Measurement of Ferromagnetic Relaxation by a Modulation Technique

Abstract

A modulation method is introduced as a novel means of studying directly the relaxation process in the case of ferrimagnetic rare earth garnets and ferrites. The method directly measures the relaxation of the spin system of the material which is indentified with the transverse relaxation time by means of the standard equations of motion. A low-power fixed frequency X-band microwave field is amplitude modulated at an rf rate up to 50 Mc while maintaining the sample in ferromagnetic resonance. The resulting precession of the magnetic moment will then contain an rf component which is a function of both the transverse relaxation time and the frequency of the rf modulation. The precession is observed by a single turn pickup loop in which the induced microwave voltage is proportional only to the rotating component of magnetization. The rf signal resulting from demodulation of this voltage then characterizes the response of the precession to the modulation frequency of the driving microwave field. The falloff in this response with increasing modulation frequency is shown to be related to the transverse relaxation time by means of the equations of motion. The predicted form of this falloff is a function proportional to the factor (1+β2τ2)−12 from which the relaxation time τ is obtained. Certain conclusions may be drawn from the excellent agreement of the experimental data with theory.