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metal particles in the mixture f = 0 . 25. The magnetic permeability of such kind of materials may vary over a wide range [63]. Below we use µ (0) = 25. The dielectric permittivity of polystyrene ε$_{d}$ ( iξ ) is presented in the form (9) with K = 4 oscillators. The parameters of oscillators g$_{j}$ , ω$_{j}$ and γ$_{j}$ are taken from [59, 69]. Specifically, at zero frequency ε$_{d}$ (0) = 2 . 56. The dielectric permittivity of the used ferromagnetic dielectric is obtained as [70] 

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which leads to ε ( n ) fd (0) = 5 . 12. The value of f chosen above belongs to the range of validity of this equation [63]. 

We start with the configuration of two similar plates ( n = 1 , 2) made of the ferromagnetic dielectric with the parameters presented above. As in previous sections, the computations are performed using Eqs. (1) and (5) where the magnetic properties are included in the zero- frequency term ( l = 0) at T = 300 K. In all terms with l ≥ 1 it is assumed that µ$_{l}$ = 1. At zero frequency the TM reflection coefficient for a ferromagnetic dielectric plate is obtained from Eq. (3), 

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The TE reflection coefficient for a ferromagnetic dielectric plate at ξ = 0 coincides with that in Eq. (11) for a ferromagnetic metal described by the Drude model [compare with Eq. (26) for a nonmagnetic dielectric]. The computational results for the Casimir free energy (a) and pressure (b) as functions of separation are shown in Fig. 9. The solid lines are computed with magnetic properties taken into account, the dashed lines are obtained with magnetic properties disregarded ( µ$_{l}$ = 1 at all l = 0 , 1 , 2 , . . . ). As can be seen in Fig. 9, the influence of magnetic properties on the Casimir force increases with the increase of separation. Thus, at separations a = 0 . 5, 2 and 6 µ m the parameter introduced in Eq. (14) takes the values η F ,fd = 54%, 166% and 203%, respectively. A similar situation holds for the Casimir pressure where η$_{P,fd}$ = 36%, 133% and 203% at the same respective separations. 

As one more example, we consider the configuration of one plate made of ferromagnetic dielectric ( n = 1) and the other plate made of a nonmagnetic metal Au ( n = 2). Let the dielectric permittivity of Au, ε$_{p,}$$_{Au}$ ( iξ ), be described by the plasma model (8) with ω$_{p}$ = 9 . 0 eV. This choice is caused by the fact that when one plate is made of a nonmagnetic Drude metal the magnetic properties of the other plate do not influence the Casimir interaction because of Eq. (27). In addition, the computational results for the Au plate described by 

