Scientists Uncover Revolutionary Magnetism Predicted by Nagaoka

Researchers Have Found a Novel Form of Magnetism

A breakthrough in physics unfolds as scientists unveil a novel form of magnetism, long theorized by Nagaoka. Delve into the research revealing the fascinating properties of this magnetic phenomenon.

– Researchers have identified a new form of magnetism, in line with Yosuke Nagaoka’s predictions, in a synthetic material.

– The discovery, published in Nature, marks a significant advancement in understanding ferromagnetism.

– This finding holds potential implications for various fields, including materials science and quantum mechanics.

The original version of this story appeared in Quanta Magazine.

The spins of electrons in an atomically thin stack of semiconductors align due to a mechanism not found in any natural material.

For the same reason, every magnet you have ever come into contact with—including the trinkets affixed to your refrigerator door—is magnetic. But what if there was an even odd method for magnetically modifying a substance?

Yosuke Nagaoka, a Japanese physicist, proposed in 1966 the concept of a kind of magnetism resulting from an apparently atypical electron dance in an imaginary substance. A group of scientists has now observed a manifestation of Nagaoka’s predictions in a synthetic substance that is only six atoms thick.

The finding, which was just released in the journal Nature, represents the most recent development in the five-decade search for Nagaoka ferromagnetism, a phenomenon in which, in contrast to conventional magnets, a material magnetizes when the electrons within it decrease their kinetic energy. Coauthor of the study Livio Ciorciaro said, “That’s why I’m doing this kind of research: I get to learn things that we didn’t know before, see things that we haven’t seen before.” Ciorciaro completed the work while pursuing a doctorate at the Institute for Quantum Electronics at the Swiss Federal Institute of Technology Zurich.

In 2020, scientists produced Nagaoka ferromagnetism in one of the tiniest systems that can support the phenomenon—a system with just three electrons. In the latest work, Ciorciaro and associates achieved this in a larger system—a moiré lattice, a patterned structure composed of sheets that are only two nanometers thin.

A collaborator of the 2020 study who finished the work at the Delft University of Technology, Juan Pablo Dehollain, called this study “a really cool use of these moiré lattices, which are relatively new.” “It approaches this ferromagnetism from a somewhat different perspective.”

Conventional ferromagnetism results from electrons’ lack of desire to interact with one another due to their dislike of one another.

Conventional ferromagnetism results from electrons’ lack of desire to interact with one another due to their dislike of one another.

Consider two electrons seated adjacent to one another. Because they both have negative electrical charges, they will resist one another. They will be separated much at their lowest energy condition. Furthermore, systems typically reach their lowest energy state.

There are a few other crucial characteristics of electrons that come from quantum mechanics. Firstly, they behave more like probabilistic clouds of mist than like individual spots. Secondly, they possess a spin quantum characteristic, which functions similarly to an internal magnet with an up/down pointing capability. Third, the quantum states of two electrons cannot coexist.

Consequently, identically spun electrons will actively want to separate from one another since they could end up in the same quantum state if they are in the same location. Electrons with parallel spins that overlap remain marginally separated from one another.

This effect can be powerful enough to get electron spins to align like tiny bar magnets in the presence of an external magnetic field, producing a macroscopic magnetic field inside the material. As long as the metal isn’t heated excessively, these electron interactions—also known as exchange interactions—are sufficiently strong in metals like iron that the induced magnetization is permanent.

Ataç İmamoğlu, a physicist at the Institute for Quantum Electronics and coauthor of the work, stated, “The strength of electron exchange interactions is the very reason that we have magnetism in our everyday lives.”

Exchange interactions, however, could not be the sole way to make a material magnetic, as Nagaoka hypothesized in the 1960s. Nagaoka envisioned a two-dimensional, square lattice with a single electron at each location. Then he calculated what would happen in specific circumstances if one of those electrons were removed. The hole left by the missing electron would skitter about the lattice as the surviving electrons interacted with one another.

When all of the electron spins on the lattice were aligned, the overall energy of the lattice would be at its lowest under Nagaoka’s scenario. Each configuration of electrons would have the same appearance, as if they were identical tiles in the most monotonous sliding tile puzzle ever created. Consequently, the material would become ferromagnetic due to these parallel spins.

Through experiments with single-layer sheets of atoms that could be piled together to make a complex moiré pattern (pronounced mwah-ray), İmamoğlu and his colleagues had an idea that they could manufacture Nagaoka magnetism. Moiré patterns have a profound effect on the behavior of electrons and, consequently, the materials in atomically thin, layered materials. For instance, in 2018 physicist Pablo Jarillo-Herrero and his associates showed that superconductivity may be achieved in graphene two-layer stacks by twisting the two layers to counterbalance each other.

