Spin Vortex Resonance in Non-planar Ferromagnetic Dots

The investigation of spin dynamics in geometrically confined ferromagnets is an important research topic due to both the technological and the basic science relevance. Some prominent examples include nanoscale spin textures with non-collinear magnetization arrangement such as skyrmions1, domain walls2,3, and spin vortices4. A vortex-type magnetization is energetically favorable for micron and sub-micron disks with no crystalline anisotropy. The long-range dipolar forces govern the spin dynamics in the vortex-state. Of particular interest is a low-frequency excitation mode associated with the vortex core gyration. Besides the magnetization of saturation, the vortex eigenfrequencies depend on the dot geometric aspect ratio5. In magnetic particles with an in-plane shape anisotropy, such as ellipses6, squares7 or triangles8 the resonance frequencies vary with not only the dot sizes, but also with the value of applied magnetic field. This is in sharp contrast to disk-shaped elements where the excitation spectrum depends rather weakly (<10%) on the value of an in-plane applied field6. Furthermore, it has been reported that the intrinsic pinning due to grain boundaries9, surface roughness10, exchange bias11 or layered dot system12,13,14 could also influence the gyration of the vortex core. While the vast majority of the above mentioned works deal with geometrically flat elements, here we have studied circular elements with intentionally altered topography. This was achieved by using a pre-patterned substrate with the characteristic lateral dimensions significantly smaller than the diameter of the desired magnetic element. In our case, the nonmagnetic disks were first defined via a lift-off process, and then covered by another patterned ferromagnetic layer with the same geometric center but a larger diameter. As result, we obtained a “hat-like” sample structure,schematically depicted in Fig. 1(a). Then the dynamic properties of these non-planar elements were systematically investigated using broadband microwave spectroscopy and micromagnetic modeling as a function of their dimensions and amplitude of the external field. As we show below, the introduced disk-shaped step (also referred as a vortex barrier) provides a strong geometric confinement and vortex core pinning effect. Figure 1 (a) A sketch of the dot with Db = 200 nm with the simulated remnant magnetization state of the engineered dot. The x-component of the magnetization is represented from red to blue in a range of +1 to −1. Scanning electron ...