Study on Ferroelectric Materials Could Lead to Materials Design of Domain Wall Based Devices

Ferromagnetic materials, such as compass needles, are useful as their magnetic polarization rotates them to align along the magnetic fields. Ferroelectric materials behave in a similar fashion, but with electric, and not magnetic fields. Since external electric fields can reorient the electric polarization of these materials, they are ideal for specific memory applications, like stored-value cards which are used in mass-transit systems. Polarization changes result in the change in shape of such materials and vice-versa, a phenomenon referred to as piezoelectricity. Ferroelectrics are also significant “smart materials” for different types of sensors, like probe-based microscopes and ultrasound machines. These materials could also be used as nanoscale motors.

The simulations show that thermal fluctuations are responsible for the first nuclei from which changes in polarization spread. (Credit: University of Pennsylvania)

University of Pennsylvania chemists are assisting the next generation research in ferroelectric materials. In a recent study reported in Nature, the researchers have demonstrated a multiscale simulation of lead titanate oxide that gives an insight into what it takes for polarizations in these materials to change.

This mathematical model is based on the principles of quantum mechanics and is not derived from physical experiments. This model would undergird efforts to discover and design novel ferroelectric materials as per requirement.

Andrew M. Rappe, Professor in the School of Arts & Sciences’ Department of Chemistry, along with his colleagues Shi Liu and Ilya Grinberg conducted the study.

There are a number of uncertainties in the theoretical principles that describe the behavior of ferroelectric materials, despite of an increase in commercial applications. Deciphering how distinct regions of different polarizations, called as domains, interact at their boundaries, or domain walls is one such uncertainty.

Rappe and his team simulated a ferroelectric material featuring titanium ions packed inside six-pointed octahedral “cages” of oxygen ions. The polarization of a certain domain is detected by the location of the cage points towards which the titanium ions move.

If you apply an electric field that's opposite to the direction of the metal atoms’ alignment, they want to move and align with the electric field, but they also feel social pressure from their neighbors to stay the same as each other. That means it takes a lot energy for them all to flip their alignment direction at the same time. It also means that, generally, most of the flipping happens at domain walls. At walls, there's already some up and some down, so the ones that are the wrong way to the electric field can deviate from half their neighbors but join the other half of their neighbors and flip.

Andrew M. Rappe, Professor, University of Pennsylvania

Domain walls “move” through ferroelectric objects like wildfire. The domains that align along the external electric fields grow as they alter the neighbors. In contrast to fire, the movement of the domain walls can be easily arrested as they hold their position upon the removal of the electric field. This phenomenon is significant to ferroelectric applications, because the state of the material is stable till another field is applied.

The Rappe team’s study is the pioneer in demonstrating that mathematical models calibrated to quantum mechanics can precisely correlate the electric field strength to the speed of the movement of the domain walls.

That’s the most important thing. There are some applications where you want the walls to be slow, and there are ones where you want the walls to be fast. If you don't know why the walls move and how the walls move, you can’t even start to pick new materials and design them to have walls that move at the speed you need.

Andrew M. Rappe, Professor, University of Pennsylvania

The scientists predicted the material’s hysteresis loop shape using their simulation. The hysteresis loop is a graph that explains the amount of energy required to transfer it from one polarization and back again. A comparison of their predictions to the data obtained from earlier physical experiments proved the Penn group’s approach.

The findings highlight that thermal fluctuations were found to be responsible for the formation of the first nuclei from which there was a spread in polarization changes. Raising the electric field strength decreases the nucleus size required to initiate the process, thereby making it easier to start.

This discovery shows that the initial barrier towards raising the domain wall acceleration is not related to the presence of defects, or pockets of physical disorder in the crystal. That mechanism was put forward to elucidate why the observed domain wall motion rate started slowly, accelerated and then slowed down again. Describing this behavior through purely quantum mechanical principles indicates that materials scientists need not struggle for outstanding crystalline purity while designing ferroelectric devices.

The Rappe team’s simulations demonstrate that the process where domain gets converted into another is independent of the precise orientations of the two adjacent domains. Earlier research from Penn team assumed that adjacent orientations that are 180° apart, like up-to-down, will switch by another mechanism than those that were 90° apart, like up-to-left. These simulations prove that the same universal mechanism rules all kinds of domain walls motion.

A thorough knowledge of this phenomenon is required for the design of piezoelectric devices that depend on accurate, repeatable changes in shape. For instance, making a ferroelectric material to drive the lens aperture on a smart phone camera, requires designers to be certain that the physical response of the material towards changes in polarization is constant over several thousands of cycles.

The Rappe team’s research follows the same principle as that of the Materials Genome Initiative, a White House program that supports research into designing of novel materials using computational approaches. These approaches are essential to shift new ferroelectrics out from the labs into the world, either by spotting the perfect material for a specific application, or discovering new applications on the basis of unique properties of hypothetical materials that would match the fundamental principles discovered by the Penn group’s simulation.

A key first step in materials design, is developing some physical understanding of how things work, and we provide that. This research is allowing us to start to do materials design of domain-wall-based devices. There are many materials where the domain wall conducts electricity, but the bulk material does not, for example. In that case, you could apply an electric field to move the wall, and it would be like moving the position of a wire within the material. You could imagine a stack of these materials that only conduct electricity when they all line up and even being able to reprogram a circuit or make some sort of logic element that way.

Andrew M. Rappe, Professor, University of Pennsylvania

The National Science Foundation funded this research through grant DMR- 1124696, grant CBET-1159736; Office of Naval Research through grant N00014-12-1-1033; Department of Energy through grant DE-FG02-07ER46431; and Carnegie Institution for Science. Computational support was received from the Department of Defense through a Challenge Grant from the High Performance Computer Modernization Office and by the Department of Energy through computer time at the National Energy Research Scientific Computing Center.

Liu is currently a Carnegie Postdoctoral Fellow at the Carnegie Institution for Science. He is currently performing research to comprehend how defects, in certain specific cases, may alter polarization switching. Grinberg is currently working as an Associate Professor at Bar-Ilan University, Israel.

This work was published in Nature News & Views article.

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