“The reason we have magnetism in our daily lives is because of the strength of electron exchange interactions,” said the study’s co-author. Ataç İmamoğluphysicist also from the Institute of Quantum Electronics.
However, as Nagaoka theorized in the 1960s, exchange interactions may not be the only way to make a material magnetic. Nagaoka imagined a two-dimensional square lattice where each site in the lattice had only one electron. He then discovered what would happen if one of those electrons were removed under certain conditions. As the remaining electrons in the lattice interacted, the hole where the missing electron had been would slide around the lattice.
In the Nagaoka scenario, the overall energy of the lattice would be at its lowest level when all of its electron spins were aligned. Each electron configuration would look the same, as if electrons were identical mosaics in the dullest world. sliding tile puzzle. These parallel spins, in turn, would make the material ferromagnetic.
When two grids with a twist form a pattern
İmamoğlu and his colleagues intuited that they could create Nagaoka magnetism by experimenting with single-layer sheets of atoms that could be stacked to form an intricate moiré (pronounced mwah-ray). In atomically thin layered materials, moiré patterns can radically alter the behavior of electrons and, therefore, the materials. For example, in 2018 the physicist Pablo Jarillo-Herrero and his colleagues proven that the two-layer graphene stacks acquired the ability to superconduct when they displaced the two layers with a spin.
Since then, moiré materials have emerged as a compelling new system for studying magnetism, nestled alongside clouds of supercooled atoms and complex materials such as cuprates. “Moiré materials provide us with a playing field to basically synthesize and study electron states in many bodies,” İmamoğlu said.
The researchers began by synthesizing a material from monolayers of semiconductors molybdenum diselenide and tungsten disulfide, which belong to a class of materials that past simulations had hinted that he might exhibit Nagaoka-style magnetism. They then applied weak magnetic fields of different strengths to the moiré material while tracking how many of the material’s electron spins aligned with the fields.
The researchers then repeated these measurements while applying different voltages across the material, which changed the number of electrons in the moiré lattice. They found something strange. The material was more likely to align with an external magnetic field (that is, to behave more ferromagnetic) only when it had up to 50 percent more electrons than lattice sites. And when the lattice had fewer electrons than the lattice sites, the researchers saw no signs of ferromagnetism. This was the opposite of what they would have expected to see if standard Nagaoka ferromagnetism had been operating.
However, the material was magnetizing, the exchange interactions did not seem to drive it. But the simplest versions of Nagaoka’s theory also did not fully explain its magnetic properties.
When your things become magnetized and you are a little surprised
In the end it all came down to movement. Electrons reduce their kinetic energy as they expand in space, which can cause the wave function describing the quantum state of an electron to overlap with that of its neighbors, linking their fates. In the team’s material, once there were more electrons in the moiré lattice than lattice sites, the energy of the material decreased as the extra electrons delocalized like fog pumped across a Broadway stage. They then fleetingly paired with electrons in the lattice to form two-electron combinations called doubloons.
These extra roaming electrons, and the doubloons they continued to form, could not delocalize and spread within the lattice unless all the electrons in the surrounding sites of the lattice had aligned spins. As the material relentlessly pursued its lowest energy state, the end result was that the doubloons tended to create small, localized ferromagnetic regions. Up to a certain threshold, the more doubloons that pass through a network, the more ferromagnetic the material becomes detectable.