FEM Modelling of Magnetostatic Modes in Hybrid Quantum Magnonic Systems

In this work, we show that the magnetostatic (MS) magnon modes (i.e., the spinwaves with wavelengths much larger than the exchange length), which are excited as a result of the coupling between the 2D microwave resonator and the YIG crystal, can be efficiently modeled by use of finite element method software (e.g., CST Studio Suite or Comsol MP). Yttrium iron garnet (YIG) has been used as a model material, which is a ferrimagnetic insulator transparent not only to MW but also to optical and telecommunication frequencies. It also has a very low damping parameter — a property advantageous from the point of view of potential applications. However, this benefit turns out in an issue in the FEM modeling because of the very high non-linearity in the EM properties of YIG near resonances due to uniform or MS modes. We found that it is possible to accelerate the FEM calculations by artificially increasing the damping constant of the model material (YIG). Our FEM modeling studies reveal an excellent agreement with experimental results. In full agreement with experimental data, our modeling study reveals a strong coupling between the YIG crystal and the microwave resonator, observed in the dispersion curves of the modes. We demonstrate the realization of the strong coupling regime, which is especially important for HQS implementations.