Vacuum Torque Without Anisotropy: Switchable Casimir Torque Between Altermagnets

Abstract

Casimir torque is conventionally associated with explicit breaking of rotational symmetry, arising from material dielectric anisotropy, geometric asymmetry, or externally applied fields that themselves break rotational invariance. Here we demonstrate a fundamentally different mechanism: an axially symmetric magnetic field can generate a Casimir torque by inducing an axially asymmetric Casimir energy - and can even reverse the torque's sign. Focusing on two-dimensional altermagnets, we show that a magnetic field applied perpendicular to the plane - while preserving in-plane rotational symmetry - activates an orientation-dependent vacuum interaction through the combined crystalline symmetry $\mathrm{C_n T}$ inherent to altermagnetic order. The resulting torque emerges continuously and scales quadratically with the magnetic field strength. We further analyze its temperature and distance dependence, revealing scaling behaviors that are qualitatively different from those found in uniaxial bulk materials. Our results identify time-reversal symmetry breaking as a powerful route for engineering both the sign and strength of Casimir torque and establish altermagnets as an exciting platform for exploring phenomena driven by vacuum quantum fluctuations.

Figures (4)

• Figure 1: Schematic figure for the Casimir torque between two Lieb-lattice altermagnets with separation distance $d$. The relative angle between the crystal axes is $\theta$. The z-axis is perpendicular to the plane.
• Figure 2: Casimir torque per unit area as a function of $\theta$ between two altermagnets with separation distance $d = 30\textup{nm}$. The temperature is set to be $T = 30\textup{K}$. The torque varies with $\theta$ sinusoidally. The magnitude of the torque increases with the increasing magnetic field.
• Figure 3: (a) The magnitude of the torque and (b) the degree of anisotropy $\delta = (\sigma_{xx} - \sigma_{yy})/(\sigma_{xx} + \sigma_{yy})$ as a function of the magnetic field $B$ at temperature $T = 30\textup{K}$. The separation is $d = 30\textup{nm}$. When $\mu_BB\ll k_BT$, the torque increases with the magnetic field quadratically, and $\delta$ increases with the magnetic field linearly. Since we are considering two identical altermagnets, the subscript of $\delta$ is omitted here. (c) The torque for $\theta = \pi/4$ at temperature $T = 30\mathrm{K}$ when placing one of the altermagnets (AM) on a ferromagnetic (FM) substrate. The separation between altermagnets is $d = 30\textup{nm}$. The ferromagnetic substrate provide an exchange bias field $B_{bias}$. The torque sign reverses when the external magnetic field $B$ cross two critical points: $B = 0$ and $B = -B_{bias}$.
• Figure 4: The magnitude of the torque as a function of separation $d$ for temperatures $T = 30\textup{K}$ (blue curve), $100\textup{K}$ (green curve) and $300\textup{K}$ (red curve) in an external magnetic field of $B=10\textup{T}$. At all distances, the torque decreases with increasing temperature. Inset figure depicts the degree of anisotropy $\delta$ as a function of the imaginary frequency at $B = 10T$. $\delta$ decreases monotonically with increasing frequency. For all frequencies, $\delta$ decreases with increasing temperature.