J. Phys. Chem. Solids zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA Pergamon Press 1965. Vol. 26, pp. 1939-1947. Printed in Great Britain. zyxwvutsrqponmlk GREEN FUNCTION METHOD IN THE THEORY OF FERROMAGNETIC THIN FILMS A. CORCIOVEI* and G. CIOBANUt (Received 26 Jumury 1965) A bstract-A thin film of atomic spins arranged in a simple cubic lattice, the Hamiltonian of which contains the exchange and magnetic anisotropy terms is considered. The dependence of the magnetization of the thin film on the temperature, for various numbers of monatomic layers of the thin film is studied by means of double-time-temperature-dependent Green function. A general formula for the magnetization is obtained which is valid in the entire range of temperatures, and which depends on the thickness of the thin film. In the case of the low temperatures the results of the spin-wave theory are obtained. IN THE zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA theoretical study of single domain ferro- magnetic thin films two methods have been widely applied, the Heisenberg traces method and Bloch spin-wave method. The Heisenberg method valid at high temperatures has developed by VALENTA~) and CORCIOVEI@*~) and the Bloch’s method, valid at low temperatures has been applied by KLEIN et ~l.1~) and DSRING.@) The spin-wave method, in the Holstein-Primakoff formulation has been used recently for the study of ferro- magnetic thin films by CORCIOVEI,@) who gives a general formula for the magnetization of the film in the range of low temperatures. Extensive calculations have been performed recently in the problem of ferromagnetism for a bulk crystal using the method of thermodynamic- double-time-temperature-dependent Green func- tion. 17-10) In the present paper, the double-time-tempera- ture-dependent Green function technique is applied to the study of a single domain ferro- magnetic thin films. We note that recently LINE+) using a similar formalism has attempted the prob- lem of calculating the Curie temperature for a simple cubic lattice bulk material with monatomic layer structures in which the exchange integral of * Institute for Atomic Physics, Bucharest, P.0.B.35, Rumania, _F Institute of Physics, Bucharest, Rumania. two nearest neighbours in a given layer differs from the exchange integral between nearest neigh- bour atoms from two nearest neighbour layers. The calculus of LINES can be applied to a thin film but only if the number of monatomic layers of thin film is very large. In the paper of LIKES the dependence of the magnetic properties (i.e. magnetization and Curie temperature) on the thickness of the thin film is not considered. In contrast with LINES, in our paper the entire atten- tion is focussed on the study of dependence of the magnetic properties on the thickness of the thin film. From this point of view the LINES result can be considered as the limiting case of our results (for neglecting the anisotropy H~iltoni~) for the case when the number 4 of monatomic layers of the thin film tends to the infinity. In our paper a general formula for the dependence of the mag- netization on temperature and thickness of the film is established, which in the range of low tem- peratures coincides with the results obtained in a previous work by CORCIOVEI@) using spin wave method. EQUATIONS FOR THE GREEN FUNCTIONS Our study will be developed in the case of a simple cubic lattice thin film possibly compressed or dilated perpendicularly to the film. We shall consider the unit vectors iZ, zyxwvutsrqponmlkjihgfedcb iy and i, of the lattice 1939