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In a published in Nature Â鶹ÒùÔºics, scientists have achieved the first experimental observation of phonon angular momentum in chiral crystals.

Phonons are the quantized lattice vibrations representing sound and heat in crystals. Theoretically, phonons have been predicted to carry finite angular momentum with potentially remarkable macroscopic consequences.

The famous Einstein-de Haas effect explains how quantum mechanical spin connects to classical angular momentum when a ferromagnetic cylinder rotates under magnetic fields. While this effect has been known for over a century, the phonon version had remained purely theoretical until now.

"In quantum materials, collective excitations are described as quasiparticles that carry and transfer quantum information. Phonons, the fundamental lattice quasiparticles, have been theoretically predicted to carry finite angular momentum."

"To test this prediction, we developed a novel experimental approach based on cantilever technology to directly measure the angular momentum of phonons," explained the research team, led by Hu Miao, Heda Zhang, and Jiaqiang Yan from Oak Ridge National Laboratory, along with Yang Zhang from the University of Tennessee, Knoxville.

A cantilever setup

The observation of phonon angular momentum has proven exceptionally challenging because traditional measurement approaches are incompatible with the requirements of phonon experiments.

Classical Einstein-de Haas experiments require freely suspended samples to observe mechanical rotation. However, phonon studies require solid thermal contacts to create the necessary temperature gradients in cryogenic environments to operate below the material's Debye temperature. This is the threshold below which quantum effects dominate over thermal noise.

This creates an experimental impasse: the low temperatures and thermal gradients needed for phonon angular momentum require solid physical contacts that prevent the free mechanical rotation used in traditional measurements.

"This experimental scheme is, however, challenging for collective quantum excitations that usually require cryogenic sample environment and solid physical contacts, preventing the observation of physical rotation," the researchers explain.

To resolve this fundamental challenge, the team built a cantilever-based measurement system that fully bypasses the necessity for rotation.

Instead of measuring rotation directly, their approach detects the mechanical torque generated by phonon angular momentum with extraordinary precision, thereby allowing them to maintain the necessary thermal contacts while still observing the quantum mechanical effect.

Choosing tellurium

The experimental design centers on ultra-sensitive micro-cantilevers equipped with built-in Wheatstone bridges that detect minute mechanical deformations.

The team placed single-crystal tellurium samples on pairs of cantilevers aligned in opposite directions. This is a crucial design element that allows them to distinguish genuine phonon angular momentum effects from thermal expansion artifacts.

"In our measurement, samples are placed on top of cantilevers that are connected to cooling thermal reservoirs. A thermal gradient is introduced by shining a laser on the samples. This thermal gradient induces phonon AM [angular momentum]."

"Due to the angular momentum conservation, the sample will rotate, inducing a mechanical torque on the cantilever," the researchers explain.

The choice of tellurium was strategic. As a chiral crystal (lacking mirror symmetry), tellurium hosts phonon modes characterized by circular atomic motions that can carry angular momentum. This circular motion is essential because it allows phonon angular momentum to be measured.

When the researchers apply a thermal gradient along the crystal's chiral axis using a precisely controlled laser, they break the time-reversal symmetry of the system, enabling finite phonon angular momentum to emerge.

The heat flow creates a preferred direction that breaks the system's symmetry, allowing circular phonon motions to add up rather than cancel out.

"The direction of thermal gradient-induced phonon angular momentum is determined by the crystal chirality. If the crystal contains both left- and right-handed chirality, the angular momentum will be canceled," the team explains, highlighting why single crystals are essential for the effect.

Validating experimental data

The team's measurements revealed torques on the order of 10^-11 Nm, matching theoretical predictions remarkably well.

Most importantly, the experiments showed the key signatures expected for phonon angular momentum: opposite torque directions on the two cantilevers for single-crystal samples, torque reversal when the thermal gradient direction is flipped, and the disappearance of the effect in polycrystalline samples lacking preferred chirality.

"Shining a laser on the sample can create thermal expansion, which can induce mechanical torque on the sample. This is the main systematic error that must be considered."

"We designed the experiment to have cantilevers pointing in opposite directions. Under this geometry, the true phonon angular momentum induced torque will have the opposite sign, while the 'trivial' laser heating effect will show the same sign," the researchers note, explaining how their experimental design isolates the genuine phonon effect.

The temperature dependence also confirmed theoretical expectations. The effect was strongest at 10 K, well below tellurium's Debye temperature of approximately 130 K, and vanished at room temperature, where thermal energy overwhelms the quantum coherence necessary for phonon angular momentum.

Future work and beyond

This finding could lead to the development of new quantum technologies, such as quantum transduction mechanisms, thermal spin state manipulation, and different quantum information processing techniques.

The ability to generate and control phonon angular momentum through thermal gradients represents a new paradigm for coupling thermal, mechanical, and quantum degrees of freedom in materials.

"Chiral quantum states, including chiral superconductivity and quantum spin liquid, are frontiers of quantum material research. Angular momentum is a key physical property of chiral quantum states."

"Our experimental setup will be applied to various chiral material platforms to reveal emergent chiral quantum excitations with potential quantum information science applications," says the team, regarding future directions.

The work also opens possibilities for entirely new classes of quantum devices that exploit the coupling between thermal gradients and mechanical torques through phonon angular momentum. Such devices could find applications in ultra-sensitive detection systems, like dark matter detection.

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