Higher-order ferromagnetic resonances in out-of-plane saturated Co/Au magnetic multilayers

Artificial ferromagnetic (FM)/nonmagnetic multilayers, with large enough FM thickness to prevent the dominance of interface anisotropies, offer a straightforward insight into the understanding and control of perpendicular standing spin wave (PSSW) modes. Here we present a study of the static and dynamic magnetic properties of ${[\mathrm{Co}(3.0\phantom{\rule{0.16em}{0ex}}\mathrm{nm})/\mathrm{Au}(0.6\phantom{\rule{0.16em}{0ex}}\mathrm{nm})]}_{1\ensuremath{\le}N\ensuremath{\le}30}$ multilayers. Magnetometry reveals that the samples exhibit magnetization reversal properties typical of an effective single layer with weak perpendicular anisotropy, with the distinctive thickness-dependent magnetization reorientation transition from uniform in-plane to out-of-plane stripe domains at remanence. However, when such multilayer systems are out-of-plane saturated, the dynamic response reveals the existence of several different ferromagnetic resonances in the form of PSSW modes that strongly depend on the material modulation characteristics along the total thickness. These modes are induced by the layer stacking itself as the effective single layer model fails to describe the observed complex dynamics. In contrast to most systems considered in the past, described by a dynamic model of a single effectively homogeneous thick layer, the specific structures investigated here provide a unique platform for a large degree of tunability of the mode frequencies and amplitude profiles. We argue that the combination of periodic magnetic properties with vertical deformation gradients, arising from heteroepitaxial strain relaxation, converts the Au interlayer regions into a vertical regular array of magnetic pinning planes for the PSSW modes, which promotes the complex dynamics observed in this system.