Vacuum Torque Without Anisotropy: Switchable Casimir Torque Between Altermagnets
Zixuan Dai · Qing-Dong Jiang
Abstract and summary · read the original at the source
In one page
Zixuan Dai and Qing-Dong Jiang, at the Tsung-Dao Lee Institute in Shanghai, show how to switch a vacuum torque on and off. Two flat surfaces held tens of nanometres apart feel the Casimir force, the push the vacuum’s own fluctuations exert on them; when the surfaces are optically lopsided those fluctuations also try to twist the two into alignment, which is the Casimir torque. Until now that twist needed a material with a built-in direction, or a shape or a field that supplied one. Dai and Jiang start instead from altermagnets — a recently identified class of magnet with no net magnetisation, whose spin pattern is tied to the crystal’s own rotation symmetry — and show that a magnetic field pointing straight through the plates, which picks out no direction in the plane at all, still switches the twist on. The torque climbs as the square of the field, and a magnetic underlay lets you choose which way it turns. It is a design for a nanoscale rotating element driven by vacuum fluctuations alone.
Why it matters hereChapter 2 rests on the vacuum being a real, structured medium, and the Casimir torque is its second mechanical signature — not only a pull between surfaces but a twist. This paper adds the knob chapter 6 wants: the twist is absent until you apply a field, grows as the square of it, and reverses sign on demand, so the vacuum interaction itself becomes an input you control rather than a property fixed when the crystal was grown. The thermal companion to this result is on this site at /library/stm-951ff458cb.
What it claims
01Casimir torque has until now been tied to an explicit breaking of rotational symmetry — the dielectric anisotropy of a birefringent crystal, a geometric asymmetry, or an applied field that itself singles out an in-plane direction — and torques of that conventional kind have been observed in the laboratory and proposed as the working principle of nanoelectromechanical elements.Introduction, first paragraph, citing references 4 to 19
Published and peer-reviewed02Between two identical two-dimensional altermagnets the Casimir torque is exactly zero with no field applied: the combined fourfold-rotation-and-time-reversal symmetry of the altermagnetic state forces the in-plane conductivity to obey sigma-xx equal to sigma-yy and sigma-xy equal to minus sigma-yx, which makes the optical response isotropic and the vacuum interaction orientation-independent.Section ’Engineering the strength and sign of Casimir torque via a magnetic field’, first paragraph; Figure 2, the B equals 0 curve
Designed, not yet built03A magnetic field applied perpendicular to the plane, which leaves in-plane rotational symmetry untouched, nevertheless breaks that combined symmetry through the Zeeman coupling and switches an orientation-dependent vacuum interaction on: the torque grows continuously from zero, scales as the square of the field strength, and follows a sine-of-twice-the-twist-angle dependence, with the anisotropy parameter itself growing linearly in the field while the Zeeman energy stays well below the thermal energy.Figures 2 and 3(a) and 3(b); computed for a gap of 30 nanometres at 30 kelvin and fields up to 10 tesla
Designed, not yet built04The sign of the torque can be flipped by adding an exchange bias — for instance by growing one altermagnet on a ferromagnetic substrate — because the torque then scales as the applied field times the sum of the applied field and the bias field, giving two zero crossings, one at zero applied field and one at minus the bias field, so near zero field the direction of the vacuum twist is reversed simply by reversing the direction of the external magnet.Figure 3(c), for a 30 nanometre gap at 30 kelvin with bias fields of plus and minus 2 tesla
Designed, not yet built05Raising the temperature reduces the torque at every separation studied, and for a different reason than in bulk crystals: here temperature directly suppresses the material’s own optical anisotropy, so the torque is substantially modified even at sub-micrometre gaps, whereas in the conventional treatment the dielectric functions are temperature-independent and thermal effects only enter beyond the thermal wavelength of roughly one micrometre.Section ’Thermal effects and distance scaling’; Figure 4 and its inset, at 30, 100 and 300 kelvin under 10 tesla
Designed, not yet built06The distance dependence is qualitatively unlike that of uniaxial bulk materials: the retarded low-temperature regime recovers a one-over-distance-cubed law between roughly 200 nanometres and 80 micrometres, the retarded high-temperature limit decays as an exponential over distance cubed carried entirely by the first Matsubara term because the zero-frequency term has no angular dependence at all, and the non-retarded limit follows no simple power law — three signatures a measurement could look for.Limits (i), (ii) and (iii) following Figure 4; Equations 5 to 8
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Read it · abstract
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 Cn 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.
Zixuan Dai and Qing-Dong Jiang, Tsung-Dao Lee Institute and School of Physics and Astronomy, Shanghai Jiao Tong University, and the Shanghai Branch of the Hefei National Laboratory. Preprint arXiv:2601.14381v1, 20 January 2026.
(Abstract only — see the rights note above for why the full text is not reproduced here. The complete preprint, with the three-band Lieb-lattice altermagnet model, the Lifshitz-style Casimir energy and its angular derivative, the four figures carrying the angular dependence, the quadratic field scaling, the exchange-bias sign reversal and the temperature and distance scalings, together with the Supplemental Material giving the reflection coefficients for a two-dimensional altermagnet, is at the source. The thermal-torque result this paper measures itself against is on this site at /library/stm-951ff458cb.)
The way in
https://arxiv.org/abs/2601.14381LICENCE. Posted as arXiv:2601.14381v1 on 20 January 2026 under the arXiv.org perpetual non-exclusive distribution licence. No Creative Commons statement appears in the text or on the arXiv record and no journal version is registered yet, so this page holds the summary, the claims and the authors’ own abstract and sends the reader to the source. The claims below are read from the preprint text, including its Supplemental Material references. The thermal-torque paper this one measures itself against, Spreng and Munday’s ’Thermal Effects in the Casimir Torque between Birefringent Plates’, is on this site at /library/stm-951ff458cb.
How to cite it
Zixuan Dai, Qing-Dong Jiang (2026) Vacuum Torque Without Anisotropy: Switchable Casimir Torque Between Altermagnets. arXiv:2601.14381
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