Subcritical switching dynamics and humidity effects in nanoscale studies of domain growth in ferroelectric thin films

Ferroelectric domain switching in c-axis-oriented epitaxial Pb(Zr$_{0.2}$Ti$_{0.8}$)O$_3$ thin films was studied using biased scanning probe microscopy tips. While linear and logarithmic dependence of domain size on tip bias and writing time, respectively, are well known, we report an additional linear dependence on relative humidity in the 28-65% range. We map out the switched domain size as a function of both the tip bias and the applied pulse time and describe a growth-limited regime for very short pulses and a nucleation-limited regime for very low tip bias. Using "interrupted-switching" measurements, we probe the nucleation regime with subcritical pulses and identify a surprisingly long relaxation time on the order of 100 ms, which we relate to ionic redistribution both on the surface and within the thin film itself.Comment: 11 pages, 4 figure

From Curved Bonding to Configuration Spaces

Bonding curves are continuous liquidity mechanisms which are used in market design for cryptographically-supported token economies. Tokens are atomic units of state information which are cryptographically verifiable in peer-to-peer networks. Bonding curves are an example of an enforceable mechanism through which participating agents influence this state. By designing such mechanisms, an engineer may establish the topological structure of a token economy without presupposing the utilities or associated actions of the agents within that economy. This is accomplished by introducing configuration spaces, which are proper subsets of the global state space representing all achievable states under the designed mechanisms. Any global properties true for all points in the configuration space are true for all possible sequences of actions on the part of agents. This paper generalizes the notion of a bonding curve to formalize the relationship between cryptographically enforced mechanisms and their associated configuration spaces, using invariant properties of conservation functions. We then proceed to apply this framework to analyze the augmented bonding curve design, which is currently under development by a project in the non-profit funding sector.Series: Working Paper Series / Institute for Cryptoeconomics / Interdisciplinary Researc

Economic Games as Estimators

Discrete event games are discrete time dynamical systems whose state transitions are discrete events caused by actions taken by agents within the game. The agents’ objectives and associated decision rules need not be known to the game designer in order to impose struc- ture on a game’s reachable states. Mechanism design for discrete event games is accomplished by declaring desirable invariant properties and restricting the state transition functions to conserve these properties at every point in time for all admissible actions and for all agents, using techniques familiar from state-feedback control theory. Building upon these connections to control theory, a framework is developed to equip these games with estimation properties of signals which are private to the agents playing the game. Token bonding curves are presented as discrete event games and numerical experiments are used to investigate their signal processing properties with a focus on input-output response dynamics.Series: Working Paper Series / Institute for Cryptoeconomics / Interdisciplinary Researc

Conduction at domain walls in insulating Pb(Zr0.2_{0.2}Ti0.8_{0.8})O3_3 thin films

Among the recent discoveries of domain wall functionalities, the observation of electrical conduction at ferroelectric domain walls in the multiferroic insulator BiFeO3 has opened exciting new possibilities. Here, we report evidence of electrical conduction also at 180{\deg} ferroelectric domain walls in the simpler tetragonal ferroelectric PZT thin films. The observed conduction shows nonlinear, asymmetric current-voltage characteristics, thermal activation at high temperatures and high stability. We relate this behavior to the microscopic structure of the domain walls, allowing local defects segregation, and the highly asymmetric nature of the electrodes in our local probe measurements

Nanoscale studies of domain wall motion in epitaxial ferroelectric thin films

Atomic force microscopy was used to investigate ferroelectric switching and nanoscale domain dynamics in epitaxial PbZr0.2Ti0.8O3 thin films. Measurements of the writing time dependence of domain size reveal a two-step process in which nucleation is followed by radial domain growth. During this growth, the domain wall velocity exhibits a v ~ exp[-(1/E)^mu] dependence on the electric field, characteristic of a creep process. The domain wall motion was analyzed both in the context of stochastic nucleation in a periodic potential as well as the canonical creep motion of an elastic manifold in a disorder potential. The dimensionality of the films suggests that disorder is at the origin of the observed domain wall creep. To investigate the effects of changing the disorder in the films, defects were introduced during crystal growth (a-axis inclusions) or by heavy ion irradiation, producing films with planar and columnar defects, respectively. The presence of these defects was found to significantly decrease the creep exponent mu, from 0.62 - 0.69 to 0.38 - 0.5 in the irradiated films and 0.19 - 0.31 in the films containing a-axis inclusions.Comment: 13 pages, 15 figures, to be published in J. App. Phys. special issue on ferroelectric

