with different magnetic properties, and also between a magnetodielectric and a metal plate. As a magnetodielectric, both diamagnetic and paramagnetic materials of the plate are con- sidered taking into account realistic dependence of their ε and µ on the frequency [35–37]. It is shown that for all diamagnets and for paramagnets in the broad sense (with exclusion of only ferromagnets) the influence of magnetic properties of plate material on the thermal Casimir force is negligibly small. This confirms the conclusion made in Ref. [24]. Special attention is paid to the case of Casimir plates made of ferromagnetic materials. From the analysis of frequency dependence of magnetic susceptibilities of ferromagnets, we arrive to the conclusion that magnetic properties can influence the thermal Casimir force only through the contribution of the zero-frequency term of the Lifshitz formula. 

For two similar plates made of ferromagnetic metal the influence of magnetic properties on the magnitude of the Casimir force strongly depends on the model of dielectric permittivity used. Below we show that if ε ( ω ) is represented within the Drude model approach [38], the magnitude of the Casimir force in the high-temperature limit may increase in two times owing to the account of magnetic properties. If the plasma model approach [39, 40] is used, the magnitude of the Casimir force at high temperature computed with account of magnetic properties may be even smaller than in the case when the magnetic properties are disregarded. For two similar plates made of ferromagnetic dielectric the thermal Casimir force at high temperature is shown to be by a factor of 3 larger owing to the account of magnetic properties. 

The role of magnetic properties in the interaction of a ferromagnetic plate with a non- magnetic metal plate also strongly depends on the model of a metal used. We demonstrate that if the Drude model is used to describe the dielectric properties of two metal plates one of which is ferromagnetic and the other is nonmagnetic, the thermal Casimir force is the same as for two nonmagnetic plates. If, however, both ferromagnetic and nonmagnetic metal plates are described by the plasma model, the inclusion of magnetic properties into the Lif- shitz theory leads to a decrease in the magnitude of the Casimir force. For a ferromagnetic dielectric plate interacting with a nonmagnetic metal plate described by the Drude model we show that the magnetic properties do not influence the Casimir force. If the nonmagnetic metal is described be the plasma model, we find that the account of magnetic properties of ferromagnetic dielectric leads to a decrease of force magnitude and may even reverse its sign by changing attraction for repulsion. The use of different approaches to the description of 

