Materials can 'remember' a sequence of events in an unexpected way

One way some materials form memories is called return-point memory, which operates much like a single dial combination lock, according to Nathan Keim, associate professor of physics in the Penn State Eberly College of Science and leader of the research team. With a lock, rotating the dial clockwise and counterclockwise in a particular sequence yields a result -- the lock opening -- that depends on how the dial was moved. Likewise, for materials with return-point memory, alternating between positive and negative deformations can leave a memory of the sequence that researchers can read or erase.

"The same underlying mechanism or mathematics of this memory formation can describe systems from the magnetization of computer hard drives to damage in solid rock," Keim said, noting that his research group recently showed that the same math also describes memories stored in disordered solids, in which the arrangement of particles seems random but actually contains details about past deformations.

Return-point memory relies on the alternating of direction of the external force, or "driving," such as the alternating of positive or negative magnetic field or pulling on a material from one side and then the other. However, materials should not be able to form return-point memory when the force only occurs in one direction. For example, Keim said, a bridge might sag slightly as cars drive over it, but it doesn't curve upwards once the cars are gone.

"The mathematical theorems for return-point memory say that we can't store a sequence if we only have this 'asymmetrical' driving in one direction," Keim said. "If the combination lock dial can't go past zero when turning counterclockwise, it only stores one number in the combination. But we found a special case when this kind of asymmetrical driving can, in fact, encode a sequence."

The researchers performed a series of computer simulations to explore the conditions under which a sequence could be encoded in a material. They manipulated a variety of factors, including the magnitude and orientation of the external driving force as well as how it is generated, to see how they impact memory formation and the length of the encoded sequence. To do so, the researchers boiled down the components of the system -- such as the particles in a solid or the microscopic domains in a magnet -- into abstract elements called hysterons.

"Hysterons are elements of a system that may not immediately respond to external conditions, and can stay in a past state," said Travis Jalowiec, an undergraduate at the time of the research who earned his bachelor's degree in physics at Penn State and an author of the paper. "Like how parts of a combination lock reflect the previous positions of the dial, and not where the dial is now. In our model, hysterons have two possible states and can work with or against each other, and this generalized model makes it applicable to as many systems as possible."

The hysterons in the model interact either in a cooperative way, where a change in one encourages a change in the other, or in a non-cooperative "frustrated" way, where a change in one discourages a change in the other. Frustrated hysterons, Jalowiec explained, are the key to forming and recovering a sequence in a system with asymmetric driving.

"A good example of frustration is a bendy straw, which has a series of little bellows that can be collapsed or popped open," Keim said. "If you pull on the ends of the straw a tiny amount and stop, one will pop open, and it being open means that the others do not. The change in one relieves the stress in the system.

The researchers found that systems with cooperative interactions could only encode a sequence if the driving was symmetric -- with alternating directions. However, just a single pair of frustrated hysterons was enough to produce an encoded sequence with asymmetric driving, so long as other conditions are met.

"Finding a pair of frustrated hysterons in a real material has been elusive," Keim said. "It's hard to observe, because often the signature of frustration is that something doesn't happen. The behavior we found is rare, but it would stand out like a sore thumb in a real material, so it gives us a new way to look for and study materials with frustration. But more immediately, we think this is a way to design artificial systems with this special kind of memory, starting with the simplest mechanical systems not much more complicated than a bendy straw and hopefully working up to something like an asymmetrical combination lock."

The researchers say these results could inspire new ways to store, recall and erase information in materials and mechanical systems.

"One key property of this memory is that it's guaranteed to store both the largest deformation and the most recent deformation," Keim said. "If you can make a system that stores a sequence of memories, you can use it like a combination lock to verify a specific history, or you could recover diagnostic or forensic information about the past. There is increasing interest in mechanical systems that sense their environments, perform computations and respond or adapt without ever using electricity. A better understanding of memory expands these possibilities."

In addition to Keim and Jalowiec, the research team includes Chloe Lindeman, graduate student at the University of Chicago at the time of the research, now a Miller Postdoctoral Fellow at Johns Hopkins University. Funding from the U.S. Department of Energy, Penn State Schreyer Honors College and Penn State Student Engagement Network supported this work.