Calculation of the green's function for the micromagnetic thin film problem

Abstract

The spatial dependence of the Green's function of the micromagnetic thin film problem is calculated. Until now, such calculations have been undertaken only in limiting cases or by the help of approximations. Introducing contours of equal function values (coupling areas) we will discuss the behaviour of the Green's function, which depends crucially on a single constant q resulting from the magnetic and geometric film parameters. In the case of a typical polycrystalline or amorphous film with q ⪡ 1 (i.e. small anisotropy and large magnetization) the contours have a typical long extended shape over a wide range of r-values. This corresponds to Hoffmann's former linear ripple theory, which supplies a good description of the essential physical features just in this case. On the other hand, in the event of q ≈ 1 or q ⪢ 1 (i.e., for very thin films with a small magnetization M s and a large anisotropy) the shape of the coupling areas shows a much stronger dependence on the distance r . This should considerably influence the magnetic properties of such films, e.g., the magnetic ripple spectrum.