Wave-Optical Aspects of Lorentz Microscopy

Abstract

The customary defocused and Foucault modes of Lorentz microscopy of magnetic films are usually described in terms of geometric optics. However, Wohlleben has shown that geometric optics has a restricted range of validity; a more fundamental approach is provided by wave optics. The defocused and Foucault modes may be discussed in terms of wave optics, and for the defocused mode, it can be shown explicitly that the geometric theory is simply the first approximation to the wave-optics theory. Consideration of wave optics also leads to the proposal of two additional modes of Lorentz microscopy: Zernike phase-contrast and interference microscopy; these modes cannot be described on the basis of geometric optics. The most fundamental problems in magnetic films which are amenable to study by Lorentz microscopy are investigations of the fine structures of domain walls and magnetization ripple. These problems are discussed in terms of wave optics for all four modes of Lorentz microscopy; in particular, the intensity distribution of the zero-width divergent domain wall is explicitly calculated for each mode. For practical experiments, the importance of coherence, i.e., of the illumination source size, is emphasized, and the experimental aid of holography is suggested. Since the Wohlleben limit is valid for all four modes, however, there is no resolution advantage inherent in any one mode. The choice of modes for solution of the domain wall and ripple problems therefore depends upon experimental convenience. It is concluded that the defocused mode seems most promising for practical application; Fresnel diffraction is preferred for the domain-wall problem, while Fraunhofer diffraction using low-angle electron-diffraction techniques is fruitful for the ripple problem.