Since its inception more than 25 years ago, Piezoresponse Force Microscopy (PFM) has become one of the mainstream techniques in the field of nanoferroic materials. This review describes the evolution of PFM from an imaging technique to a set of advanced methods, which have played a critical role in launching new areas of ferroic research, such as multiferroic devices and domain wall nanoelectronics. The paper reviews the impact of advanced PFM modes concerning the discovery and scientific understanding of novel nanoferroic phenomena and discusses challenges associated with the correct interpretation of PFM data. In conclusion, it offers an outlook for future trends and developments in PFM.

Local perturbations in complex oxides such as domain walls 1,2 , strain 3,4 and defects 5,6 are of interest because they can modify the conduction or the dielectric and magnetic response and even promote phase transitions. Here we show that the interaction between different types of local perturbations in oxide thin films is an additional source of functionality. Taking SrMnO 3 as a model system, we use nonlinear optics to verify the theoretical prediction that strain induces a polar phase, and density functional theory to show that strain simultaneously increases the concentration of oxygen vacancies. These vacancies couple to the polar domain walls where they establish an electrostatic barrier to electron migration. The result 2 is a state with locally structured room-temperature conductivity consisting of conducting nanosized polar domains encased by insulating domain boundaries, which we resolve using scanning probe microscopy. Our "nanocapacitor" domains can be individually charged, suggesting stable capacitance nanobits with a potential for information storage technology.At first we verify the occurrence of strain-induced polar order in SrMnO 3 thin films.Motivated by the search for novel multiferroic materials, which combine magnetic and ferroelectric orders in the same phase, density functional theory (DFT) predicted the occurrence of ferroelectricity in the perovskite-structure alkaline-earth manganites at larger-than-equilibrium lattice parameters 7,8,9 . For bulk SrMnO 3 this prediction was confirmed by partial substitution of Sr by Ba which induces negative chemical pressure and leads to a polar state 10 . According to DFT, epitaxial SrMnO 3 films should develop a polarisation along one of the pseudocubic <110> axes under >1% epitaxial tensile strain 8 .20-nm films of single-phase SrMnO 3 were grown using pulsed laser deposition on (001)-oriented (LaAlO 3 ) 0.3 (Sr 2 AlTaO 6 ) 0.7 (LSAT) with 1.7% tensile strain (see Methods). We characterised the strain state of the films using scanning transmission electron microscopy (STEM) and X-ray and electron diffraction. Figure 1a shows a cross-sectional STEM image evidencing the high quality of the films on the atomic scale with a sharp SrMnO 3 /LSAT (001) interface. The reciprocal space map in Fig. 1a verifies that the films are tetragonal and coherently strained. The electron diffraction In the anisotropy plot in Fig. 1c we present the optical polarisation analysis of the SHG signal obtained on a test area of 0.1 mm 2 . We fitted the angular dependence of the SHG signal by assuming a distribution of four polar domain states denoted as P 1+ , P 1− , P 2+ , P 2− . The indices refer to the orientation of the polar axis according to 1 ± ↔ ±[110] and 2 ± ↔ ±[1 10], see Fig. 1c. The coincidence of the measured data and the fit is excellent with a fitted ratio r = P 1 /P 2 = 0.53 in the population of P 1 -and P 2 -type domain states (r varied between different test areas). In contrast, fits assuming a polarisation along the[100] and [010] directions failed. We co...

Ferroelectric domain walls hold great promise as functional 2D-materials because of their unusual electronic properties. Particularly intriguing are the so-called charged walls where a polarity mismatch causes local, diverging electrostatic potentials requiring charge compensation and hence a change in the electronic structure. These walls can exhibit significantly enhanced conductivity and serve as a circuit path. The development of all-domain-wall devices, however, also requires walls with controllable output to emulate electronic nano-components such as diodes and transistors. Here we demonstrate electric-field control of the electronic transport at ferroelectric domain walls. We reversibly switch from resistive to conductive behavior at charged walls in semiconducting ErMnO 3. We relate the transition to the formation-and eventual activation-of an inversion layer that acts as the channel for the charge transport. The findings provide new insight to the domain-wall physics in ferroelectrics and foreshadow the possibility to design elementary digital devices for all-domain-wall circuitry.

Domain walls in ferroelectric semiconductors show promise as multifunctional two-dimensional elements for next-generation nanotechnology. Electric fields, for example, can control the direct-current resistance and reversibly switch between insulating and conductive domain-wall states, enabling elementary electronic devices such as gates and transistors. To facilitate electrical signal processing and transformation at the domain-wall level, however, an expansion into the realm of alternating-current technology is required. Here, we demonstrate diode-like alternating-to-direct current conversion based on neutral ferroelectric domain walls in ErMnO. By combining scanning probe and dielectric spectroscopy, we show that the rectification occurs at the tip-wall contact for frequencies at which the walls are effectively pinned. Using density functional theory, we attribute the responsible transport behaviour at the neutral walls to an accumulation of oxygen defects. The practical frequency regime and magnitude of the direct current output are controlled by the bulk conductivity, establishing electrode-wall junctions as versatile atomic-scale diodes.

