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.PACS numbers:

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.

The interpretation of ferroelectric domain images obtained with a piezoresponse force microscope (PFM) is discussed. The influence of an inherent experimental background on the domain contrast in PFM images (enhancement, nulling, inversion) as well as on the shape and the location of the domain boundaries are described. We present experimental results to evidence our analysis of the influence of the background on the domain contrast in PFM images.

Ferroelectric domain imaging with piezoresponse force microscopy (PFM) relies on the converse piezoelectric effect: a voltage applied to the sample leads to mechanical deformations. In case of PFM one electrode is realized by the tip, therefore generating a strongly inhomogeneous electric field distribution inside the sample which reaches values up to 10 8 V/m directly underneath the apex of the tip. Although often assumed, this high electric field does not lead to an enhancement of the piezoelectric deformation of the sample. On the contrary, internal clamping of the material reduces the observed deformation compared to the theoretically expected value which depends only on the voltage thus being independent of the exact field distribution. [5], piezoresponse force microscopy (PFM) has become a standard technique in recent years mainly because of its easy use. However, the interpretation of the obtained images is still challenging, therefore quantitative data is published very rarely. This deficiency is often justified by the presumption that due to the strong dependency of the electric field on the tip radius, which in general is not known exactly, a quantitative analysis of the data is not possible. Arguing that way, however, ignores the fact that, at least in a first approximation, not the electric field distribution but only the applied voltage determines the piezoelectric deformation of the sample. Although this statement is self-evident from theoretical considerations, we carried out experiments with different single-domain crystals, comparing the measured deformation underneath the tip with and without an additional top electrode.PFM is based on the deformation of the sample due to the converse piezoelectric effect. The piezoresponse force microscope is a scanning force microscope (SFM) operated in contact mode with an additional alternating voltage applied to the tip. In piezoelectric samples this voltage causes thickness changes and therefore vibrations of the surface which lead to oscillations of the cantilever that can be read out with a lock-in amplifier. In ferroelectric samples different orientations of the polar axis of adjacent domains lead to a domain contrast, i. e., the domain faces are displayed as bright or dark areas in PFM images (an overview of the PFM technique can be found in [6]). The generally observed frequency * Electronic address: soergel@uni-bonn.de dependence of those measurements [7,8,9] was recently be explained by a system-inherent background [10]. We also proposed a detection scheme that allows a straight forward quantitative analysis of the obtained data [11]. In this contribution we investigate the influence of the strongly inhomogeneous electric field of the tip on the piezoelectric deformation measured with PFM.The (longitudinal) converse piezoelectric effect says that in an external electric field E a piezoelectric material of thickness t undergoes a thickness change ∆t proportional to the appropriate piezoelectric coefficient d:Note that the thickness change ∆t does n...

Continuous wave ultraviolet laser irradiation at = 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 microstructuring approach when followed by chemical etching. © 2008 American Institute of Physics. ͓DOI: 10.1063/1.2884185͔ Domain engineering 1,2 of lithium niobate ͑LN͒ is a subject of extensive research and a simple, cheap, and robust method of fabrication of well-defined periodic domaininverted structures on submicron scales is highly desirable. Spatial domain engineering is used for many optical processes in bulk crystals and waveguides and can also allow for the creation of both freestanding 3 and surface relief structures 4 through the differential etching characteristics of the polar z faces of the crystal. If achievable on the submicron scale, surface structuring through differential etching will allow the implementation of a range of interesting applications such as tunable photonic crystals, ridge waveguide lasers, and multifunctional micromachines.Previous work has shown that ultraviolet ͑UV͒ and visible laser light can either directly invert 5 or assist the domain inversion process in LN. [6][7][8][9] In this paper, however, a different effect is presented whereby illumination of the +z face with UV light at = 244 nm ͑with photon energy greater than the LN band gap͒ inhibits domain inversion in illuminated areas during subsequent electric field poling ͑EFP͒. Of major importance, the inhibited domains are not restricted in their shape or alignment with the crystal x or y axes, hence, arbitrarily shaped domains can be formed. Some initial results of this effect and its applicability in the creation of micro/nano structures in LN are presented.A beam from a frequency-doubled Ar-ion laser was focused to a spot size of ϳ2.5 m on the +z or −z face of either an undoped congruent or 5 mol % MgO-doped LN crystal. Positioning and exposure control of the crystal was achieved by a computer-controlled, three-axis stage system coupled with a mechanical shutter.For dynamic exposures, sets of parallel lines were drawn on the z faces of the crystals along the crystallographic x or y directions by moving the stages at speeds ranging from 0.05 to 0.3 mm s −1 . For static exposures, arrays of illuminated spots with identical exposure times, ranging from a few milliseconds to a few tens of seconds, were formed. The separation between the edges of adjacent illuminated spots in the arrays varied from 0 to 6 m which permitted us to verify if any proximity effect existed such as that observed in pulsed laser direct poling 5 where the closest approa...