Magnetic anisotropy and ferromagnetic resonance in inhomogeneous demagnetizing fields near edges of thin magnetic films
Using local ferromagnetic resonance spectroscopy, we have studied the magnetic properties near edges of thin tangentially magnetized permalloy films, in which a well-defined uniaxial magnetic anisotropy was induced perpendicular to one of the edges. In the experiment, two samples with thicknesses of 90 and 300 nm and with slightly different compositions were examined. To explain the magnetization dynamics near edges, we propose a simple yet effective model of a film in the form of a rectangular prism, which yields the modified Kittel formula for the resonance frequency. In this formula, the locally averaged distance-dependent demagnetizing field that emerges near the edges is included as an additional uniaxial anisotropy term. The measurements reveal that at a certain distance from the edge, the resulting (apparent) anisotropy, determined from the angular dependencies of the resonance field, almost vanishes. Moreover, its easy axis reorients to become parallel to the edge. The model predictions agree well with these results, proving that the main resonance mode behavior near the film edges can be accurately described by introducing additional effective uniaxial anisotropy, provided the measuring area is relatively large. However, for the thick (300 nm) sample, additional precession modes are also observed. These modes distort the angular dependence of the main mode, thus demonstrating the limitations of the model.