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at which µ ( iξ ) drops toward unity [35–37]. Thus, for ferromagnetic metals µ ( iξ ) becomes equal to unity at frequencies above of order 10 $^{5}$Hz (see, e.g., [53]) and for ferromagnetic di- electrics at frequencies above of order 10 $^{9}$Hz (see, e.g., [54]). The first Matsubara frequency ξ$_{1}$ at T = 300 K is of order 10 $^{14}$Hz. Thus, ξ$_{1}$ is much larger than the frequencies where magnetic permeability of ferromagnets drops to unity. Because of this, in all applications of the Lifshitz formulas (1) and (5) at room temperature (and even at much lower temper- atures) one can put µ$_{l}$ = 1 at all l ≥ 1 and include ferromagnetic properties only in the zero-frequency term with l = 0. Keeping in mind that the contribution of the zero-frequency term (and thereby magnetic properties) increases with the increase of separation between the plates, below we perform all computations in the region from 0 . 5 µ m to 6 µ m. Near the left boundary of this interval the contribution of the zero-frequency term is of order of a few percent and at the right boundary this term determines the total values of the Casimir free energy and pressure (at larger separations the Casimir interaction becomes too small to be measured). 

In addition to the magnetic permeability, one needs to know the frequency-dependent di- electric permittivity for the materials under consideration in order to compute the Casimir free energy and pressure. For metals, at separations above 0 . 5 µ m the contribution of the interband transitions into the Casimir interaction is negligible. At such separations inter- action is completely determined by the role of free conduction electrons. Main approaches to the calculation of the Casimir force between metal plates used in the literature describe conduction electrons by means of the Drude model [6, 14, 38, 55, 56] or the plasma model [14, 39, 40, 47, 57]. Within the Drude model approach the dielectric permittivity along the imaginary frequency axis is given by 

<img src='content_image/332315.jpg'>

where ω$_{p}$ is the plasma frequency and γ is the relaxation parameter. The dielectric permit- tivity of the plasma model is obtained from (7) by putting γ = 0. 

<img src='content_image/332316.jpg'>

Both models lead to markedly different theoretical predictions for the Casimir pressure between two metal plates. Predictions based on the Drude model have been experimentally excluded at high confidence level in experiments using a micromechanical torsional oscillator 

