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/.
A. URBANIAK-KUCHARCZYK and Z. OSETEKThe theory of Mossbauer line shape in fluctuating environment is applied to the case of thin film of a diluted alloy. The distribution of the spin autocorrelation time characterizing the line shape in the vicinity of phase transition point across the sample is calculated. It is shown that the change of concentration of magnetic atoms in diluted alloys leads to a variety of Mossbauer spectra a t the same sample temperature. All the results obtained are calculated for the particular case of S = 1/2 and for a film with b.c.c. lattice, aIthough another crystallographic Iattices may be consider as well.Die Theorie der MoBbauer-Linienform in fluktuierenden Systemen wird auf dunne Schichten aus verdunnten ferromagnetischen Legierungen angewandt. Die Auto-Spinkorrelationszeit, die die Linienform in der Umgebung des Phaseniibergangs charakterisiert, wird in Abhangigkeit von der Schichtdicke berechnet. Es wird gezeigt, daB bei fester Probentemperatur die b d e r u n g der Konzentration der magnetischen Atome in der ferromagnetischen Legierung zu verschiedenen MOBbaner-Spektren fuhrt. Die erhaltenen Ergebnisse werden fur den speziellen Fall S = 1/2 und fur ein k.r.z.-Gitter berechnet, obwohl auch andere Gittertypen einbezogen werden konnen. IntroductionThe effect of time-dependent perturbations on the lineshape of Mossbauer y-rays has been actively investigated since the work of Bradford and Marshall [l]. Special attention was payed to the region of temperatures not far from the critical temperature of magnetic samples 12 to 41.Recently the problem of magnetic properties of diluted ferromagnetic alloys is of great interest [5 to 71. The object of the present paper is the extension of earlier theoretical results concerning thin magnetic films as well as diluted alloys for the case of the Mossbauer lineshape. Spin Autocorrelation TimeTime-dependent or dynamic properties of magnetic samples in the vicinity of a phase transition point are related to spin fluctuations which can be detected in the Mossbauer experiment because they induce corresponding fluctuations in the hyperfine field. This in turn leads to the Mossbauer line broadeningif the field fluctuations are either too fast or too slow. The fundamental property of interest here is the spin autocorrelation time describing the shape of a Mossbauer line [l, 8,
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