🔬 materials science

Soft and chiral phonons in chiral phase of K3NiO2

This study combines Raman scattering experiments and theoretical calculations to confirm that the structural phase transition in K₃NiO₂ near 400 K is driven by a soft phonon at the Z point, which splits into A₁ and B₁ modes in the low-temperature chiral phase, while also revealing that certain phonons with nonzero momentum in this phase exhibit pronounced circular atomic motion and nonzero angular momentum.

Original authors: Hong Dang Nguyen, Fedir Borodavka, Miroslav Lebeda, Nazar Zaremba, Peter Hoehn, Eteri Svanidze, Jan Drahokoupil, Ales Vlk, Stanislav Kamba

Published 2026-08-24

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CC BY 4.0

Original authors: Hong Dang Nguyen, Fedir Borodavka, Miroslav Lebeda, Nazar Zaremba, Peter Hoehn, Eteri Svanidze, Jan Drahokoupil, Ales Vlk, Stanislav Kamba

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the solid world of crystals, atoms are rarely still. Even in a rigid stone, they vibrate constantly, jiggling in place like tiny springs. These vibrations, known as phonons, carry energy and sound through the material. Usually, these vibrations are simple back-and-forth movements. But in certain special crystals, the atoms can move in circles, spinning around a center point as they vibrate. This circular motion gives the vibration a kind of spin, or angular momentum, much like a spinning top. When a crystal structure lacks a mirror image—meaning it cannot be superimposed on its reflection, like a left hand cannot fit into a right-handed glove—it is called chiral. In these chiral crystals, scientists have long suspected that these spinning vibrations could be controlled or even created by the structure itself, opening a door to new ways of manipulating energy and information at the atomic scale.

A team of researchers in the Czech Republic and Germany recently set out to test these ideas in a specific material called K3NiO2. This compound is known to change its internal structure as it cools down. At high temperatures, the atoms arrange themselves in a symmetrical, non-chiral pattern. But as the temperature drops below roughly 420 Kelvin, the structure shifts into a chiral form, twisting into a shape that has a distinct handedness. Theoretical physicists had predicted that this transformation was triggered by a specific type of vibration that becomes unstable and "softens" as the material cools, eventually forcing the atoms to rearrange into the twisted shape. The researchers wanted to see if they could catch this vibration in the act and determine if the resulting spinning atoms possessed the angular momentum that makes them truly chiral.

To do this, the team first had to create the material. They developed a new, safer way to grow tiny crystals of K3NiO2, mixing potassium and nickel oxides in a sealed tube under argon gas. The resulting grains were reddish-brown and incredibly fragile, degrading almost instantly if exposed to air, so they had to be kept in sealed glass tubes filled with gas for the entire experiment. The researchers then shined a laser beam at these crystals and measured the light that bounced back. This technique, called Raman spectroscopy, acts like a fingerprint reader for vibrations; when the laser hits the atoms, the scattered light changes color slightly depending on how the atoms are moving. By cooling the sample down to 80 Kelvin and using different polarizations of light, they could isolate specific vibrations and see how they behaved.

The measurements confirmed the theoretical prediction. As the material cooled toward the transition point, the researchers observed two distinct vibrations that slowed down significantly, a behavior known as "softening." These vibrations disappeared entirely once the material warmed up past 420 Kelvin, exactly as the theory suggested. This proved that the structural change from a symmetrical shape to a chiral one is indeed driven by these specific atomic vibrations. However, when the team looked closer to see if these vibrations were spinning, the results were more nuanced. They used circularly polarized light, which can detect if a vibration is rotating clockwise or counter-clockwise, but they found no evidence that these specific soft vibrations were chiral. The calculations showed that these two vibrations were simple, non-degenerate movements that did not split or rotate in the way a chiral phonon should.

This does not mean the material lacks chiral vibrations entirely. The researchers ran detailed computer simulations of the entire crystal lattice to map out all possible atomic movements. These simulations revealed that while the soft vibrations responsible for the phase change were not chiral, other vibrations at different points in the crystal's internal geometry did exhibit clear circular motion. For instance, a vibration at a frequency of 168 cm⁻¹ showed oxygen atoms moving in a distinct circle, carrying angular momentum. The team concluded that while the specific vibrations that trigger the structural twist are not themselves chiral, the chiral nature of the crystal does allow for other vibrations to spin. The study successfully identified the mechanism behind the material's shape-shifting and clarified exactly which atomic movements carry the spin, separating the cause of the transition from the resulting chiral properties of the crystal.

