Thermal Spin Waves from Accelerating Domain Walls via the Unruh Effect

We consider a wire consisting of a conducting ferromagnetic layer and an insulating antiferromagnetic layer that are coupled. The ferromagnet hosts a domain wall, which is dynamically driven by a charge current. We show that for a specific time-dependent current, the domain wall moves according to a Rindler trajectory. This motion excites spin waves in the antiferromagnetic insulator, and their emission spectrum is characterised by an effective temperature analogous to the Unruh temperature, $T_U = \hbar a/2πc k_B$, with a the acceleration of the domain wall, c the maximum antiferromagnetic spin wave velocity, and kB the Boltzmann constant. This thermal signature is a direct consequence of the Unruh effect and could be experimentally observed. Our results establish magnetism as a promising platform for probing relativistic quantum field phenomena. Moreover, since the Unruh effect is inherently linked to entanglement, our proposal provides a route for entangling magnetic domain walls via relativistic effects.

💡 Research Summary

This paper proposes a magnetic system as a novel analogue gravity platform to demonstrate the Unruh effect, a quantum field theoretic phenomenon where an uniformly accelerated observer perceives a thermal bath of particles. The core idea leverages the fact that spin waves (magnons) in an antiferromagnetic insulator are described by a relativistic Klein-Gordon field theory in the long-wavelength limit, with a maximum propagation speed ‘c’ much smaller than the speed of light.

The proposed setup is a wire consisting of a conducting ferromagnetic (FM) layer and an insulating antiferromagnetic (AFM) layer, coupled via a weak RKKY interaction through a non-magnetic spacer. The FM layer hosts a domain wall (DW). The authors show that by applying a specific time-dependent charge current I(t) to the FM layer, the DW can be driven to move along a Rindler trajectory—a path of constant proper acceleration ‘a’—as defined by the relativistic dynamics of the AFM spin waves.

The theoretical framework is built stepwise. First, the Lagrangian for the coupled FM-AFM system is derived. Integrating out the small magnetization of the AFM yields an effective Lagrangian for the Neel vector fluctuations, which are the spin waves. This results in a Klein-Gordon equation for the spin wave field φ(x,t), with a source term j(x,t) that is directly proportional to the transverse components of the FM’s magnetization. Thus, the moving FM DW acts as a source for AFM spin waves.

Next, the dynamics of the FM DW itself are analyzed. Using a collective coordinate approach for a DW described by its position r(t) and internal angle φ0(t), equations of motion are derived from the FM Lagrangian and a Rayleigh dissipation functional. By solving these equations under the condition of being below the Walker breakdown limit, the required time-dependent spin-transfer torque velocity v_s(t) (proportional to the charge current) for the DW to follow a Rindler trajectory r(t) = c√(t² + c²e^(2aξ/c²)/a²)/a is determined (Eq. (7)). This current starts linearly and saturates at a maximum value.

The central result is presented in the analysis of the spin wave emission from this accelerating DW. The solution to the Klein-Gordon equation with the moving source is found by expressing the source in terms of modes appropriate for an accelerated observer (Rindler modes). Transforming this solution back into the basis of inertial (Minkowski) modes allows the calculation of the average spin wave amplitude A_M (Eq. (12)). The analysis reveals that the spectrum of emitted spin waves is thermal, characterized precisely by the Unruh temperature T_U = ħa/(2πck_B). This means the accelerating DW emits spin waves as if it were immersed in a thermal bath at temperature T_U, providing a direct analogue of the Unruh effect.

The authors conclude that magnetic systems, due to their high tunability, offer a promising and versatile testbed for observing analogue gravity phenomena like the Unruh effect, which are otherwise inaccessible in high-energy physics experiments. Furthermore, they highlight a profound implication: since the Unruh effect is linked to quantum entanglement, their proposal suggests a pathway to entangle two co-accelerating magnetic textures (like domain walls or skyrmions) via relativistic effects, opening new avenues in the emerging field of quantum magnonics.