Thermal quench effects on ferroelectric domain walls

Using piezoresponse force microscopy on epitaxial ferroelectric thin films, we have measured the evolution of domain wall roughening as a result of heat-quench cycles up to 735C, with the effective roughness exponent \zeta\ changing from 0.25 to 0.5. We discuss two possible mechanisms for the observed \zeta\ increase: a quench from a thermal 1-dimensional configuration, and from a locally-equilibrated pinned configuration with a crossover from a 2- to 1-dimensional regime. We find that the post-quench spatial structure of the metastable states, qualitatively consistent with the existence of a growing dynamical length scale whose ultra slow evolution is primarily controlled by the defect configuration and heating process parameters, makes the second scenario more plausible. This interpretation suggests that pinning is relevant in a wide range of temperatures, and in particular, that purely thermal domain wall configurations might not be observable in this glassy system. We also demonstrate the crucial effects of oxygen vacancies in stabilizing domain structures.Comment: 17 pages (preprint), 4 figure

Thermal Effects in the dynamics of disordered elastic systems

Many seemingly different macroscopic systems (magnets, ferroelectrics, CDW, vortices,..) can be described as generic disordered elastic systems. Understanding their static and dynamics thus poses challenging problems both from the point of view of fundamental physics and of practical applications. Despite important progress many questions remain open. In particular the temperature has drastic effects on the way these systems respond to an external force. We address here the important question of the thermal effect close to depinning, and whether these effects can be understood in the analogy with standard critical phenomena, analogy so useful to understand the zero temperature case. We show that close to the depinning force temperature leads to a rounding of the depinning transition and compute the corresponding exponent. In addition, using a novel algorithm it is possible to study precisely the behavior close to depinning, and to show that the commonly accepted analogy of the depinning with a critical phenomenon does not fully hold, since no divergent lengthscale exists in the steady state properties of the line below the depinning threshold.Comment: Proceedings of the International Workshop on Electronic Crystals, Cargese(2008

Domain wall roughness in epitaxial ferroelectric PbZr0.2Ti0.8O3 thin films

The static configuration of ferroelectric domain walls was investigated using atomic force microscopy on epitaxial PbZr0.2Ti0.8O3 thin films. Measurements of domain wall roughness reveal a power law growth of the correlation function of relative displacements B(L) ~ L^(2zeta) with zeta ~ 0.26 at short length scales L, followed by an apparent saturation at large L. In the same films, the dynamic exponent mu was found to be ~ 0.6 from independent measurements of domain wall creep. These results give an effective domain wall dimensionality of d=2.5, in good agreement with theoretical calculations for a two-dimensional elastic interface in the presence of random-bond disorder and long range dipolar interactions.Comment: 5 pages, 4 figure

Understanding polarization vs. charge dynamics effects in ferroelectric-carbon nanotube devices

To optimize the performance of multifunctional carbon nanotube-ferroelectric devices, it is necessary to understand both the polarization and charge dynamics effects on their transconductance. Directly comparing ferroelectric Pb(Zr0.2Ti0.8)O3 and dielectric SrTiO3 field effect transistors, we show that the two effects strongly compete, with transient charge dynamics initially masking up to 40% of the ferroelectric field effect. For applications, it is therefore crucial to maximize the quality of the ferroelectric film and the interface with the carbon nanotube to take full advantage of the switchable polarization.Comment: 5 pages, 4 figure