🔬 condensed matter

Phonon angular momentum transfer torque

This paper proposes and analyzes the phonon angular momentum transfer torque (PAMTT), a mechanism where thermal gradients or noncentrosymmetry generate polarized phonons that transfer angular momentum to magnetic order, potentially enabling measurable frequency shifts and nanosecond-scale magnetization reversal.

Original authors: Verena Brehm, Daniel A. Bustamante Lopez, Shu Zhang, Dominik Juraschek

Published 2026-09-29

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CC BY 4.0

Original authors: Verena Brehm, Daniel A. Bustamante Lopez, Shu Zhang, Dominik Juraschek

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

Inside the solid materials that make up our world, atoms are never truly still. Even in a rigid crystal, they constantly vibrate, jiggling in place like tiny springs. These vibrations, known as phonons, are usually thought of simply as heat or sound moving through a material. However, physicists have long known that these vibrations can also carry a hidden property called angular momentum. Imagine a spinning top; it possesses a specific kind of motion that allows it to resist falling over. In the microscopic world, certain atomic vibrations can spin in a similar way, carrying their own version of this rotational force. For decades, scientists have learned to control magnetism—the force that makes a compass point north or a hard drive store data—by using electric currents to push these spins. But electricity requires wires and conductors, which limits where and how we can apply these forces. A new question has emerged: can we control magnetism using only heat and the vibrations of atoms, without any electricity at all?

A team of researchers has now proposed a way to do exactly this, introducing a mechanism they call the phonon angular momentum transfer torque. In their work, they describe how a specific arrangement of heat can cause atoms to vibrate in a way that generates a steady stream of rotational force. When this force reaches the boundary of a magnetic material, it can push against the magnetic order, much like a hand pushing a spinning wheel. The researchers suggest that by heating one side of a material more than the other, they can create a situation where these vibrating atoms accumulate a net spin. This accumulation acts as a torque, a twisting force, that can be transferred directly to a neighboring magnetic layer. This process offers a potential route to manipulate magnets in insulating materials, where electricity cannot flow, opening the door to new types of devices that run on thermal gradients rather than electric currents.

To understand how this works, the researchers looked at two specific ways to generate this rotational force from heat. The first method relies on crystals that lack a center of symmetry, meaning their atomic structure is not identical if you look at it from opposite directions. In these materials, a flow of heat can cause the atoms to vibrate in elliptical paths, creating a buildup of angular momentum within the material itself. The second method involves a phenomenon similar to the Hall effect, but for vibrations instead of electric charges. Here, a temperature difference across a material can cause a current of angular momentum to flow sideways, perpendicular to the heat flow. When this sideways flow hits a boundary or an edge, it piles up, creating a localized concentration of rotational force right at the interface where a magnetic material sits.

The team calculated the strength of this effect using realistic estimates for common materials. They found that the amount of angular momentum generated by these thermal methods is significant enough to be measured. In their models, this force could shift the frequency at which a magnet naturally wobbles, a change that could be detected with standard laboratory equipment. More importantly, they simulated what would happen if this force were strong enough to overcome the natural resistance that keeps a magnet stable. Their calculations suggest that with favorable conditions at the interface between the vibrating material and the magnet, this thermal torque could flip the direction of the magnet's north and south poles. This flipping, or switching, could happen on timescales as fast as tens of nanoseconds, which is fast enough for practical use in information processing.

The researchers emphasize that these results are based on theoretical models and numerical simulations rather than direct experimental measurement. They have not yet built a device that demonstrates this effect in a lab, but their work provides a clear roadmap for how it could be achieved. They point out that the strength of the interaction depends heavily on how well the two materials are coupled at their boundary and on the specific properties of the atoms involved. While the effect is predicted to be measurable, the ability to actually reverse a magnet's direction requires a strong connection between the vibrating atoms and the magnetic spins. The authors suggest that future experiments could look for the predicted shifts in magnetic resonance frequencies as the first sign that this transfer of angular momentum is occurring.

This work connects the fields of heat transport and magnetism in a novel way, suggesting that the chaotic jiggling of atoms can be organized into a useful tool for controlling magnetic states. If realized, this phonon angular momentum transfer torque could allow engineers to build devices that operate in environments where electricity is impractical or impossible to use. It represents a shift from thinking of heat merely as waste energy to viewing it as a precise controller for the magnetic properties of matter. The study concludes that while the challenge of building such a system remains, the fundamental physics supports the idea that heat-driven vibrations can indeed push and pull on magnets, offering a new chapter in the story of how we might control the invisible forces that shape our technology.

Technical Summary: Phonon Angular Momentum Transfer Torque

Problem Statement
Controlling the transport and transfer of angular momentum is central to spintronic applications. While established electrical methods (spin-transfer, spin-orbit, and orbital torques) utilize spin- or orbital-polarized currents to manipulate magnetization, there is a growing interest in insulating materials where electrical currents are absent. In this context, lattice vibrations (phonons) have emerged as alternative carriers of angular momentum, characterized by atomic displacements following elliptical trajectories. However, a theoretical framework for transferring this thermally generated, incoherent phonon angular momentum to magnetic order in insulating heterostructures has been lacking.

