We show that the improper ferroelectric phase transition in the multiferroic hexagonal manganites displays appropriate symmetry-breaking characteristics for testing the Kibble-Zurek mechanism originally proposed to describe early-universe phase transitions. We present an analysis of the Kibble-Zurek theory of topological defect formation applied to the hexagonal manganites, discuss the conditions determining the range of cooling rates in which Kibble-Zurek behavior is expected, and show that recent literature data are consistent with our predictions. Finally, we explore experimentally the crossover out of the Kibble-Zurek regime and find a surprising reversal of the scaling behavior.

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...

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.

1The emergence of the spontaneous polarization in the hexagonal RMnO 3 system (R = Sc, Y, In, Dy -Lu) is one of the singular properties and, at the same time, one of the greatest mysteries of this class of compounds. Taking YMnO 3 as reference compound for the series (see Methods), Curie temperatures inexplicably spreading from 910 K to 1250 K have been reported 10-16, 18, 19 . In some of these cases ferroelectricity has been claimed to emerge together with a trimerizing lattice distortion in a single-step transition 16,18,19 . In other cases these two features have been proposed to occur separately [10][11][12][13][14][15] . On the theoretical side, the two-transition scenario has initially been supported by density-functional-theory calculations 20 . A more detailed analysis, however, suggests improper ferroelectricity triggered by the lattice trimerization in a single-step transition 21,22 , in which secondary anomalies are yet possible due to the breaking of residual symmetries 23 . Direct measurement of the spontaneous polarization as function of temperature would clarify this puzzling situation. This was done once in a pyrocurrent measurement which pointed to an onset of ferroelectricity at 933 K 16 . All attempts to reproduce this experiment failed, however. Thus, in spite of 50 years of research, the emergence of the polar order in the hexagonal RMnO 3 multiferroics is surrounded by contradictions. This uncertainty extends to the universality class of this ferroelectric transition, as this basic question depends on the precise nature of the state undergoing the polar instability. The universality class and the corresponding critical behavior determines important physical properties from the macro-to the nanoscale. Understanding such functionalities is infinitely more difficult if the emergence of the ferroelectric order itself is unclear. Thus, for putting the intense research on the unusual properties of ferroelectric order in the hexagonal RMnO 3 system 2, 3, 5,8,9 onto a solid basis, this situation must be resolved. 2Here we present nonlinear optical experiments in which the electromagnetic field of a frequency-doubled light wave couples directly and linearly to the spontaneous polarization of YMnO 3 .They reveal a polarization emerging at T C 1259 K with a subdued increase in amplitude showing no anomalies or discontinuities. Piezoresponse force microscopy (PFM) confirms that the ferroelectric domain pattern is seeded right below T C . Monte-Carlo simulations reveal how topologically created vortex-like defects in the MnO 5 tilt pattern determine the ferroelectric state and many of its unusual properties. In particular, we show that the "second transition" below T C is not associated to a phase transition, but caused by a finite-size scaling effect.At room temperature, the spontaneous polarization P s = 5.6 µC/cm 2 of YMnO 3 is observed together with unit-cell-trimerizing tilts of the MnO 5 bipyramids and Y displacements along the c axis. The tilt is parameterized 22, 23 by the observable amplitude ...

The controversy regarding the ferroelectric behavior of hexagonal InMnO 3 is resolved by using a combination of x-ray diffraction (XRD), piezoresponse force microscopy (PFM), second harmonic generation (SHG), and density functional theory (DFT). While XRD data show a symmetry-lowering unit-cell tripling, which is also found in the multiferroic hexagonal manganites of P6 3 cm symmetry, PFM and SHG do not detect ferroelectricity at ambient or low temperature, in striking contrast to the behavior in the multiferroic counterparts. We propose instead a centrosymmetric P3c phase as the ground state structure. Our DFT calculations reveal that the relative energy of the ferroelectric and nonferroelectric structures is determined by a competition between electrostatics and oxygen-R-site covalency, with an absence of covalency favoring the ferroelectric phase.

