In a crystal, magnetic atoms (iron) connect through bridges (oxygen) at various angles. This angle determines whether their microscopic compasses will point in the same direction (magnet) or in different ones. Quantum entanglement and superposition turn this into a dance, whose rules were derived by Heisenberg, Landau and Bloch.
The new program combines a general scan of the crystal with targeted angle measurements — like a choreographer watching each dancer. Trained on computer simulations of thousands of structures, it uses machine learning to predict magnetic strength 20% more accurately and doesn't confuse two types of order.
The angular patterns turned out to be cosmic: similar geometry likely governs magnetic reconnection in stars and the interiors of magnetars — the strongest magnets in the universe.
The neural network independently rediscovered the Goodenough–Kanamori–Anderson rules, derived on paper in the 1950s: a 90° angle between atoms creates a magnet, while 180° creates its opposite.