Technical Summary: Soft and Chiral Phonons in the Chiral Phase of K3NiO2

Problem Statement
The study addresses the structural phase transition in potassium nickel oxide (K3NiO2), which transforms from an achiral tetragonal phase (space group P42/mnm) at high temperatures to a chiral tetragonal phase (space groups P41212 and P43212) upon cooling below approximately 423 K. While theoretical work by Fava et al. predicted that this transition is driven by a doubly degenerate soft phonon at the Z-point of the Brillouin zone (BZ) that folds to the $\Gamma$ -point in the low-temperature phase, experimental confirmation was lacking. Furthermore, the nature of the resulting phonons—specifically whether the soft modes in the chiral phase possess angular momentum (chirality) and how this manifests in Raman spectra—remained an open question.

Methodology
The authors employed a combination of advanced synthesis, experimental spectroscopy, and computational modeling:

Synthesis: A novel, safer synthetic route was developed to produce high-quality K3NiO2 microcrystals (10–20 $\mu$ m) using K, K2O, and NiO without azide decomposition. Due to the material's sensitivity to moisture and air, samples were measured directly in argon-filled quartz capillaries.
Experimental Spectroscopy: Temperature-dependent Raman scattering was performed using a He-Ne laser (633 nm) in both linear (VV and HV) and circular polarization geometries. Measurements spanned 5–1000 cm⁻¹, with a focus on the low-frequency region (<40 cm⁻¹) where soft modes are expected. Spectra were fitted using a sum of damped harmonic oscillators.
Computational Modeling: Phonon dispersions and atomic displacements were calculated across the entire Brillouin zone for both phases using universal machine-learning interatomic potentials (MLIPs), specifically PET-MAD-1.5-S and SevenNet-Nano-5.5. These models were chosen for their ability to reproduce dynamical stability differences between phases at a lower computational cost than Density Functional Theory (DFT). Factor-group analysis was also conducted to determine theoretical phonon symmetries and selection rules.

Key Results

Confirmation of Soft Mode Mechanism: Raman spectra confirmed the theoretical prediction that the phase transition is induced by a soft phonon originating from the Z-point. In the low-temperature chiral phase, this mode activates at the $\Gamma$ -point, splits into two components with $A_1$ and $B_1$ symmetries, and exhibits softening behavior consistent with Cochran's law as the temperature approaches the critical point ( $T_c \approx 420$ K).
Nature of the Soft Modes: The study determined that the observed soft modes are singly degenerate ( $A_1$ and $B_1$ ). Consequently, they do not split under circularly polarized Raman scattering, nor do they exhibit angular momentum at the $\Gamma$ -point. This contrasts with the doubly degenerate nature of the mode in the high-temperature phase.
Chirality at Non-Zero Wavevectors: While the soft modes at the $\Gamma$ -point are achiral, the calculations revealed that phonons with non-zero wavevectors ( $k \neq 0$ ) in the chiral phase do possess angular momentum. Specifically, the authors identified a pronounced circular motion of atoms in a Dirac-type topological phonon at the M-point (frequency $\approx 168$ cm⁻¹) and a Weyl phonon at 43.15 cm⁻¹.
Circular Polarization Sensitivity: Circularly polarized Raman measurements at 80 K revealed additional weak modes (near 210 and 237 cm⁻¹) not seen in linear polarization, demonstrating the technique's sensitivity. However, no frequency splitting was observed for the soft modes or other low-frequency phonons, likely due to the spectrometer's resolution limits or the specific symmetry of the modes at the $\Gamma$ -point.

Significance and Claims
The paper claims to provide the first experimental confirmation that the structural phase transition in K3NiO2 is a displacive transition driven by a geometric chiral soft phonon from the Z-point of the Brillouin zone. The authors successfully validated the theoretical framework proposed by Fava et al., demonstrating that the folding of the Brillouin zone activates the soft mode in Raman spectra.

Crucially, the work clarifies the distinction between structural chirality and phonon chirality in this system. The authors conclude that while the crystal structure is chiral, the specific soft phonons responsible for the phase transition (at the $\Gamma$ -point) are not chiral in the sense of carrying angular momentum. Instead, the angular momentum is a property of specific topological phonons at non-zero wavevectors (e.g., the Dirac phonon at the M-point). The study also highlights the utility of foundation machine-learning potentials as an efficient alternative to DFT for screening phonon stability and calculating dispersions in complex chiral systems, provided their quantitative predictions are validated against experimental data.

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