Patterns and transformations

Based on ideas recognized by the 2016 Nobel Prize for Physics, a Brazilian group proposes ways to alter the electrical and magnetic properties of materials

José Carlos Egues / IFSC-USP Side view: magnetic pattern formed by the concentration of spins aligned in different directionsJosé Carlos Egues / IFSC-USP

A new technology that promises to increase the storage capacity of computer magnetic memory discs recalls the old habit of tying a piece of string to your finger in order to remember something important. Instead of visible reminders, though, the idea is to use specific properties of atomic particles to create intricate geometric patterns in materials used in microelectronic components. These patterns are called topological states of matter. In recent years, they have begun to be developed in laboratories and studied in detail thanks to advances in the articles published in the 1970s and 1980s and later recognized in 2016 with the Nobel Prize in Physics.

The idea is somewhat abstract. Atoms and some of the particles from which they are made, like electrons, have a property called spin that behaves like the magnetic needle in a compass. Under the influence of a magnetic field, the spins of these particles align in the same direction and generate a simple geometric pattern. Over the last few years, physicists and engineers have been developing ways to alter the spin directions in order to produce more complex geometric patterns known as skyrmions, which resemble a swirl or whirlwind.

Physicists became interested in skyrmions because the pattern they form is as difficult to undo as a double knot in a piece of string. Theoretical and experimental studies indicate that they can resist the variations in temperature and electromagnetic field to which the microelectronic components are subjected. Skyrmions seem to maintain their pattern even when there are impurities or defects in the materials in which they form. This robustness is attractive because it could protect the information encoded in the spins from involuntary deletion, such as that caused by temperature fluctuations or magnetic interference.

Since they are smaller than 1 nanometer (a millionth of a millimeter), some researchers claim that skyrmions can be inserted into simpler spin patterns. Thus, they would preserve the information encoded in the spins in the form of binary numbers — zero or one — from magnetic perturbations. Thus, skyrmions would act like a type of comma in a sentence, separating sequences of spins that point in different directions.

Imagine if you could record this information in films of a magnetic material that — except for the nanometric dimensions — resembles the cassette tapes used in the past to record music. About 100 times smaller than magnetic domains, the elementary information blocks in today’s hard drives, skyrmions would allow storage of 100 times more information than conventional magnetic memory. “Technology based on skyrmions will take a few years to be developed,” says theoretical physicist José Carlos Egues of the São Carlos Physics Institute (IFSC) of the University of São Paulo (USP).

Until now, researchers from other groups have only been able to produce skyrmions in the laboratory using unconventional materials with crystalline structures that are complicated to manufacture and generate physical phenomena that are difficult to describe mathematically. “There is still much to learn about skyrmions,” the physicist acknowledges.

In an article recently accepted for publication by the journal Physical Review Letters, Egues and his colleagues presented calculations showing that one can produce skyrmions in an easier manner, using an electric field to manipulate the spins of the electrons in a gallium arsenide (GaAs) film, a material common in the optoelectronics industry. According to Egues, his team’s calculations assume realistic conditions, similar to those of experiments carried out years ago in laboratories in the United States. In the tests published in 2009, the U.S. researchers made the spins of the GaAs electrons form helical patterns. “The correct combination of these helicoidal patterns, in orthogonal positions, should result in the skyrmion pattern we are proposing,” explains Egues, who in October 2016 presented his ideas to European experimental physicists interested in testing them.

José Carlos Egues / IFSC-USP Top view of the magnetic whirlwind formed by the spins of atoms and electrons: a complex geometric pattern, resistant to temperature fluctuations and electromagnetic oscillationsJosé Carlos Egues / IFSC-USP

Topological insulators
With calculations similar to those presented in Physical Review Letters, Egues and the physicist Sigurdur Erlingsson of the University of Reykjavik, Iceland, had proposed, in 2015, a simple method to radically transform the electronic properties of a film of indium arsenide (InAs), a conventional material like GaAs.  Under normal conditions, InAs behaves like a semiconductor and conducts electricity only above a certain voltage. Egues and Erlingsson predicted, however, that the application of electric fields with certain characteristics would transform the indium arsenide film into an electrically insulating material in the innermost region and into an efficient conductor on its edges. This type of material is called a topological insulator.

There is a practical reason to try to transform ultrafine indium arsenide films (considered two-dimensional) into topological insulators. The materials used today, such as mercury telluride (TeHg), are difficult to manipulate and few groups worldwide, such as that of Gennady Gusev of the USP Physics Institute in São Paulo, can produce samples to see how they behave.

At least in theory, these films are the ideal material for developing new, smaller and more efficient electronic devices. “Electrons with opposing spins flow in opposite directions in a topological insulator. Despite this, they do not collide, which reduces electrical resistance,” explains IF-USP Professor Luís Gregório Dias da Silva, who is investigating the movement of electrons in these materials and has worked with Egues in the past.

Topological insulators and skyrmions are some of the phenomena discovered in the last decade thanks to the application of topological concepts to materials science. Topology is the area of mathematics that studies how some geometric objects can be transformed into others, as if they were made of Play-Doh. Mathematicians can imagine, for example, a donut transforming into a tea cup. Most physicists were not interested in topology before the publication of the pioneering theoretical articles by British physicists David Thouless, Duncan Haldane and Michael Kosterlitz, who were awarded the Nobel Prize for Physics in 2016. In the 1970s and 1980s, they suggested that transformations in the electrical and magnetic properties observed in certain materials could be explained by analyzing the topology of the abstract geometric spaces that describe the behavior of the atoms and electrons in the materials.

Topological insulators and Majorana fermions (nº 2016/08468-0); Grant Mechanism Regular research project; Principal Investigator José Carlos Egues de Menezes (IFSC-USP); Investment R$84,229.50.

Scientific article
FU, J. et al. Persistent skyrmion lattice of non-interacting electrons with spin-orbit coupling. Physical Review Letters. In production.