A first-principle model of the magnetic contrast in ultrathin films with perpendicular magnetization

In ultrathin films, the energy competition between the perpendicular magnetic anisotropy and the in-plane magnetostatic coupling can originate stripe domains. In such systems, the perpendicular magnetization component has a periodic modulation, pointing alternately upwards and downwards as the stripes are crossed. A measurement technique that is widely used to study these kind of domains is the magnetic force microscopy (MFM). As known, the MFM signal cannot be related immediately to the sample magnetization and the interpretation of the results is not always straightforward. Therefore, the achievement of a reliable contrast model for this technique in simple specific cases that could be directly compared with experimental results is highly desirable. In this paper, a first-principle model of the MFM contrast in the case of 1D magnetic nanostructures is proposed. An immediate application of the model pertains to the study of ultrathin films with perpendicular magnetization.