Methodology and Theoretical Formalism
The authors formulate a Phonon Angular Momentum Transfer Torque (PAMTT) as a lattice analogue to spin-transfer torque. The theoretical approach adapts the Landau-Lifshitz-Gilbert-Slonczewski (LLGS) equation to include a torque term at the interface between a bulk crystal and a thin-film magnetic insulator.

The modified equation of motion for the normalized magnetic moment $m_i$ is:
$\partial_t m_i = \frac{\gamma_{el}}{1 + \kappa_{el}^2} \left[ m_i \times B^0_i + \kappa_{el} m_i \times (m_i \times B^0_i) \right] - \tau_L \left[ \beta_P m_i \times l_{ph} + \beta_R m_i \times (m_i \times l_{ph}) \right]$
where the second line represents the PAMTT. Here, $L_{ph} = L l_{ph}$ is the local phonon angular momentum (PAM) accumulation, with $L$ as its magnitude and $l_{ph}$ as the unit polarization direction. The torque coefficients $\beta_P$ (precession) and $\beta_R$ (relaxation) are treated as dimensionless scaling factors dependent on interface and material properties, analogous to those in spin-torque theories. The coupling strength is governed by $\tau$ , which relates to the phonon magnetic moment and electron gyromagnetic ratio.

Generation and Transfer Mechanisms
The paper identifies two thermal routes for generating the local PAM accumulation ( $L_{ph}$ ) required to drive the torque:

Phonon Edelstein Effect: In noncentrosymmetric crystals, a heat current drives the phonon population out of equilibrium, creating an imbalance between modes carrying opposite PAM. This results in a bulk accumulation ( $L^E_i$ ) proportional to the temperature gradient ( $\nabla T$ ). The direction of induced PAM depends on crystal symmetry (orthogonal in polar crystals, parallel in helical crystals).
Phonon Angular Momentum (PAM) Hall Effect: A longitudinal temperature gradient generates a transverse PAM current due to the mixing of Cartesian vibrational polarizations by force constants. The termination of this current at boundaries or spatial variations leads to edge accumulation ( $L^H_i$ ).

The authors estimate the magnitude of these accumulations using realistic parameters. For the Edelstein effect in materials like wurtzite GaN or helical Te, $L$ is estimated at $\sim 10^{-4}\hbar$ . For the Hall effect in graphene and silicon, edge accumulations are estimated at $\sim 10^{-3}\hbar$ to $10^{-2}\hbar$ .

Key Results and Simulations
Using order-of-magnitude estimates and numerical simulations of macrospin dynamics (solving the modified LLGS equation), the authors demonstrate the potential impact of PAMTT:

Ferromagnetic Resonance (FMR) Modification: The PAMTT introduces a shift in the FMR angular frequency ( $\Delta \omega$ ) and modifies the Gilbert damping. The frequency shift is proportional to the precession coefficient $\beta_P$ and the torque strength. For realistic parameters ( $L \sim 0.005\text{--}0.01\hbar$ ), the predicted frequency difference is in the range of 0.07 MHz to 13 MHz, which is detectable via standard FMR measurements. Reversing the temperature gradient reverses the PAM direction, allowing background signals to be filtered.
Magnetization Switching: The relaxation component of the torque can reduce the effective Gilbert damping. When the torque strength exceeds a critical threshold ( $\tau_L > \tau_0$ $τ_{L} > τ_{0}$ ), the magnetic state becomes linearly unstable, leading to magnetization reversal.
- Simulations indicate that for a conservative estimate of coupling, switching times are on the order of microseconds.
- For an optimistic estimate (assuming strong interfacial coupling and $L = 0.01\hbar$ ), switching times are reduced to the nanosecond scale (approx. 30–110 ns).
- If the coupling is too weak (below the threshold), no switching occurs, highlighting the sensitivity to interfacial conditions.

Significance and Claims
The paper claims to provide a theoretical route for manipulating magnetization in insulating heterostructures that combine magnetic components with noncentrosymmetric, nonmagnetic chiral-phonon materials. By enabling the interconversion between spin and lattice angular momentum, PAMTT offers a mechanism to drive magnetization dynamics without electrical currents.

The authors suggest that PAMTT could be induced in state-of-the-art setups designed for detecting PAM. The primary significance lies in the potential to observe measurable FMR frequency shifts and, under favorable interfacial coupling conditions, achieve magnetization reversal on nanosecond timescales. The authors note that while the study focuses on ferromagnetic systems, the formalism is extensible to antiferromagnetic systems and implies a reciprocal pumping process from the magnetic system back to the phononic system. They anticipate that PAMTT may become relevant for novel information-processing applications, including neuromorphic spintronics, drawing a direct analogy to the role of electronic spin-transfer torque.

Technical Summary: Phonon Angular Momentum Transfer Torque

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