(Received July 26, 1962)
The spectrum of spin waves in ferromagnetic metals where ferromagnetism is caused by the so-called s-d exchange interaction between localized spins and conduction electrons is investigated theoretically without taking an adiabatic approximation which is usually used. The dynamical susceptibility of the system is calculated by making use of the two-time Green's function, and the spectrum is determined as divergent points of the susceptibility. As non-adiabatic effects, there appear some features in the spectrum which have not been considered in usual adiabatic theories. First, if the wave number of spin waves is not so large, there are two or more modes of collective oscillations of the system, among which one may well be called acoustical mode where two spin systems, localized spins and conduction electron spins, oscillate in phase, and another an optical mode where they oscillate in antiphase. Further, as to the acoustical mode, the spectrum has a dip in the vicinity of a certain wave number where an adiabatic approximation becomes incorrect.
URL : http://ptp.ipap.jp/link?PTP/28/1033/
DOI : 10.1143/PTP.28.1033