  A general theory is developed for describing the nonlinear relaxation of spin
systems from a strongly nonequilibrium initial state, when, in addition, the
sample is coupled to a resonator. Such processes are characterized by nonlinear
stochastic differential equations. This makes these strongly nonequilibrium
processes principally different from the spin relaxation close to an
equilibrium state, which is represented by linear differential equations. The
consideration is based on a realistic microscopic Hamiltonian including the
Zeeman terms, dipole interactions, exchange interactions, and a single-site
anisotropy. The influence of cross correlations between several spin species is
investigated. The critically important function of coupling between the spin
system and a resonant electric circuit is emphasized. The role of all main
relaxation rates is analyzed. The phenomenon of self-organization of transition
coherence in spin motion, from the quantum chaotic stage of incoherent
fluctuations, is thoroughly described. Local spin fluctuations are found to be
the triggering cause for starting the spin relaxation from an incoherent
nonequilibrium state. The basic regimes of collective coherent spin relaxation
are studied.
