Historical research guide · 0668 · 2026
Vacuum Torque Without Anisotropy: Switchable Casimir Torque Between Altermagnets
Zixuan Dai · Qing-Dong Jiang
In one minute
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.
Connection
Chapter 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.
From the source
Casimir 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
Between 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
A 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
The 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
Raising 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
The 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
The way in
https://arxiv.org/abs/2601.14381How to cite it
Zixuan Dai, Qing-Dong Jiang (2026) Vacuum Torque Without Anisotropy: Switchable Casimir Torque Between Altermagnets arXiv:2601.14381