Enhanced repulsive Casimir forces between gold and thin magnetodielectric plates
C. Shelden · B. Spreng · J. N. Munday
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In one page
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.
Why it matters hereChapter 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.
What it claims
01For 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
Published and peer-reviewed02The 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
Published and peer-reviewed03For 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
Published and peer-reviewed04Thinner 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
Published and peer-reviewed05Temperature 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
Published and peer-reviewed06The 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
Designed, not yet built
The way in
https://doi.org/10.1103/PhysRevA.108.032817LICENCE. Published as Physical Review A volume 108, article 032817, 2023, by Calum Shelden, Benjamin Spreng and Jeremy N. Munday of the Department of Electrical and Computer Engineering, University of California, Davis. Licence checked directly: the version of record carries the American Physical Society default licence and the accepted-manuscript licence, neither of which is a Creative Commons grant, and Crossref, Unpaywall and OpenAlex all mark the article closed. TEXT. No text is reproduced here. The summary and the claims below are the site’s own and were written from the authors’ complete preprint, arXiv 2302.00865 version 2, posted 13 June 2023, read on 2026-09-08; that posting carries the arXiv non-exclusive distribution licence, which is also not a Creative Commons grant, so it too is linked rather than quoted. The locators cite the preprint’s numbered sections and figures, which carry the same results as the published article. The work was supported by the Defense Advanced Research Projects Agency QUEST programme under contract HR00112090084, and Calum Shelden by a National Science Foundation Graduate Research Fellowship, grant 2036201. Two companion sheets carry the rest of this conversation: the measured long-range repulsive Casimir-Lifshitz force of Munday, Capasso and Parsegian at /library/stm-bd8d775581, and Spreng, Shelden, Gong and Munday on Casimir repulsion with biased semiconductors at /library/stm-46be43d5f1.
How 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
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