Through experiments with single-layer sheets of atoms that could be piled together to make a complex moiré pattern (pronounced mwah-ray), İmamoğlu and his colleagues had an idea that they could manufacture Nagaoka magnetism. Moiré patterns have a profound effect on the behavior of electrons and, consequently, the materials in atomically thin, layered materials. For instance, in 2018 physicist Pablo Jarillo-Herrero and his associates showed that superconductivity may be achieved in graphene two-layer stacks by twisting the two layers to counterbalance each other.

Since then, moiré materials—which fit in with clouds of supercooled atoms and complex materials like cuprates—have become an intriguing new system in which to explore magnetism. “Moiré materials offer us a platform for essentially creating and examining many-body states of electrons,” stated İmamoğlu.

Using monolayers of the semiconductors molybdenum diselenide and tungsten disulfide—which are members of a class of materials that previous simulations had suggested would exhibit Nagaoka-style magnetism—the researchers first created a material. The moiré material was then exposed to weak magnetic fields of various intensities, and the number of electron spins in the material that aligned with the fields was monitored.

Subsequently, the scientists conducted these tests again, varying the voltage across the material to alter the moiré lattice’s electron count. They discovered an oddity. Only when the material’s electron content exceeded that of the lattice sites by up to 50% did it exhibit a greater propensity to align with an external magnetic field and exhibit ferromagnetic behavior. Additionally, the researchers did not observe any evidence of ferromagnetism when the lattice contained fewer electrons than lattice sites. In contrast to what they would have anticipated, if standard-issue Nagaoka ferromagnetism had been at play, this was what they observed.

Exchange interactions didn’t seem to be driving the material’s magnetism, despite its properties. However, the most basic iterations of Nagaoka’s theory were also unable to adequately account for its magnetic properties.

It all came down to mobility in the end. By dispersing over space, electrons reduce their kinetic energy. This can lead to the wave function describing one electron’s quantum state overlapping with that of its neighbors, tying their destiny. The extra electrons in the team’s material delocalized like fog poured across a Broadway stage, causing the material’s energy to drop as soon as there were more electrons in the moiré lattice than there were lattice sites. Afterwards, they briefly teamed up with lattice electrons to create doublons, which are two-electron pairings.

It all came down to mobility in the end. By dispersing over space, electrons reduce their kinetic energy. This can lead to the wave function describing one electron’s quantum state overlapping with that of its neighbors, tying their destiny. The extra electrons in the team’s material delocalized like fog poured across a Broadway stage, causing the material’s energy to drop as soon as there were more electrons in the moiré lattice than there were lattice sites. Afterwards, they briefly teamed up with lattice electrons to create doublons, which are two-electron pairings.

If the electrons in the nearby lattice sites didn’t all have aligned spins, these roaming additional electrons and the doublons they kept forming couldn’t delocalize and spread out throughout the lattice. Ultimately, doublons tended to form small, localized ferromagnetic areas as the material doggedly pursued its lowest-energy state. The more doublons flowing through a lattice, up to a particular threshold, the more ferromagnetic the material becomes.

Most importantly, Nagaoka predicted that this effect would also hold true in the case of a lattice with fewer electrons than lattice sites—a scenario that the researchers did not observe. However, that discrepancy stems from the geometric peculiarities of the triangular lattice that the researchers employed as opposed to the square one in Nagaoka’s computations, according to their theoretical work, which was published in Physical Review Research in June ahead of the practical results.

That is a-Moiré.

It seems unlikely that kinetic ferromagnets will be added to refrigerators anytime soon, unless you cook in an extremely cold location. At a chilly 140 millikelvins, researchers assessed the moiré material’s ferromagnetic properties.

Nevertheless, according to İmamoğlu, the material opens up fascinating new possibilities for examining how electrons behave in solids—and for uses that Nagaoka could only have imagined. Together with the theoretical physicists Eugene Demler and Ivan Morera Navarro of the Institute for Theoretical Physics, he hopes to investigate whether charged particles could be made to pair up through kinetic mechanisms similar to those at work in the moiré material. This could lead to the discovery of a new mechanism for superconductivity.

He clarified, “I’m not saying that this is possible yet.” “That’s my preferred destination.”

Conclusion

The revelation of Nagaoka-style magnetism opens doors to new possibilities in physics and materials science. As researchers delve deeper, they aim to uncover further insights into the behavior of electrons and potentially discover new phenomena like superconductivity. This milestone underscores the enduring relevance of theoretical predictions in driving scientific exploration.