The study was led by scientists from the Helmholtz-Zentrum Dresden-Rossendorf (HZDR), the Fritz Haber Institute of the Max Planck Society, and collaborators in Berlin, Dresden, Jülich, and Eindhoven. Their findings were published in Nature Physics.

A Longstanding Mystery About Magnetism

In physics, quantities such as energy, momentum, and angular momentum are conserved, meaning they cannot disappear or be created from nothing. Instead, they move between different parts of a system. Angular momentum is familiar in everyday life through spinning objects like bicycle wheels or merry-go-rounds, but at the atomic scale it is deeply connected to magnetism.

More than a century ago, Albert Einstein and Wander Johannes de Haas demonstrated that changing the magnetization of a material could physically cause it to rotate. Their famous experiment showed that magnetic and mechanical angular momentum are linked together. Since then, scientists have tried to understand exactly how angular momentum spreads through the internal structure of solids.

Now, researchers have directly watched that process unfold inside a crystal.

Powerful Lasers Reveal Hidden Atomic Motion

The team studied how angular momentum travels between lattice vibrations, which are coordinated motions of atoms inside a crystal. To observe this, the scientists used ultra-strong terahertz laser pulses to drive one vibration into a circular motion. A second ultrafast laser pulse then tracked how that motion interacted with another coupled vibration in the material.

During the experiment, the researchers observed something surprising. As angular momentum moved from one vibration to another, the direction of rotation flipped.

The effect comes from the rotational symmetry of the crystal lattice. In this system, certain rotational states are physically equivalent even when they spin in opposite directions. According to the researchers, the result acts as a direct quantum mechanical signature of angular momentum conservation inside solids.

A Strange "1 + 1 = −1" Quantum Effect

The material used in the experiment, bismuth selenide, displayed especially unusual behavior. The angular momenta tied to its lattice vibrations combined in a way that produced a new rotation moving at twice the frequency but in the opposite direction.

Researchers describe this as a kind of "1 + 1 = −1" effect. In physics, this phenomenon resembles an Umklapp process, where motion is effectively reversed because of the symmetry of the crystal structure. Although Umklapp processes are already known in other areas of condensed matter physics, this is the first experimental demonstration 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."

Future Applications for Quantum Technologies

Beyond solving a longstanding physics question, the findings could also have practical implications. Researchers say the work may help scientists gain greater control over ultrafast processes in quantum materials, potentially contributing to future information technologies and next generation memory devices.

Participating institutions included the Fritz Haber Institute of the Max Planck Society (Berlin), Helmholtz-Zentrum Dresden-Rossendorf, TU Dresden, Forschungszentrum Jülich, and Eindhoven University of Technology (Netherlands).