On the g-Value of Ferrimagnetic Resonance

We performed the quantum mechanical calculation of the effective g-value of three-spin-system in which there exists the exchange interaction among three spins of 1/2, of which one spin has a different g-value. The object of this paper is to analyse the simplest model of ferrimagnetic substances which have the unsolved problem concerning the determination of exact g-value. The present result can be expressed as follows : When the exchange interaction is positive, the effective g-value of the three-spin-system coincides with that of the classical calculation. But when the ferrimagnetic interaction exists, the effective g-value of this system is different from the result of the classical theory of ferrimagnetic resonance. This is caused by the characteristic of the three spin wave functions which are symmetric for ferromagnetic ground state but show asymmetry for ferrimagnetic state in exchanging each spin coordinate. And if this effect can be applicable in the same manner to the case of actual ferrite, for example Ni-ferrite, the effective g-value to be shown in the microwave resonance absorption must be expressed as g^* = 2g_+g_/3 On the other hand however the result of the classical calculation shows g^* =g_. Here g_ and g_ represent the g-values of Ni^_ and Fe^_ ions respectively. Of course, this relation must be reevaluated in the case of actual ferrites which have many electrons acting on one another with strong exchange interaction. But it may be pointed out that the determination of g-values in ferrites only from the classical point of view must be reconsidered