Materials Contrast in Piezoresponse Force Microscopy

Piezoresponse Force Microscopy contrast in transversally isotropic material corresponding to the case of c+ - c- domains in tetragonal ferroelectrics is analyzed using Green's function theory by Felten et al. [J. Appl. Phys. 96, 563 (2004)]. A simplified expression for PFM signal as a linear combination of relevant piezoelectric constant are obtained. This analysis is extended to piezoelectric material of arbitrary symmetry with weak elastic and dielectric anisotropies. This result provides a framework for interpretation of PFM signals for systems with unknown or poorly known local elastic and dielectric properties, including nanocrystalline materials, ferroelectric polymers, and biopolymers.Comment: 20 pages, 3 figures, 1 table, accepted to Appl. Phys. Lett. (without Appendices), algebraic errors were correcte

Impact of elasticity on the piezoresponse of adjacent ferroelectric domains investigated by scanning force microscopy

As a consequence of elasticity, mechanical deformations of crystals occur on a length scale comparable to their thickness. This is exemplified by applying a homogeneous electric field to a multi-domain ferroelectric crystal: as one domain is expanding the adjacent ones are contracting, leading to clamping at the domain boundaries. The piezomechanically driven surface corrugation of micron-sized domain patterns in thick crystals using large-area top electrodes is thus drastically suppressed, barely accessible by means of piezoresponse force microscopy

Magnetodielectric coupling in Mn3O4

We have investigated the dielectric anomalies associated with spin ordering transitions in the tetragonal spinel Mn$_3$O$_4$, using thermodynamic, magnetic, and dielectric measurements. We find that two of the three magnetic ordering transitions in Mn$_3$O$_4$ lead to decreases in the temperature dependent dielectric constant at zero applied field. Applying a magnetic field to the polycrystalline sample leaves these two dielectric anomalies practically unchanged, but leads to an increase in the dielectric constant at the intermediate spin-ordering transition. We discuss possible origins for this magnetodielectric behavior in terms of spin-phonon coupling. Band structure calculations suggest that in its ferrimagnetic state, Mn$_3$O$_4$ corresponds to a semiconductor with no orbital degeneracy due to strong Jahn-Teller distortion.Comment: 6 pages, 7 figure

Quantum Flexoelectricity in Low Dimensional Systems

Symmetry breaking at surfaces and interfaces and the capability to support large strain gradients in nanoscale systems enable new forms of electromechanical coupling. Here we introduce the concept of quantum flexoelectricity, a phenomenon that is manifested when the mechanical deformation of non-polar quantum systems results in the emergence of net dipole moments and hence linear electromechanical coupling proportional to local curvature. The concept is illustrated in carbon systems, including polyacetylene and nano graphitic ribbons. Using density functional theory calculations for systems made of up to 400 atoms, we determine the flexoelectric coefficients to be of the order of ~ 0.1 e, in agreement with the prediction of linear theory. The implications of quantum flexoelectricity on electromechanical device applications, and physics of carbon based materials are discussed.Comment: 15 pages, 3 figure

Towards a microscopic theory of toroidal moments in bulk periodic crystals

We present a theoretical analysis of magnetic toroidal moments in periodic systems, in the limit in which the toroidal moments are caused by a time and space reversal symmetry breaking arrangement of localized magnetic dipole moments. We summarize the basic definitions for finite systems and address the question of how to generalize these definitions to the bulk periodic case. We define the toroidization as the toroidal moment per unit cell volume, and we show that periodic boundary conditions lead to a multivaluedness of the toroidization, which suggests that only differences in toroidization are meaningful observable quantities. Our analysis bears strong analogy to the modern theory of electric polarization in bulk periodic systems, but we also point out some important differences between the two cases. We then discuss the instructive example of a one-dimensional chain of magnetic moments, and we show how to properly calculate changes of the toroidization for this system. Finally, we evaluate and discuss the toroidization (in the local dipole limit) of four important example materials: BaNiF_4, LiCoPO_4, GaFeO_3, and BiFeO_3.Comment: replaced with final (published) version, which includes some changes in the text to improve the clarity of presentatio

Scaled free energies, power-law potentials, strain pseudospins and quasi-universality for first-order structural transitions

