Longitudinal spin dynamics in ferrimagnets: Multiple spin wave nature of longitudinal spin excitations

Motivated by the existing controversy about the physical mechanisms that govern longitudinal magnetization dynamics under the effect of ultrafast laser pulses, in this paper we study the microscopic model of longitudinal spin excitations in a two-sublattice ferrimagnet using the diagrammatic technique for spin operators. The diagrammatic approach provides us with an efficient procedure to derive graphical representations for perturbation expansion series for different spin Green's functions and thus to overcome limitations typical for phenomenological approaches. The infinite series involving all distinct loops built from spin wave propagators are summed up. These result in an expression for the longitudinal spin susceptibility chi(zz)(q,omega) applicable in all regions of frequency. and wave vector q space beyond the hydrodynamical and critical regimes. A strong renormalization of the longitudinal spin oscillations due to processes of virtual creation and annihilation of transverse spin waves has been found. We have shown that the spectrum of longitudinal excitations consists of a quasirelaxation mode forming a central peak in chi(zz)(q,omega) and two (acoustic and exchange) precessionlike modes. As the main result, it is predicted that both acoustic and exchange longitudinal excitations are energetically above similar modes of transverse spin waves at the same temperature and wave vector. The existence of the exchange longitudinal mode at such frequencies can result in a new form of excitation behavior in ferrimagnetic system, which could be important for understanding the physics of nonequilibrium magnetic dynamics under the effect of ultrafast laser pulses in multisublattice magnetic materials.