroic order in thin films and heterostructures, with a focus on non-invasive optical second harmonic generation (SHG). For more than 50 years, SHG has served as an established technique for probing ferroic order in bulk materials. Here, we will survey the specific new aspects introduced to SHG investigation of ferroelectrics and multiferroics by working with thin film structures. We show how SHG can probe complex ferroic domain patterns non-invasively and even if the lateral domain size is below the optical resolution limit or buried beneath an otherwise impenetrable cap layer. We emphasize the potential of SHG to distinguish contributions from individual (multi-) ferroic films or interfaces buried in a device or multilayer architecture. Special attention is given to monitoring switching events in buried ferroic domain- and domain-wall distributions by SHG, thus opening new avenues towards the determination of the domain dynamics. Another aspect studied by SHG is the role of strain. We will finally show that by integrating SHG into the ongoing thin film deposition process, we can monitor the emergence of ferroic order and properties in situ, while they emerge during growth. Our review closes with an outlook, emphasizing the present underrepresentation of ferroic switching dynamics in the study of ferroic oxide heterostructures.

Hexagonal ABO₃ oxides (A, B = cation) are a class of rich materials for realizing novel quantum phenomena. Their hexagonal symmetry, oxygen trigonal bipyramid coordination, and quasi-two dimensional layering give rise to properties distinct from those of the cubic ABO₃ perovskites. As bulk materials, most of the focus in this class of materials has been on the rare-earth manganites, RMnO₃ (R = rare earth); these materials display coupled ferroelectricity and antiferromagnetic order. In this review, we focus on the thin-film manifestations of the hexagonal ABO₃ oxides. We cover the stability of the hexagonal oxides and substrates which can be used to template the hexagonal structure. We show how the thin-film geometry not only allows for further tuning of the bulk-stable manganites but also allows for the realization of metastable hexagonal oxides such as the RFeO₃ that combine ferroelectricity with weak ferromagnetic order. The thin-film geometry is a promising platform to stabilize additional metastable hexagonal oxides to search for predicted high-temperature superconductivity and topological phases in this class of materials.

We investigate the ferroelectric domain architecture and its operando response to an external electric field in ${\mathrm{BaTiO}}_3$-based electro-optic heterostructures integrated on silicon. By noninvasive optical second-harmonic generation, we identify the preexistence of in-plane ($a$-) domains dispersed within a predominantly out-of-plane- ($c$-) oriented matrix. Monitoring the poling behavior of the respective domain populations, we show that the spontaneous polarization of these $a$-domains lack a predominant orientation in the pristine state, yet can be selectively aligned with an in-plane electric field, leaving the $c$-domain population intact. Hence, domain reorientation of a ferroelastic $c$-to-$a$ type was directly excluded. Such independent electrical control of ferroelectric $a$-domains in a $c$-oriented ${\mathrm{BaTiO}}_3$ film on silicon is a valuable platform for engineering multidirectional electro-optic functionality in integrated photonic devices.

The current burst of device concepts based on nanoscale domain-control in magnetically and electrically ordered systems motivates us to review the recent development in the design of domain engineered oxide heterostructures. The improved ability to design and control advanced ferroic domain architectures came hand in hand with major advances in investigation capacity of nanoscale ferroic states. The new avenues offered by prototypical multiferroic materials, in which electric and magnetic orders coexist, are expanding beyond the canonical low-energy-consuming electrical control of a net magnetization. Domain pattern inversion, for instance, holds promises of increased functionalities. In this review, we first describe the recent development in the creation of controlled ferroelectric and multiferroic domain architectures in thin films and multilayers. We then present techniques for probing the domain state with a particular focus on non-invasive tools allowing the determination of buried ferroic states. Finally, we discuss the switching events and their domain analysis, providing critical insight into the evolution of device concepts involving multiferroic thin films and heterostructures.

Diode effects are of great interest for both fundamental physics and modern technologies. Electrical diode effects (nonreciprocal transport) have been observed in Weyl systems. Optical diode effects arising from the Weyl fermions have been theoretically considered but not probed experimentally. Here, we report the observation of a nonlinear optical diode effect (NODE) in the magnetic Weyl semimetal CeAlSi, where the magnetization introduces a pronounced directionality in the nonlinear optical second-harmonic generation (SHG). We demonstrate a six-fold change of the measured SHG intensity between opposite propagation directions over a bandwidth exceeding 250 meV. Supported by density-functional theory, we establish the linearly dispersive bands emerging from Weyl nodes as the origin of this broadband effect. We further demonstrate current-induced magnetization switching and thus electrical control of the NODE. Our results advance ongoing research to identify novel nonlinear optical/transport phenomena in magnetic topological materials and further opens new pathways for the unidirectional manipulation of light.