Electronic domain‐wall conductance is controlled by chemical aliovalent doping in the p‐type semiconductor Er1‐xCaxMnO3. Coexisting bound (top panel) and mobile (lower panel) charges at the walls are analyzed using electrostatic force micro­scopy. Emergent doping‐related variations are quantified by local transport measurements and explained based on phenomenological theories.

The spontaneous transformations associated with symmetry-breaking phase transitions generate domain structures and defects that may be topological in nature. The formation of these defects can be described according to the Kibble-Zurek mechanism, which provides a generic relation that applies from cosmological to interatomic lengthscales. Its verification is challenging, however, in particular at the cosmological scale where experiments are impractical. While it has been demonstrated for selected condensed-matter systems, major questions remain regarding e.g. its degree of universality. Here we develop a global Kibble-Zurek picture from the condensed-matter level. We show theoretically that a transition between two fluctuation regimes (Ginzburg and mean-field) can lead to an intermediate region with reversed scaling, and we verify experimentally this behavior for the structural transition in the series of multiferroic hexagonal manganites. Trends across the series allow us to identify additional intrinsic features of the defect formation beyond the original Kibble-Zurek paradigm. arXiv:1703.08321v1 [cond-mat.mtrl-sci]

We deduce the intrinsic conductivity properties of the ferroelectric domain walls around the topologically protected domain vortex cores in multiferroic YMnO3. This is achieved by performing a careful equivalent-circuit analysis of dielectric spectra measured in single-crystalline samples with different vortex densities. The conductivity contrast between the bulk domains and the less conducting domain boundaries is revealed to reach up to a factor 500 at room temperature, depending on sample preparation. Tunneling of localized defect charge carriers is the dominant charge-transport process in the domain walls that are depleted of mobile charge carriers. This work demonstrates that via equivalent-circuit analysis, dielectric spectroscopy can provide valuable information on the intrinsic charge-transport properties of ferroelectric domain walls, which is of high relevance for the design of new domain-wall-based microelectronic devices.The hexagonal manganites RMnO3 (R = Sc, Y, In, and Dy-Lu) form a unique group of multiferroics where a geometrically-driven mechanism triggers improper ferroelectricity [1]. Additional interest in this material class arose from the reported occurrence of vortex-like ferroelectric domain patterns [2,3,4]. Around the vortex cores, forming the centers of "cloverleaf" patterns of six domains, the polarization changes sign six times. These cores, evolving at a high-temperature structural transition [5], represent stable topological defects. Even strong electric fields only lead to a variation of ferroelectric domain sizes in these materials, but are unable to completely eradicate unfavorable domains and to generate a mono-domain state [2,6]. Moreover, there is a strict coupling of ferroelectric and antiferromagnetic domain walls (DWs), the latter forming at much lower temperatures around 100 K [7].Recently it was shown that these complex domain properties also may be of relevance from an application point of view: Conductive atomic-force microscopy (c-AFM) on ErMnO3 [4] and HoMnO3 [8] revealed that the conductance of the ferroelectric DWs is either enhanced or suppressed compared to the domains, being determined by the polarization orientation of the adjacent domains. As the DWs can be easily tuned by external fields, this opens the possibility of domain-boundary engineering and applications in microelectronics using the nanoscale DWs instead of the domains themselves as active device elements [9,10,11,12,13]. The hexagonal manganites seem especially suited for this kind of functionality: Their DWs are robust and represent persistent interfaces as they are attached to the vortex cores, but within these constraints they can be moved by an external field thus enabling switching [4,12,13].In general, insulating domain walls, also observed in various other systems as SrMnO3 thin films [14] and (Ca,Sr)3Ti2O7 [15], have shifted into the focus of interest, due to their possible applications, e.g., as rewritable nanocapacitors. The conductivity contrast between these DWs and the domains should be...