Ferromagnetic resonance hysteresis in hybrid magnetic trilayers with combined in-plane and perpendicular magnetic anisotropies

We present an experimental study on hybrid magnetic systems based on hardmagnetic NdCo x films with weak perpendicular magnetic anisotropy, which are dipolar coupled to a softmagnetic layer with in-plane magnetic anisotropy, such as permalloy, via a nonmagnetic Al spacer. Using broadband ferromagnetic resonance, we have investigated the magnetization dynamics in this sample system, which exhibits a host of unique magnetic properties including a frequency hysteresis. We provide an explanation for the origin of this hysteresis, which is intimately related to the regular magnetic hysteresis, by accounting for the switching between acoustic and optical resonances, that naturally occur in unsaturated systems with different magnetic domains. Our model is ultimately supported by a simple expression relating the frequency difference between these two types of modes at their transition field to the periodicity of the stripe domain pattern imprinted into the permalloy film. Moreover, we show that these unique features in the FMR spectra can also be observed when substituting the ferromagnetic metal permalloy for a ferrimagnetic insulator such as yttrium iron garnet.