Adjustable microwave permeability of nanorings: A micromagnetic investigation

•The microwave permeability can be tailored by a designed nanoring structure.•The resonant frequency of the nanoring is adjustable.•Snoekʼs law is enhanced in nanoring.

Based on the three-dimensional micromagnetic simulations, we present a method to tailor the microwave permeabilities of magnonic metamaterials cells by a designed nanoring structure. The results show that the permeabilities and resonant frequency are depended on the wallʼs thickness of nanorings. The underlying mechanism is ascribed to the presence of strong demagnetization fields, which are associated to the ringʼs wall. In addition, the products of magnetic susceptibility and resonant frequency are larger than that predicted from Snoekʼs law in polycrystalline particles. These results are direct manifestations of the bi-anisotropy model.