Ferroelectric and ferroelastic domain walls are two-dimensional (2D) topological defects with thicknesses approaching the unit cell level. When this spatial confinement is combined with observations of emergent functional properties, such as polarity in non-polar systems or electrical conductivity in otherwise insulating materials, it becomes clear that domain walls represent a new and exciting state of matter. In this review, we discuss the exotic polarisation profiles that can arise at domain walls with multiple order parameters and the different mechanisms that lead to domain wall polarity in non-polar ferroelastic materials. The emergence of energetically degenerate variants of the domain walls themselves suggests the existence of interesting quasi-1D topological defects within such walls. We also provide an overview of the general notions which have been postulated as fundamental mechanisms responsible for domain wall conduction in ferroelectrics. We then discuss the prospect of combining domain walls with transition regions observed at phase boundaries, homo-and heterointerfaces, and other quasi-2D objects, enabling emergent properties beyond those available in today's topological systems. Key points• In ferroelectrics, the emergence of a second polarisation component leads to analogues of Bloch and Néel walls. The stabilization of these walls opens the possibility for quasi-1D topological defects separating wall regions of opposite polarities.• Polar domain walls in ferroelastics rely on two mechanisms: a polarity imposed by the natural symmetry of strain-compatible domain walls, which can often be described by flexoelectric gradient coupling, and the emergence of a potentially switchable polarity when their natural symmetry is broken.• Several mechanisms are responsible for domain wall conduction in ferroelectrics: extrinsic intra-bandgap defect states, intrinsic suppression of the conduction band and intrinsic shift of the band structure induced by local electric fields.• Transition regions occurring at phase boundaries, homo-and heterointerfaces, and other quasi-2D objects probably exist at a smaller length scale, in the vicinity of domain walls, and could lead to exceptional properties and coupling phenomena.

During the last decade a wide variety of novel and fascinating correlation phenomena has been discovered at domain walls in multiferroic bulk systems, ranging from unusual electronic conductance to inseparably entangled spin and charge degrees of freedom. The domain walls represent quasi-2D functional objects that can be induced, positioned, and erased on demand, bearing considerable technological potential for future nanoelectronics. Most of the challenges that remain to be solved before turning related device paradigms into reality, however, still fall in the field of fundamental condensed matter physics and materials science. In this topical review seminal experimental findings gained on electric and magnetic domain walls in multiferroic bulk materials are addressed. A special focus is put on the physical properties that emerge at so-called charged domain walls and the added functionality that arises from coexisting magnetic order. The research presented in this review highlights that we are just entering a whole new world of intriguing nanoscale physics that is yet to be explored in all its details. The goal is to draw attention to the persistent challenges and identify future key directions for the research on functional domain walls in multiferroics.

A magnetic helix arises in chiral magnets with a wavelength set by the spin-orbit coupling.We show that the helimagnetic order is a nanoscale analog to liquid crystals, exhibiting topological structures and domain walls that are distinctly different from classical magnets. Using magnetic force microscopy and micromagnetic simulations, we demonstrate that -similar to cholesteric liquid crystals -three fundamental types of domain walls are realized in the helimagnet FeGe. We reveal the micromagnetic wall structure and show that they can carry a finite skyrmion charge, permitting coupling to spin currents and contributions to a topolog-arXiv:1704.06288v1 [cond-mat.str-el] 20 Apr 2017 ical Hall effect. Our study establishes a new class of magnetic nano-objects with non-trivial topology, opening the door to innovative device concepts based on helimagnetic domain walls.

The complex interplay between the 3d and 4 f moments in hexagonal ErMnO 3 is investigated by magnetization, optical second harmonic generation, and neutron-diffraction measurements. We revise the phase diagram and provide a microscopic model for the emergent spin structures with a special focus on the intermediary phase transitions. Our measurements reveal that the 3d exchange between Mn 3+ ions dominates the magnetic symmetry at 10 K < T < T N with Mn 3+ order according to the Γ 4 representation triggering 4 f ordering according to the same representation on the Er 3+ (4b) site. Below 10 K the magnetic order is governed by 4 f exchange interactions of Er 3+ ions on the 2a site. The magnetic Er 3+ (2a) order according to the representation Γ 2 induces a magnetic reorientation (Γ 4 → Γ 2 ) at the Er 3+ (4b) and the Mn 3+ sites. Our findings highlight the fundamentally different roles the Mn 3+ , R 3+ (2a), and R 3+ (4b) magnetism play in establishing the magnetic phase diagram of the hexagonal RMnO 3 system.