By the perturbation calculation and the Hartree-Fock approximation, the free energy of electrons in metals is expanded as a power series of deviations of electron and spin densities from those in the ferromagnetic state up to the fourth power. From the expansion, the wave-vector-dependent dielectric constant and spin susceptibilities of itinerant electrons in the ferromagnetic state are calculated. It is shown that in the ferromagnetic state the external electric (magnetic) field induces not only an electron (spin) density but also a spin (electron) density.
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Takahashi et al. (1970) studied this question.