Quantitative analysis of ferroelectric domain imaging with piezoresponse force microscopy

The contrast mechanism for ferroelectric domain imaging via piezoresponse force microscopy (PFM) is investigated. A novel analysis of PFM measurements is presented which takes into account the background caused by the experimental setup. This allows, for the first time, a quantitative, frequency independent analysis of the domain contrast which is in good agreement with the expected values for the piezoelectric deformation of the sample and satisfies the generally required features of PFM imaging

A stochastical model for periodic domain structuring in ferroelectric crystals

A stochastical description is applied in order to understand how ferroelectric structures can be formed. The predictions are compared with experimental data of the so-called electrical fixing: Domains are patterned in photorefractive lithium niobate crystals by the combination of light-induced space-charge fields with externally applied electrical fields. In terms of our stochastical model the probability for domain nucleation is modulated according to the sum of external and internal fields. The model describes the shape of the domain pattern as well as the effective degree of modulation

Electrostatic topology of ferroelectric domains in YMnO3_3

Trimerization-polarization domains in ferroelectric hexagonal YMnO$_3$ were resolved in all three spatial dimensions by piezoresponse force microscopy. Their topology is dominated by electrostatic effects with a range of 100 unit cells and reflects the unusual electrostatic origin of the spontaneous polarization. The response of the domains to locally applied electric fields explains difficulties in transferring YMnO$_3$ into a single-domain state. Our results demonstrate that the wealth of non-displacive mechanisms driving ferroelectricity that emerged from the research on multiferroics are a rich source of alternative types of domains and domain-switching phenomena

Contrast Mechanisms for the Detection of Ferroelectric Domains with Scanning Force Microscopy

We present a full analysis of the contrast mechanisms for the detection of ferroelectric domains on all faces of bulk single crystals using scanning force microscopy exemplified on hexagonally poled lithium niobate. The domain contrast can be attributed to three different mechanisms: i) the thickness change of the sample due to an out-of-plane piezoelectric response (standard piezoresponse force microscopy), ii) the lateral displacement of the sample surface due to an in-plane piezoresponse, and iii) the electrostatic tip-sample interaction at the domain boundaries caused by surface charges on the crystallographic y- and z-faces. A careful analysis of the movement of the cantilever with respect to its orientation relative to the crystallographic axes of the sample allows a clear attribution of the observed domain contrast to the driving forces respectively.Comment: 8 pages, 8 figure

Sol-Gel Derived Ferroelectric Nanoparticles Investigated by Piezoresponse Force Microscopy

Piezoresponse force microscopy (PFM) was used to investigate the ferroelectric properties of sol-gel derived LiNbO$_3$ nanoparticles. To determine the degree of ferroelectricity we took large-area images and performed statistical image-analysis. The ferroelectric behavior of single nanoparticles was verified by poling experiments using the PFM tip. Finally we carried out simultaneous measurements of the in-plane and the out-of-plane piezoresponse of the nanoparticles, followed by measurements of the same area after rotation of the sample by 90$^{\circ}$ and 180$^{\circ}$. Such measurements basically allow to determine the direction of polarization of every single particle

Impact of the tip radius on the lateral resolution in piezoresponse force microscopy

We present a quantitative investigation of the impact of tip radius as well as sample type and thickness on the lateral resolution in piezoresponse force microscopy (PFM) investigating bulk single crystals. The observed linear dependence of the width of the domain wall on the tip radius as well as the independence of the lateral resolution on the specific crystal-type are validated by a simple theoretical model. Using a Ti-Pt-coated tip with a nominal radius of 15 nm the so far highest lateral resolution in bulk crystals of only 17 nm was obtained

Critical Casimir effect in classical binary liquid mixtures

If a fluctuating medium is confined, the ensuing perturbation of its fluctuation spectrum generates Casimir-like effective forces acting on its confining surfaces. Near a continuous phase transition of such a medium the corresponding order parameter fluctuations occur on all length scales and therefore close to the critical point this effect acquires a universal character, i.e., to a large extent it is independent of the microscopic details of the actual system. Accordingly it can be calculated theoretically by studying suitable representative model systems. We report on the direct measurement of critical Casimir forces by total internal reflection microscopy (TIRM), with femto-Newton resolution. The corresponding potentials are determined for individual colloidal particles floating above a substrate under the action of the critical thermal noise in the solvent medium, constituted by a binary liquid mixture of water and 2,6-lutidine near its lower consolute point. Depending on the relative adsorption preferences of the colloid and substrate surfaces with respect to the two components of the binary liquid mixture, we observe that, upon approaching the critical point of the solvent, attractive or repulsive forces emerge and supersede those prevailing away from it. Based on the knowledge of the critical Casimir forces acting in film geometries within the Ising universality class and with equal or opposing boundary conditions, we provide the corresponding theoretical predictions for the sphere-planar wall geometry of the experiment. The experimental data for the effective potential can be interpreted consistently in terms of these predictions and a remarkable quantitative agreement is observed.Comment: 30 pages, 17 figure

Precision nanoscale domain engineering of lithium niobate via UV laser induced inhibition of poling

Continuous wave ultraviolet (UV) laser irradiation at lambda=244 nm on the +z face of undoped and MgO doped congruent lithium niobate single crystals has been observed to inhibit ferroelectric domain inversion. The inhibition occurs directly beneath the illuminated regions, in a depth greater than 100 nm during subsequent electric field poling of the crystal. Domain inhibition was confirmed by both differential domain etching and piezoresponse force microscopy. This effect allows the formation of arbitrarily shaped domains in lithium niobate and forms the basis of a high spatial resolution micro-structuring approach when followed by chemical etching

Collective magnetism at multiferroic vortex domain walls

Topological defects have been playgrounds for many emergent phenomena in complex matter such as superfluids, liquid crystals, and early universe. Recently, vortex-like topological defects with six interlocked structural antiphase and ferroelectric domains merging into a vortex core were revealed in multiferroic hexagonal manganites. Numerous vortices are found to form an intriguing self-organized network. Thus, it is imperative to find out the magnetic nature of these vortices. Using cryogenic magnetic force microscopy, we discovered unprecedented alternating net moments at domain walls around vortices that can correlate over the entire vortex network in hexagonal ErMnO3 The collective nature of domain wall magnetism originates from the uncompensated Er3+ moments and the correlated organization of the vortex network. Furthermore, our proposed model indicates a fascinating phenomenon of field-controllable spin chirality. Our results demonstrate a new route to achieving magnetoelectric coupling at domain walls in single-phase multiferroics, which may be harnessed for nanoscale multifunctional devices.Comment: 18 pages, 10 figure