This image shows the similarity between the doubling of domains in barium titanate (left) and a bifurcating pyramidal neuron (right). Image: left panel – Beatriz Noheda; right panel – Ramón y Cajal.
This image shows the similarity between the doubling of domains in barium titanate (left) and a bifurcating pyramidal neuron (right). Image: left panel – Beatriz Noheda; right panel – Ramón y Cajal.

A phenomenon that is well known from chaos theory has been observed in a material for the first time ever by scientists from the University of Groningen in the Netherlands. A structural transition in a ferroelastic material, caused by an increase or decrease in temperature, resembles the periodic doubling seen in non-linear dynamical systems.

This 'spatial chaos' in a material was first predicted in 1985 and could find use in applications such as adaptable neuromorphic electronics. The scientists report their findings in a paper in Physical Review Letters.

The physicists from the University of Groningen, led by Beatriz Noheda, a professor of functional nanomaterials, made their observation in thin films of the ferroelastic material barium titanate (BaTiO3). Ferroic materials are characterized by their ordered structure, which can be in shape (ferroelastic), charge (ferroelectric) or magnetic moment (ferromagnetic).

“These materials are always crystals in which the atoms are arranged with characteristic symmetries,” says Noheda.

In ferroelectric or ferromagnetic materials, the electric or magnetic dipoles are aligned within domains in the crystals. “However, the dipoles could be pointing up or down, as both states are equivalent,” says Noheda. As a result, crystals of these materials will have both types of domain.

The same goes for ferroelastic materials, best known for their shape memory. In this case, however, the situation is a bit more complicated. “The unit cells in these crystals are elongated, which means that domains of the different unit cells do not easily match in shape,” she says. “This creates an elastic strain that reduces the crystal stability.”

The crystal can improve its stability by forming twins of domains, which are slightly tilted in opposite directions, to relieve the stress. The result is a material in which these twinned pairs form alternating domains, with a fixed periodicity. Heating causes a phase change in the material, altering both the direction and periodicity of the domain. “The question was how this change takes place,” says Noheda.

Increasing the temperature increases the disorder (entropy) in the material. This starts a tug-of-war between the material’s intrinsic tendency for order and the increasing entropy. It is this process that was observed for the first time in BaTiO3 by the Groningen team, using atomic force microscopy.

When heating samples from 25°C to 70°C, a phase change takes place, altering the position of the domain walls. When the transition starts, the domain walls of the new phase appear gradually, and both phases exist together at intermediate temperatures (30°C to 50°C).

“This doesn't happen in a random way, but by repeated doubling,” says Noheda. Cooling the material reduces the periodicity of the domains by repeated halving.

“This doubling or halving is well known in non-linear dynamical systems, when they are close to the transition to chaotic behavior,” explains Noheda, “However, it had never been observed in spatial domains, but only in time periods.”

The similarity between the behavior of the thin films and non-linear systems suggests that the material is at the edge of chaos during heating. “This is an interesting observation, because it means that the response of the system is highly dependent on initial conditions. Thus, we could get very diverse responses following a small change in these conditions.”

The paper includes theoretical calculations from researchers at Penn State University and the University of Cambridge in the UK, which show that the behavior observed in barium titanate is generic for ferroic materials. Thus, a ferroelectric material at the edge of chaos could give a highly diverse response over a small range of input voltages.

“That is exactly what you want, to create the type of adaptable response needed for neuromorphic computing, such as reservoir computing, which benefits from non-linear systems that can produce highly diverse input-output sets,” says Noheda.

This study is a proof-of-principle, showing how a material can be designed to exist at the edge of chaos, where it is highly responsive. Noheda also points out how the doubling of domains creates a structure similar to the bifurcating dendrites connecting pyramidal cells in the brain, which play an important role in cognitive abilities. Ultimately, ferroic materials on the edge of chaos may be used to create electronic brain-like systems for complex computing.

This story is adapted from material from the University of Groningen, with editorial changes made by Materials Today. The views expressed in this article do not necessarily represent those of Elsevier. Link to original source.