Interference induced microwave transmission in the YIG-microstrip cavity system

We reveal the multiple-path microwave interference induced microwave transmission in a cavity-magnonic system composed of a yttrium-iron-garnet (YIG) film and a microstrip cavity circuit. By changing the position of the YIG in the circuit, we identify that the magnon in YIG is driven by the standing microwave from the cavity or by the traveling wave through the microstrip. We observe that the microwave transmission spectra show an anti-crossing dispersion named mode repulsion and an anomalous dispersion named mode attraction, respectively. The characteristic of anti-cross dispersion spectra is theoretically predicted using the coupling between the magnon and the cavity. Without coupling, the anomalous dispersion in our experiment is well interpreted by the multiple-path microwave interference between the indirect paths through the cavity and the magnon and the direct path through the traveling wave. And the anomalous dispersion is caused by the redistribution of the microwave transmission intensity. We also find the phases of the magnon in two cases changes $\pi$, which can be the key physical factor to understand the change of microwave transmission characteristics. Our work highlights the role played by the multiple-path microwave interference in magnonic microwave devices, which will be an important issue in designing microwave circuits based on the magnon.