content_image/350769.jpg content_image/350770.jpg content_image/350771.jpg content_image/350772.jpg content_image/350778.jpg content_image/350779.jpg
(10) and (11) into Eqs. (1) and (5) and preserving only the terms with l = 0, one arrives at 

<img src='content_image/350769.jpg'>

where ζ ( z ) is the Riemann zeta function and Li$_{n}$( z ) is the polylogarithm function. Note that at a = 6 µ m Eq. (15) leads to the same values of the Casimir free energy and pressure as those computed in Figs. 1 and 3. Using the equalities 

<img src='content_image/350770.jpg'>

we easily obtain from (15) the asymptotic results for the case of very high magnetic perme- ability µ (0) ≫ 1, 

<img src='content_image/350771.jpg'>

and for nonmagnetic Drude metals 

<img src='content_image/350772.jpg'>

The equalities in (17) coincide with respective results obtained for the nonmagnetic metals described by the plasma model in the limit of large separations (the standard ideal-metal results [14]). Similar approximate equalities were noted above on the basis of computations performed at shorter separations. As to Eq. (18), it coincides with the prediction of the Drude model approach for nonmagnetic metals at large separations [6, 14, 38, 55, 56], as it should be. 

For plates made of ferromagnetic metal described by the plasma model the asymptotic behavior of the Casimir interaction at large separations is a bit more cumbersome. For brevity, we restrict ourselves by the calculation of the Casimir free energy. Introducing the dimensionless variable y = 2 ak ⊥ , we can rearrange Eq. (12) to the form 

where the dimensionless plasma frequency is defined as 

<img src='content_image/350778.jpg'>

<img src='content_image/350779.jpg'>

