Magnetic Susceptibility of Non‐Uniform Media

Abstract

We present calculations of the dynamic susceptibility for a non-uniform ferromagnetic metal system with interatomic exchange included. The results obtained are general and can be applied t o ordered alloys, thin films, and other non-uniform media.We consider a system described by the Hamiltonian H =xtij aldajd + 7 u . n . n. -1 ~. . $ . 3 .where a:' is the creation operator for a n electron of spin 0 at the lattice site i, t.. is the hopping integral, U. is the intraatomic Coulomb integral, and J.. is the interatomic exchange integral: We assume the'system t o b e ferromagnetic but not necessarily translationally invariant.We aim at calculating the dynamical magnetic susceptibility. The tran9-v e r s e susceptibility is given by the Green function where spin operators on the right side are in Heisenberg picture and thermal average of the commutator is taken.The magnetic susceptibility of such a model was calculated for uniform media in RPA in /1/ and in another approximation in /2/. Our approximation is essentially similar but not identical t o the one used in /2/.

The General Theory of the Dynamic Susceptibility in Thin Ferromagnetic Films

“…The possibility of the appearance of surface spin waves has also been discussed [5] and the complete dispersion relation for the surface modes has been found [6]. The analytic expression for the thin-film dynamic susceptibility in the case when the exchange interactions between different lattice sites are taken into account, has also been obtained [7]. I n all papers dealing with the dynamic susceptibility of thin films, which have appeared so far within the framework of the itinerant electron model, only the one-band model has been used.…”