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Magnetic-field tuning of the Casimir force


The quantum fluctuation-induced Casimir force can be either attractive or repulsive, depending on the dielectric permittivities and magnetic permeabilities of the materials involved. However, it is challenging to manipulate the dielectric permittivities of most materials using external fields. In contrast, the magnetic permeabilities of ferrofluids can be readily tuned by magnetic fields, which opens up the possibility of magnetic-field tuning of the Casimir force. Here, we demonstrate that this tuning can be achieved for a gold sphere and a silica plate immersed in water-based ferrofluids. Our theoretical calculations predict that, by varying the magnetic field, separation distance and ferrofluid volume fraction, the Casimir force can be tuned from attractive to repulsive over a wide range of parameters in this system. Experimentally, we develop a cantilever designed to conduct measurements within water-based ferrofluids. Using this setup, we observe the predicted transitions. These findings may lead to the development of switchable micromechanical devices based on the Casimir effect.

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Fig. 1: The magnetic-field-tunable Casimir force in ferrofluids.
Fig. 2: The experiment setup and the cantilever design.
Fig. 3: The Casimir force between a gold-coated sphere and an SiO2 plate in a ferrofluid.
Fig. 4: The Casimir force between a gold-coated sphere and a gold-coated plate in a ferrofluid.

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Data availability

Further data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request. Source data are provided with this paper.

Code availability

Codes for reproducing the calculation results are available from the corresponding author upon reasonable request.


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Y.Z., H.Z., X.W., Y.W., Y.L., S.L., T.Z., C.F. and C.Z. were supported by the National Key Research and Development Program of China (grant no. 2023YFA1406300), the Innovation Program for Quantum Science and Technology (grant no. 2021ZD0302800), the National Natural Science Foundation of China (grant nos. 92165201, 92265201 and 12074357), Anhui Provincial Key Research and Development Project (grant no. 2023z04020008), the CAS Project for Young Scientists in Basic Research (grant no. YSBR-046), the Geek Center Project of USTC and the Fundamental Research Funds for the Central Universities (grant nos. WK9990000118 and WK2310000104). Part of this work was carried out at the USTC Center for Micro and Nanoscale Research and Fabrication.

Author information

Authors and Affiliations



C.Z. and H.Z. designed and supervised the work. Y.Z. and H.Z. performed the experiments with assistance from X.W., Y.L., S.L., T.Z. and C.F. Y.Z. performed the theoretical calculation and analysis. C.Z., Y.Z. and H.Z. analysed the data and wrote the manuscript with assistance from Y.W. and C.F. All authors contributed to the scientific discussion and manuscript revisions.

Corresponding authors

Correspondence to Hui Zhang or Changgan Zeng.

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The authors declare no competing interests.

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Nature Physics thanks Daniel Dantchev, Giovanni Volpe and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 Calculated dielectric permittivities of materials used in this work.

a, Calculated dielectric permittivities of Au, SiO2, H2O, Fe3O4 and kerosene respectively. The inset is a zoom-in plot of the dielectric permittivities with the Matsubara energy in the range between 100 eV and 500 eV. b, Calculated dielectric permittivities of water-based ferrofluids with different volume fractions. The dielectric permittivities of Au and SiO2 are also shown for comparison.

Extended Data Fig. 2 Magnetization curve of 4.9% ferrofluid measured by vibrating sample magnetometer.

The square dots are the measured results. The orange line is the theoretical fitting by first-order modified mean-field model (see Supplementary Note 3). No apparent hysteresis is observed.

Extended Data Fig. 3 Calculated Casimir force between a gold sphere and a silica plate in ferrofluid as a function of separation distance and magnetic field.

a-d, 3.5%, 4.9%, 5.5% and 9% volume fractions, respectively. Iso-lines are plotted in bright dashed lines to show the magnitude of the Casimir force.

Source data

Extended Data Fig. 4 Measured Casimir force in 5.5% water-based ferrofluid between gold-coated sphere and SiO2 plate.

Measurements data at μ0H = 0 and 8.6 mT are averaged from eleven and six measurements respectively, with error bars indicating the standard deviation. The fitting results according to the Lifshitz theory are presented by solid lines.

Source data

Supplementary information

Supplementary Information

Supplementary Sections 1–6 and Figs. 1–5.

Source data

Source Data Fig. 2

Statistical source data.

Source Data Fig. 3

Statistical source data.

Source Data Fig. 4

Statistical source data.

Source Data Extended Data Fig./Table 3

Statistical source data.

Source Data Extended Data Fig./Table 4

Statistical source data.

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Zhang, Y., Zhang, H., Wang, X. et al. Magnetic-field tuning of the Casimir force. Nat. Phys. (2024).

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