Silin's Spin Waves in the Conduction Electron Plasma of a Crystal in a Quantizing Magnetic Field

We dedicate this paper to the memory of Victor Pavlovich Silin. The paper contains a modern formulation of the principles and main results of the quantum theory of spin waves in a conduction electron system in a crystal that does not have spontaneous spin ordering. Based on the quantum Fermi-liquid kinetic equation, we describe the propagation of electron spin oscillations in an isotropic system along the direction of a quantizing magnetic field while analyzing the dispersion equation, including the classical and quantum contributions. We present the fundamental results on quantum physics of Silin's spin waves consisting in the existence of quantum magnetic field oscillations of wave frequencies in the region, where the classical collisionless absorption is absent and new quantum spin waves appear in the transparency windows formed due to quantum suppression of classical absorption.