Itinerant electron ferromagnetism at zero temperature

A theory of the itinerant-electron ferromagnetism is formulated by use of the Ward-Takahashi relations, which are derived from the requirement of the spin rotational invariance. The calculation follows the loop expansion rule which is so formulated that the internal lines in the diagrams include not only the electrons but also the electron bound states (i.e., magnon). Furthermore, all the quantities appearing in the diagrams are renormalized ones. The expressions for the magnetization, the magnon frequency, the spectral functions for the quasielectron and the magnon, the renormalization factor for the electron-electron interaction constant, etc., are obtained. The result of our analysis shows that the Stoner excitation effect is as significant as the real magnon effect. The numerical calculation, when using the parabolic band model with a contact interaction, shows that the amplitude of the wave function for the quasielectron with the minority spin is drastically reduced at the Fermi level and that the bare interaction constant $\lambda$ is renormalized as $\sqrt{\lambda }$ when $\lambda$ is large. These facts may be important for explanation of the photoemission and tunneling experiments in ferromagnetic metals. The calculated intensity of the magnon spectral function qualitatively agrees with recent neutron-diffraction experiments.