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The paper overviews recent investigations of thermodynamics and magnetic dynamics of itinerant electron magnets with strongly coupled (anharmonic) spin fluctuations (SF). A novel classification scheme for SF, dependent on their spatial dispersion and quantum effects is presented, including the generalized Fermi liquid (FL), soft-mode (SM), and localized moments (LM) regimes. It is shown that the conventional SCR theory of Moriya holds only in the weak coupling limit of the SM regime and cannot be applied to real magnets where spin anharmonicity induced by zero-point SF is expected to be strong. To account for the effects of strong spin anharmonicity, a variational SM theory of SF is presented. These effects essentially influence thermodynamics of itinerant magnets and affect the criterion for magnetic instabilities, equations of state, low temperature specific heat, non-FL and quantum critical behavior, etc. Nonlinear magnetic dynamics of itinerant magnets is analyzed based on the phenomenological spin-invariant dynamical equations both in the spin wave and relaxational regimes. Macroscopic magnetic dynamics and different mechanisms of magnon damping in the spin wave regime are shown to be essentially different from the results arising for the Heisenberg magnets. The relaxational regime may be strongly influenced by nonlinear effects of mode-mode couplings. The spectrum of overdamped longitudinal SF is shown to be radically changed due to their scattering by magnons, which may result in a quasielasic peak in the SF spectrum and inelastic SF near the magnon frequencies, depending on nonlinear coupling. The quasielastic SF are suppressed at low temperatures and develop at elevated temperatures, dominating near the Curie point. The results are applied to the magnetoresistive manganites.

Abstract. We present the phenomenological analysis of the spectrum of longitudinal spin fluctuations in isotropic itinerant electron antiferromagnets with account of spin anharmonicity giving rise to coupling of transverse and longitudinal normal modes. The spectrum consists of a quasielastic part forming a central peak or a dip, depending on temperature and the Landau relaxation rate. Effects of spin fluctuation coupling also give rise to an inelastic part of the spectrum which has a form of resonances or antiresonances near the magnon frequencies related to non-propagating longitudinal excitations.Essentially, magnetic dynamics in itinerant electron magnets differs from that in

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