We consider ferroelastic first-order phase transitions with $N_{OP}$ order-parameter strains entering Landau free energies as invariant polynomials, that have $N_V$ structural-variant Landau minima. The total free energy includes (seemingly innocuous) harmonic terms, in the $n = 6 -N_{OP}$ {\it non}-order-parameter strains. Four 3D transitions are considered, tetragonal/orthorhombic, cubic/tetragonal, cubic/trigonal and cubic/orthorhombic unit-cell distortions, with respectively, $N_{OP} = 1, 2, 3$ and 2; and $N_V = 2, 3, 4$ and 6. Five 2D transitions are also considered, as simpler examples. Following Barsch and Krumhansl, we scale the free energy to absorb most material-dependent elastic coefficients into an overall prefactor, by scaling in an overall elastic energy density; a dimensionless temperature variable; and the spontaneous-strain magnitude at transition $\lambda <<1$. To leading order in $\lambda$ the scaled Landau minima become material-independent, in a kind of 'quasi-universality'. The scaled minima in $N_{OP}$-dimensional order-parameter space, fall at the centre and at the $N_V$ corners, of a transition-specific polyhedron inscribed in a sphere, whose radius is unity at transition. The `polyhedra' for the four 3D transitions are respectively, a line, a triangle, a tetrahedron, and a hexagon. We minimize the $n$ terms harmonic in the non-order-parameter strains, by substituting solutions of the 'no dislocation' St Venant compatibility constraints, and explicitly obtain powerlaw anisotropic, order-parameter interactions, for all transitions. In a reduced discrete-variable description, the competing minima of the Landau free energies induce unit-magnitude pseudospin vectors, with $N_V +1$ values, pointing to the polyhedra corners and the (zero-value) center.Comment: submitted to PR

High-pressure neutron study of the morphotropic PZT: phase transitions in a two-phase system

In piezoelectric ceramics the changes in the phase stabilities versus stress and temperature in the vicinity of the phase boundary play a central role. The present study was dedicated to the classical piezoelectric, lead-zirconate-titanate (PZT) ceramic with composition Pb(Zr$_{0.54}$Ti$_{0.46}$)O$_3$ at the Zr-rich side of the morphotropic phase boundary at which both intrinsic and extrinsic contributions to piezoelectricity are significant. The pressure-induced changes in this two-phase (rhombohedral $R3c$+monoclinic $Cm$ at room temperature and $R3c+P4mm$ above 1 GPa pressures) system were studied by high-pressure neutron powder diffraction technique. The experiments show that applying pressure favors the $R3c$ phase, whereas the $Cm$ phase transforms continuously to the $P4mm$, which is favored at elevated temperatures due to the competing entropy term. The $Cm\rightarrow R3c$ phase transformation is discontinuous. The transformation contributes to the extrinsic piezoelectricity. An important contribution to the intrinsic piezoelectricity was revealed: a large displacement of the $B$ cations (Zr and Ti) with respect to the oxygen anions is induced by pressure. Above 600 K a phase transition to a cubic phase took place. Balance between the competing terms dictates the curvature of the phase boundary. After high-pressure experiments the amount of rhombohedral phase was larger than initially, suggesting that on the Zr-rich side of the phase boundary the monoclinic phase is metastable.Comment: 6 figure

Late Holocene palynology and palaeovegetation of tephra-bearing mires at Papamoa and Waihi Beach, western Bay of Plenty, North Island, New Zealand.

The vegetation history of two mires associated with Holocene dunes near the western Bay of Plenty coast, North Island, New Zealand, is deduced from pollen analysis of two cores. Correlation of airfall tephra layers in the peats, and radiocarbon dates, indicate that the mires at Papamoa and Waihi Beach are c. 4600 and c. 2900 conventional radiocarbon years old, respectively. Tephras used to constrain the chronology of the pollen record include Rotomahana (1886 AD), Kaharoa (700 yr B.P.), Taupo (Unit Y; 1850 yr B.P.), Whakaipo (Unit V; 2700 yr B.P.), Stent (Unit Q; 4000 yr B.P.), Hinemaiaia (Unit K; 4600 yr B.P.), and reworked Whakatane (c. 4800 yr B.P.) at Papamoa, and Kaharoa and Taupo at Waihi Beach. Peat accumulation rates at Papamoa from 4600 - 1850 yr B.P. range from 0.94 to 2.64 mm/yr (mean 1.37 mm/yr). At Waihi Beach, from 2900 yr B.P. - present day, they range from 0.11 to 0.21 mm/yr (mean 0.20 mm/yr). Peat accumulation at both sites was slowest from 1850 to 700 yr B.P., suggesting a drier overall climate during this interval. At both sites, the earliest organic sediments, which are underlain by marine or estuarine sands, yield pollen spectra indicating salt marsh or estuarine environments. Coastal vegetation communities declined at both sites, as sea level gradually fell or the coast prograded, and were eventually superseded by a low moor bog at Papamoa, and a mesotrophic swamp forest at Waihi Beach. These differences, and the marked variation in peat accumulation rates, probably reflect local hydrology and are unlikely to have been climatically controlled. The main regional vegetation during this period was mixed northern conifer-angiosperm forest. Kauri (Agathis australis) formed a minor component of these forests, but populations of this tree have apparently not expanded during the late Holocene at these sites, which are near its present southern limit. Occasional shortlived forest disturbances are detectable in these records, in particular immediately following the deposition of Taupo Tephra. However, evidence for forest clearance during the human era is blurred by the downward dislocation of modern adventi ve pollen at these sites, preventing the clear differentiation of the Polynesian and European eras

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

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