Impact of magnetic nanoparticles on the Casimir pressure in three-layer systems

The Casimir pressure is investigated in three-layer systems where the intervening stratum possesses magnetic properties. This subject is gaining in importance in connection with ferrofluids and their use in various microelectromechanical devices. We present general formalism of the Lifshitz theory adapted to the case of ferrofluid sandwiched between two dielectric walls. The Casimir pressure is computed for the cases of kerosene- and water-based ferrofluids containing a 5% fraction of magnetite nanoparticles with different diameters between silica glass walls. For this purpose, we have found the dielectric permittivities of magnetite and kerosene along the imaginary frequency axis employing the available optical data and used the familiar dielectric properties of silica glass and water, as well as the magnetic properties of magnetite. We have also computed the relative difference in the magnitudes of the Casimir pressure which arises on addition of magnetite nanoparticles to pure carrier liquids. It is shown that for nanoparticles of 20 nm diameter at 2 micrometer separation between the walls this relative difference exceeds 140% and 25% for kerosene- and water-based ferrofluids, respectively. An interesting effect is found that at a fixed separation between the walls an addition of magnetite nanoparticles with some definite diameter makes no impact on the Casimir pressure. The physical explanation for this effect is provided. Possible applications of the obtained results are discussed.