A Quantum Statistical Theory of Ferromagnetic Resonance with Parallel Pumping. II Correlation Function Treatment of Parametric Spin Wave Excitation and Nonlinear Interactions

Abstract

A bstrac tBaaed on equations, symmetry and boundary conditions of quantum statistical correhtion functions of renormalized spin wave excitations in a HEISENBERG fernmagnet including dipolar coupling, the parallel pumping effect under special considering the nonlinear three magnon interaction is discmeed. An clsymptotic approximation procedure enableaus to interpret the fundamental equations in terms of the LANGE~IN theory of BRomian motion and to find solutions by eeperation ansatzea. For all WE of practical intereet, the differences between the clwical and the quantum statistical threshold condition can be neglected. The validity of QCHL~MANN'E subthreshold X" formula is proved. Above the threshold, the steady state X" is larger than proposed by semicla~~ical theoriea because the strongly excited spin waves are influenced by a certain nonlinear 5uctuating field; for YIG, a sufficient agreement between experimental and theoretical X" values and a qualitative explanation of the parameter dependence are found. Some non-equilibrium correlation functions are given explicitly.