Atoms vibrate on circular paths – with an unexpected twist 

An international team of researchers from the Fritz Haber Institute of the Max Planck Society and the Helmholtz-Zentrum Dresden-Rossendorf (HZDR) directly observed how angular momentum is transferred and conserved within a crystal lattice. Using intense terahertz laser pulses, the researchers were able to selectively control these processes, which unveiled a surprising effect: during the angular momentum transfer, the direction of rotation reverses – caused by the rotational symmetry of the material. The results provide new insights into the foundation of magnetism and open up possibilities for tailored control of quantum materials.

Key aspects

• The core question: How is angular momentum, a fundamental physical quantity, conserved and transferred among collective vibrations of a crystal lattice?
• The experiment: The research team used highly-intense terahertz light pulses with circular polarization to drive specific atomic motions of a solid onto circular pathways. Consecutively, with ultrashort laser pulses, they could stroboscopically trace the pathways and thus the angular momentum of the coupled lattice vibration.
• The finding: The initial atomic motion converts into a new, higher-frequency atomic motion that rotates in the exact opposite rotational direction.
• Fundamental insight: This reversal of circular atomic motion is fundamentally dictated by the conservation of angular momentum in a solid due to its discrete rotational symmetry. We therefore experimentally verify the conservation of energy, linear momentum and - for the first time - angular momentum for phonon-phonon scattering processes.

Conserved quantities such as energy, momentum, and angular momentum determine the fundamental laws of nature. In a closed system, these quantities are always conserved: they cannot be created or destroyed, only transformed or transferred. While angular momentum is familiar in everyday life through rotating carousels or riding a bicycle, it plays a central role at the quantum level – for example as the fundamental origin of magnetism.

A century-old question in physics

More than 100 years ago, Albert Einstein and Wander Johannes de Haas demonstrated in their famous experiment that changing the magnetization of a material induces a measurable mechanical rotation, revealing that magnetic and mechanical angular momentum are intrinsically linked. Since then, researchers have sought to understand how the resulting angular momentum is distributed inside a solid – in other words, how it is transferred through the crystal lattice, the regular arrangement of atoms.

Now, an international team of physicists from Berlin, Dresden, Jülich, Tel Aviv and Eindhoven has succeeded in directly observing this process for the first time. The researchers show how angular momentum is transferred between different lattice vibrations – collective motions of atoms within the crystal. Their findings provide an important foundation for understanding how magnetism stabilizes and equilibrates in solids.

Tailored control of angular momentum with terahertz laser light

Moreover, the team succeeded in selectively controlling the rotational direction of atomic circular motions using ultra-strong laser pulses in the terahertz spectral range. These invisible laser pulses drive a specific lattice vibration into a circular trajectory, while a second ultrashort laser pulse probes another coupled vibration of the crystal. In doing so, the researchers observed a surprising effect: during the transition between these vibrations, the direction of angular momentum reverses.

This effect arises from the special rotational symmetry of the crystal lattice: certain rotational states are physically equivalent, even though they rotate in opposite directions. The experimental observation therefore represents a direct quantum-mechanical “fingerprint” of angular momentum conservation in solids.

For the quantum material investigated here, bismuth selenide, an unusual picture emerges: the angular momenta bound to lattice vibrations – so-called lattice angular momenta – can combine in such a way that a rotation with twice the frequency but opposite rotational direction is generated. Conceptually, this “1 + 1 = −1” behavior corresponds to a so-called Umklapp process, in which the direction of motion is effectively reversed by the symmetry of the crystal lattice. Such a process has now been experimentally demonstrated for lattice angular momentum for the first time.

“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, group leader in the Physical Chemistry Department a the Fritz Haber Institute and Department head at the Institute of Radiation Physics at HZDR, who led 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.”

In the long term, these findings pave the way for the targeted control of ultrafast processes in quantum materials and may provide new directions for future information technologies and novel memory devices.