Researchers discovered that atomic rotations inside a crystal can unexpectedly flip direction while still obeying the laws of angular momentum conservation.
An international team of researchers, including scientists from the Helmholtz-Zentrum Dresden-Rossendorf (HZDR) and the Fritz Haber Institute of the Max Planck Society, has directly observed for the first time how angular momentum moves and remains conserved inside a crystal lattice. By using powerful terahertz laser pulses, the team was able to precisely manipulate these motions and discovered an unexpected effect: during the transfer process, the direction of rotation flips because of the material’s rotational symmetry.
The study, published in Nature Physics, offers new insight into the origins of magnetism and could help researchers develop more precise ways to control quantum materials.
Understanding Angular Momentum in Solids
Quantities such as energy, momentum, and angular momentum are governed by conservation laws, meaning they cannot be created or destroyed in a closed system. Instead, they can only be transferred or converted into other forms. Although angular momentum is commonly associated with spinning objects like bicycles or carousels, it is also fundamental to quantum physics and plays a key role in magnetism.
More than a century ago, Albert Einstein and Wander Johannes de Haas showed that altering a material’s magnetization could produce measurable mechanical rotation. Their experiment demonstrated that magnetic and mechanical angular momentum are closely connected. Since then, scientists have tried to determine exactly how angular momentum spreads through solids by moving across the crystal lattice, the organized arrangement of atoms inside a material.
Researchers from Berlin, Dresden, Jülich, and Eindhoven have now managed to observe this process directly. Their experiments revealed how angular momentum passes between different lattice vibrations, which are coordinated movements of atoms within the crystal. The findings improve scientists’ understanding of how magnetism forms and stabilizes in solid materials.
Laser Pulses Reveal a Reversal Effect
The team also showed they could control the rotational direction of atomic motions using extremely intense terahertz laser pulses. One laser pulse drove a lattice vibration into a circular motion, while a second ultrafast pulse measured another connected vibration in the crystal.
During this transfer between vibrations, the researchers saw something unexpected: the angular momentum reversed direction.
According to the team, this happens because of the crystal lattice’s rotational symmetry. Some rotational states are physically identical even though they spin in opposite directions. The researchers say the observation acts as a direct quantum mechanical signature of angular momentum conservation inside solids.
A Quantum “1 + 1 = −1” Effect
The experiments focused on the quantum material bismuth selenide. In this material, angular momentum linked to lattice vibrations, known as lattice angular momentum, can combine to create a new rotation with twice the frequency but the opposite rotational direction.
The researchers compare this unusual “1 + 1 = −1” effect to an Umklapp process, where the symmetry of the crystal lattice effectively reverses the direction of motion. According to the team, this is the first experimental demonstration of such behavior involving lattice angular momentum.
“I find it extraordinarily elegant how the laws of physics are directly dictated by the symmetries of nature,” says Olga Minakova, doctoral researcher at the Fritz Haber Institute of the Max Planck Society and central experimental physicist of the study.
Sebastian Maehrlein, head of department at the Institute of Radiation Physics at HZDR, professor at TU Dresden, and leader of the study, adds: “For me, these are exceptionally exciting results. We have discovered something fundamentally new that will hopefully make its way into the textbooks.”
The researchers say the work could eventually lead to better control of ultrafast processes in quantum materials and may support the development of future information technologies and advanced memory devices.
Reference: “Observation of angular momentum transfer among crystal lattice modes” by Olga Minakova, Carolina Paiva, Maximilian Frenzel, Michael S. Spencer, Joanna M. Urban, Christoph Ringkamp, Martin Wolf, Gregor Mussler, Dominik M. Juraschek and Sebastian F. Maehrlein, 12 May 2026, Nature Physics.
DOI: 10.1038/s41567-026-03274-8
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