Historical research guide · 0462 · 2023
Enhanced repulsive Casimir forces between gold and thin magnetodielectric plates
C. Shelden · B. Spreng · J. N. Munday
In one minute
Calum Shelden, Benjamin Spreng and Jeremy Munday of the University of California, Davis ask a practical question about the vacuum: what would it take to make it push two plates apart rather than pull them together? Timothy Boyer showed in 1974 that pairing a mirror with a strongly magnetic surface flips the sign of the Casimir force, and this paper works out how magnetic a real material has to be. Using Lifshitz theory the team finds the repulsion comes almost entirely from one channel, the zero-frequency transverse-electric mode, and that thinning the magnetic plate to a few nanometres relaxes the requirement into a simple rule of thumb: repulsion survives as long as the plate’s low-frequency magnetic response is at least as large as its electrical one. Push the permeability past a thousand, keep the film near a nanometre thick, run slightly warm, and the predicted push reaches the millipascal scale a few hundred nanometres out, inside the reach of today’s force microscopes.
Connection
Chapter 2 needs the vacuum to be a medium you can engineer rather than a background you endure, and a repulsive Casimir force measured in vacuum would be the plainest demonstration yet that the field’s pressure can be steered by material design alone. Chapter 6 needs that same asymmetry, because every proposal for drawing work from the field begins with plates that do not simply stick together.
From the source
For a magnetodielectric plate ten nanometres thick or thinner, the condition for Casimir repulsion against gold collapses to a simple linear rule: the plate’s zero-frequency permeability must be at least as large as its zero-frequency permittivity. For thick plates the same condition was an asymptote near a permittivity of eight, a far tighter ceiling.Abstract; Section III and Figure 4a, arXiv 2302.00865v2
The whole of the repulsion comes from the zero-frequency transverse-electric mode. The zero-frequency transverse-magnetic mode and every mode at nonzero frequency are attractive, which is why the interaction attracts at short separations and repels beyond a transition distance.Section II B and Figure 3b, arXiv 2302.00865v2
For a worked example — semi-infinite gold facing a one-micrometre yttrium iron garnet plate at 300 kelvin — the force vanishes and turns repulsive at about 2.26 micrometres, with the largest repulsion near 2.96 micrometres.Section II B and Figure 3a, arXiv 2302.00865v2
Thinner is better only up to a point. The maximum repulsion rises as the magnetic film is thinned, peaks at a critical thickness set by the permeability, and then falls back towards zero, because a plate of no thickness is no cavity at all.Section IV and Figure 6, arXiv 2302.00865v2
Temperature is a usable tuning knob: raising the system from 300 to 310 kelvin moves the attraction-to-repulsion transition inwards by 36.4 nanometres at a permeability of 20, and by 5.6 nanometres at a permeability of 160, provided the material is kept below its Curie point.Section V and Figure 7, arXiv 2302.00865v2
The design target that follows: a zero-frequency permeability above one thousand, a film about one nanometre thick, and a warm cavity give millipascal-scale repulsion within a few hundred nanometres — reachable by existing force-gradient measurement with an atomic force microscope. Magnetic van der Waals materials are named as the candidate class, and such a plate could be levitated above gold.Section VI, Conclusions, arXiv 2302.00865v2
The way in
https://doi.org/10.1103/PhysRevA.108.032817How to cite it
C. Shelden, B. Spreng, J. N. Munday (2023) Enhanced repulsive Casimir forces between gold and thin magnetodielectric plates doi:10.1103/PhysRevA.108.032817