In the lab, AI reads hidden magnetic patterns inside ultrathin magnets

Above a magnet only a few atomic layers thick, a diamond sensor records a map of the magnetic field, and the magnet itself stays out of sight. That is the problem a team at the University of Vienna set out to solve. Modern microscopes measure the field outside the material, not the pattern inside it, and many different internal patterns can produce the same external field. Working backwards has long been a challenge. In a study published in Physical Review Letters, the Vienna group, with colleagues in Dresden, Singapore and Ulsan, reports a method that reconstructs the hidden structure and also finds the distance to the sensor.

The trick is to stop guessing. The team, led by Claas Abert, combines machine learning with the laws of magnetism. The algorithm evaluates possible magnetic patterns and keeps the one that minimizes the material's physical energy while matching the measured field. 'We let the physical energy of the magnet decide which solution is realistic,' Abert says. Patterns that break basic physical laws are excluded automatically. The same logic applies to the sensor height. Magnetic fields weaken rapidly with distance, so a small error in that height distorts the reconstructed pattern. The software therefore solves for the pattern and the height at the same time, and finds a distance of 81 nanometers.

The method was tested on measurements made at the Max Planck Institute for Chemical Physics of Solids in Dresden. The samples, of an ultrathin magnet called Fe₃₋ₓGaTe₂, were synthesized at the National University of Singapore. The sensor was a diamond device based on an atomic defect known as a nitrogen-vacancy center, sitting tens of nanometers above the magnetic layer. 'In experiments, the exact sensor height is usually unknown,' says Uri Vool, group leader in Dresden. 'Extracting the distance directly from the magnetic measurement removes a major source of error.'

For materials researchers, the immediate gain is a more reliable map, obtained without knowing the sensor height in advance. The approach relies on the energy of the magnetic state rather than on the diamond sensor itself, so the team says the same principle can be adapted to other magnetic imaging techniques. The energy calculation uses NeuralMag, an open-source micromagnetic package developed in Vienna, and the reconstruction code is also freely available. Setescak hopes other laboratories will apply the framework to their own measurements. The team is already preparing the next step, extending the approach to 3D X-ray imaging of complex magnetic nanostructures. The study gives no timeline for industrial use.

The limits are clear. The results come from laboratory measurements on one type of ultrathin magnet and one kind of sensor. The study does not show a working device, and the stated goals, faster computers and data storage, remain targets. What the work changes is the reliability of the map scientists use to design those materials, and its value will depend on whether other groups reproduce it on their own measurements.