Spin-wave Circulation in a Ferromagnetic Resonator with Two Adjacent Layers

Abstract

The early development of photonic devices [1, 2] is leading the way for their magnonic analogs [3] such as spin-wave (SW) generators [4], couplers [5, 6], and phase shifters [7]. Such basic functional components are necessary for the development of miniaturized and energy-effcient magnetic circuits for processing high-frequency microwave signals. Our study goes along further development of SW devices, to demonstrate circulation [8] and other functionalities using ferromagnetic conduits coupled by resonators in analogy to photonic channel add-drop filters [1].We investigate the propagation behavior of SW in a cobalt (Co) bi-layer structure separated by a non-magnetic material and coupled with a permalloy (Py) stripe placed between two layers. The layers have a thickness of 5 nm, the separation between the stripe and the layers is of 10 nm and the stripe has a thickness of 50 nm. All elements are saturated in the same in-plane direction, perpendicular to the propagation of SWs. We investigate numerically the SW dynamics governed by the Landau-Lifshitz-Gilbert equation, solved numerically using the software COMSOL Multiphysics. We study the SWs dynamics with two different approaches. In the first approach, we investigate the SW dispersion relation of the system in the frequency domain. The lattice constant of the system is set at 500 nm. To analyze the origin of different type of interactions and possible functionalization we calculate the dispersion relations for two layers, the stripe only, three layers, and finally for the two layers coupled with the Py stripe. The dispersion relations allow to determine propagation properties, the coupling between the modes and their hybridization. We found that the coupling between the elements is strong at some frequencies at which suitable conditions for control of propagating SWs are formed.As a second approach, we used the time-domain simulations to demonstrate functionality of the proposed system. We excite the system with an antenna generating SWs with a single frequency. We found interesting propagation properties for a 19-GHz spin wave. The excitation of a wave in the top layer generates an edge mode in the Py resonator (Fig. 1a) and the SW is fully transmitted to the bottom layer propagating in the left. The excitation in the bottom layer (Fig. 1b) is not transferring to the top layer even if the Py resonator is weakly excited. Due to inversion symmetry with respect to the horizontal mid-plane, the analogous properties are for SW excited on the right side of the resonator. Thus, we demonstrated the functionality of a circulator in the system which is suitable for further miniaturization through decreasing the size of a resonant element. The proposed system composed of two thin-film SW conduits coupled by a ferromagnetic resonator can operate with different functionalities in dependence on the frequency. The next investigations, at other frequencies, positioned at proximity of other Py resonances, offer other functionalities, like magnetostatic screening from the direct coupling between the waveguides. The operation can be further tuned by changing the magnetization characteristics, magnetic field, and by exploring the third dimension.The research leading to these results has received funding from the Polish National Science Centre, project No. UMO-2018/30/Q/ST3/00416. **