where the penetration depth of the electromagnetic oscillations into Au, δ$_{02}$ , is defined in accordance with Eq. (21). The Casimir free energy in Eq. (36) can be both negative and positive leading to the attractive and repulsive Casimir force, respectively, in the configuration of a sphere above a plate used in most of recent experiments [14, 47]. Keeping in mind that δ$_{02}$ ≪ a , the Casimir free energy is negative if the following condition is satisfied: Li$_{3}$ [ ε (0) − 1 ε (0) + 1 ] > ∣ [ 1 − µ (0) 1 + µ (0) ]∣ ∣ ( 1 − 2 δ$_{02}$ a ) . (37) If, on the opposite, it holds then the Casimir free energy is positive and the Casimir force acting in the sphere-plate configuration is repulsive. Li$_{3}$ [ ε (0) − 1 ε (0) + 1 ] < ∣ [ 1 − µ (0) 1 + µ (0) ]∣ ∣ ( 1 − 2 δ$_{02}$ a ) , (38) In Fig. 11 we show the region of attraction (below the solid line) and repulsion (above the solid line) in the [ ε (0) , µ (0)]-plane at separation distance a = 6 µ m. For points belonging to the solid line the Casimir force acting between the sphere and the plate vanishes [for the coordinates of these points the inequalities (37) and (38) become equalities]. Keeping in mind that for ferromagnetic dielectrics ε (0) is typically not very small (for the material discussed above it is equal to 5.12) the region of the repulsive Casimir force is rather restricted. This is connected with the fact that the solid line in Fig. 11 has the vertical asymptote ε (0) = 8 . 45. Thus, there is no repulsive Casimir force at a = 6 µ m in the sphere-plate configuration for ferromagnetic dielectrics possessing larger values of ε (0). Note that although the analytic results (37) and (38) can be used only at sufficiently large separations ( a ≥ 6 µ m), the results of numerical computations presented in Fig. 10 show that the Casimir repulsion due to magnetic properties of ferromagnetic dielectric may exist at shorter separations as well. As mentioned in Sec. II, at the Curie temperature T$_{C}$ specific for each material ferro- magnets undergo a magnetic phase transition [50, 52]. At higher temperatures they become paramagnets in the narrow sense which are characterized by negligibly small magnetic prop- erties with respect to the Casimir force. In this section we consider the behavior of the VI. THE CASIMIR FORCE IN THE VICINITY OF CURIE TEMPERATURE 21