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...

We measured the gradient of the Casimir force between an Au sphere and a plate made of ferromagnetic metal (Ni). It is demonstrated that the magnetic properties influence the force magnitude. This opens prospective opportunities for the control of the Casimir force in nanotechnology and for obtaining Casimir repulsion by using ferromagnetic dielectrics.

We present measurement results for the gradient of the Casimir force between an Au-coated sphere and an Au-coated plate obtained by means of an atomic force microscope operated in a frequency shift technique. This experiment was performed at a pressure of 3 × 10 −8 Torr with hollow glass sphere of 41.3 µm radius. Special attention is paid to electrostatic calibrations including the problem of electrostatic patches. All calibration parameters are shown to be separationindependent after the corrections for mechanical drift are included. The gradient of the Casimir force was measured in two ways with applied compensating voltage to the plate and with different applied voltages and subsequent subtraction of electric forces. The obtained mean gradients are shown to be in mutual agreement and in agreement with previous experiments performed using a micromachined oscillator. The obtained data are compared with theoretical predictions of the Lifshitz theory including corrections beyond the proximity force approximation. An independent comparison with no fitting parameters demonstrated that the Drude model approach is excluded by the data at a 67% confidence level over the separation region from 235 to 420 nm. The theoretical approach using the generalized plasma-like model is shown to be consistent with the data over the entire measurement range. Corrections due to the nonlinearity of oscillator are calculated and the application region of the linear regime is determined. A conclusion is made that the results of several performed experiments call for a thorough analysis of the basics of the theory of dispersion forces.

A significant decrease in the magnitude of the Casimir force (from 21% to 35%) was observed after an indium tin oxide sample interacting with an Au sphere was subjected to the UV treatment. Measurements were performed by using an atomic force microscope in high vacuum. The experimental results are compared with theory and a hypothetical explanation for the observed phenomenon is proposed.

The gradient of the Casimir force between a Si-SiO 2 -graphene substrate and an Au-coated sphere is measured by means of a dynamic atomic force microscope operated in the frequency shift technique. It is shown that the presence of graphene leads to up to 9% increase in the force gradient at the shortest separation considered. This is in qualitative agreement with the predictions of Lifshitz theory using the dielectric permittivities of Si and SiO 2 and the Dirac model of graphene.

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We present the complete results for the dynamic experiment on measuring the gradient of the Casimir force between magnetic (Ni-coated) surfaces of a plate and a sphere. Special attention is paid to the description of some details of the setup, its calibration, error analysis and background effects. Computations are performed in the framework of the Lifshitz theory at nonzero temperature with account of analytic corrections to the proximity force approximation and of surface roughness using both the Drude and the plasma model approaches. The theory of magnetic interaction between a sphere and a plate due to domain structure of their surfaces is developed for both out-of-plane and in-plane magnetizations in the absence and in the presence of spontaneous magnetization. It is shown that in all cases the magnetic contribution to the measured force gradients is much smaller than the total experimental error. The comparison between experiment and theory is done using the rigorous statistical method. It is shown that the theoretical approach taking into account dissipation of free electrons is excluded by the data at a 95% confidence level.The approach neglecting dissipation is confirmed by the data at more than 90% confidence level.We prove that the results of experiments with Ni-Ni, Ni-Au and Au-Au surfaces taken together cannot be reconciled with the approach including free electrons dissipation by the introduction of any unaccounted background force, either attractive or repulsive.

We present complete results of the experiment on measuring the Casimir force between an Aucoated sphere and an untreated or, alternatively, UV-treated indium tin oxide film deposited on a quartz substrate. Measurements were performed using an atomic force microscope in a high vacuum chamber. The measurement system was calibrated electrostatically. Special analysis of the systematic deviations is performed, and respective corrections in the calibration parameters are introduced. The corrected parameters are free from anomalies discussed in the literature. The experimental data for the Casimir force from two measurement sets for both untreated and UVtreated samples are presented. The random, systematic and total experimental errors are determined at a 95% confidence level. It is demonstrated that the UV treatment of an ITO plate results in a significant decrease in the magnitude of the Casimir force (from 21% to 35% depending on separation). However, ellipsometry measurements of the imaginary parts of dielectric permittivities of the untreated and UV-treated samples did not reveal any significant differences. The experimental data are compared with computations in the framework of the Lifshitz theory. It is found that the data for the untreated sample are in a very good agreement with theoretical results taking into account the free charge carriers in an ITO film. For the UV-treated sample the data exclude the theoretical results obtained with account of free charge carriers. These data are in a very good agreement with computations disregarding the contribution of free carriers in the dielectric permittivity. According to the hypothetical explanation provided, this is caused by the phase transition of the ITO film from metallic to dielectric state caused by the UV-treatment. Possible applications of the discovered phenomenon in nanotechnology are discussed.