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Spin and valley wave collective modes in metals with population imbalance

Alexander Zyuzin

The effect of electron-electron exchange interaction in metals with non-equilibrium spin orientation will be first reviewed. It will be shown, that as a result of the interaction, there exists a spin wave mode, describing the spin precession in the absence of applied magnetic field. The dispersion relation of the mode is gapless, proportional to the square of the wave vector at small frequencies, and inversely proportional to the electron-electron exchange interaction energy. The valley wave analog will be then discussed for the case of metals with valley population imbalance. Doped graphene and three-dimensional Weyl-Dirac semimetals will be considered as particular material candidates. The spin and valley waves serve as the energy gain sources for the external field, that generates the spin or inter-valley transitions.