Demonstration of the Casimir Force between Ferromagnetic Surfaces of a Ni-Coated Sphere and a Ni-Coated Plate

Abstract

We demonstrate the Casimir interaction between two ferromagnetic boundary surfaces using the dynamic atomic force microscope. The experimental data are found to be in excellent agreement with the predictions of the Lifshitz theory for magnetic boundary surfaces combined with the plasma model approach. It is shown that for magnetic materials the role of hypothetical patch potentials is opposite to that required for reconciliation of the data with the Drude model. PACS numbers: 78.20.Ls, 12.20.Fv, 78.67.Bf 1 The Casimir effect [1] is of much interest due to its promising multidisciplinary applications in nanotechnology, condensed matter physics, physics of elementary particles, and in gravitation and cosmology [2,3]. Many experiments on measuring the Casimir force between boundary surfaces made of different materials separated by a vacuum gap or a liquid have been performed in the last 15 years [4][5][6]. It was shown that the magnitude of the Casimir force can be controlled by using different boundary materials [7,8], phase transitions [9][10][11][12][13], and by using the boundary surfaces structured with nanoscale corrugations [14][15][16][17].An unified description of both the van der Waals and Casimir forces is given by the Lifshitz theory [18] in terms of the dielectric permittivity ε(ω) and magnetic permeability µ(ω). The role of magnetic materials in the Casimir force has been studied theoretically [19][20][21][22][23][24][25][26][27][28][29][30]. The interest stems from the possibility to obtain a repulsive Casimir force for application in micromachines. Using real magnetic materials [21,25] did not validate the early results which used constant ε and µ. As µ(iξ) can be large only at ξ < 10 5 − 10 9 Hz, its entire contribution to the Lifshitz formula is through the zero Matsubara frequency [27,28]. For metals, the zero-frequency term is strongly influenced by the inclusion (Drude model approach) or neglect (plasma model approach) of the relaxation properties of free electrons [4]. Thus using µ provides another parameter to study the role of the relaxation properties of free electrons in the Casimir effect. Some experiments demonstrate strong disagreement between the measured data and theoretical predictions when the relaxation properties of electrons are taken into account for metals [4,31,32] or the dc conductivity is included for dielectrics [4,12,13]. The same data are found to be consistent with theory when the relaxation properties are neglected for metals or the dc conductivity of dielectrics is disregarded. Two other experiments [33,34] are claimed to be in favor of the Drude model approach (see critical discussion in [35][36][37][38] Here we have used the same apparatus and cantilever preparation as in Refs. [32,40].The gradient of the Casimir force was measured acting between a Ni-coated hollow glass microsphere of R = 61.71 ± 0.09 µm radius attached to the tip of a rectangular Si cantilever and a Si plate also coated with Ni. The thicknesses of Ni coating were 210 ± 1 nm and 250 ± 1 n...

Casimir interaction at liquid nitrogen temperature: Comparison between experiment and theory

“…Here,C ≡ πω 0 R/k is the calibration constant [we label C with a tilde to indicate the difference with C = ω 0 /(2k) used in the literature 15,16,40 ], ǫ 0 is the permittivity of free space and the numerical coefficients c i can be found in Refs. 7,8,17 .…”

“…[17][18][19][20][21][22][23][24] ). Quite unexpectedly, the experimental data of many experiments performed at room temperature 13,15,16,18,[23][24][25][26] were found to exclude the theoretical predictions taking into account the relaxation properties of conduction electrons for metals and the contribution of free charge carriers for semiconductors of the dielectric type. The same data were found to be consistent with theory neglecting the relaxation properties of conduction electrons for metals and the free charge carriers for dielectric-type semiconductors (the two experiments which claim confirmation of the role of relaxation properties of free electrons for metallic test bodies 27,28 are critically discussed in the literature [29][30][31][32] ).…”

“…However, measurements of the Casimir force between magnetic surfaces 16,40 demonstrated that this suggestion does not lead to the desired result.…”

“…Specifically, measurements with different levels of precision were done between two metallic surfaces (see, e.g., Refs. [11][12][13][14][15][16] ) and between a metallic and a semiconductor surfaces (see, e.g., Refs. [17][18][19][20][21][22][23][24] ).…”

Constraints on corrections to Newtonian gravity from two recent measurements of the Casimir interaction between metallic surfaces

“…Each of these experiments is highly significant, as compared with all earlier measurements of the Casimir interaction. In the first [28] the dynamic AFM was used to measure the gradient of the Casimir force between a plate and a sphere both coated with the ferromagnetic metal Ni with no spontaneous magnetization. As a result, the predictions of the Lifshitz theory generalized for the case of magnetic materials more than 40 years ago [29] were experimentally confirmed.…”