This article has been reviewed according to Science X's editorial process and policies. Editors have highlighted the following attributes while ensuring the content's credibility: To build faster and more energy-efficient computers, researchers need to understand nanoscale magnetic materials. But looking inside these tiny magnets is surprisingly difficult: Modern microscopes only measure the magnetic field outside the material, not the magnetic pattern inside.
Because many different internal patterns can produce the exact same field, working backwards has long been a challenge. Physicists at the University of Vienna, together with colleagues in Dresden, Singapore, and Ulsan, have now solved this problem by building the laws of physics directly into modern machine learning methods. Their method reveals the realistic magnetic structure and even determines the precise distance between the sensor and the sample.
The study is published in Physical Review Letters, and the software is freely available as open source. Magnetic materials only a few atomic layers thick could play a key role in future data storage and energy-efficient electronics. To develop them, scientists use advanced instruments like diamond quantum sensors or magnetic force microscopes to scan their surfaces.
Yet these tools cannot see the magnet directly. They only record the magnetic field extending into the space around the sample. "Trying to reconstruct the magnet from this external field is like trying to guess the shape of a light bulb from the beam of light on a wall without knowing how far away it is held," says Alexander Setescak, a doctoral researcher at the University of Vienna and first author of the study.
"Countless different internal arrangements can produce virtually identical fields outside." The Vienna-led team solved this challenge by combining modern machine learning methods with the fundamental laws of magnetism. Rather than guessing, their physics-informed algorithm evaluates possible magnetic patterns and selects the state that minimizes the material's physical energy while matching the measured field. Patterns that violate basic physical laws are automatically ruled out.
"We let the physical energy of the magnet decide which solution is realistic," says Claas Abert, who led the study at the University of Vienna. "The algorithm finds the state the material would naturally form in nature." The researchers tested their approach on measurements from the Max Planck Institute for Chemical Physics of Solids in Dresden. The team examined samples of an ultrathin magnet, Fe₃−ₓGaTe₂, synthesized at the National University of Singapore.
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