The fields of cavity quantum electrodynamics and magnetism have recently merged into 'cavity spintronics', investigating a quasiparticle that emerges from the strong coupling between standing electromagnetic waves confined in a microwave cavity resonator and the quanta of spin waves, magnons. This phenomenon is now expected to be employed in a variety of devices for applications ranging from quantum communication to dark matter detection. To be successful, most of these applications require a vast control of the coupling strength, resulting in intensive e↵orts to understanding coupling by a variety of di↵erent approaches. Here, the electromagnetic properties of both resonator and magnetic samples are investigated to provide a comprehensive understanding of the coupling between these two systems. Because the coupling is a consequence of the excitation vector fields, which directly interact with magnetisation dynamics, a highly-accurate electromagnetic perturbation theory is employed which predicts the resonant hybrid mode frequencies for any field configuration within the cavity resonator. The coupling is shown to be strongly dependent not only on the excitation vector fields and sample's magnetic properties but also on the sample's shape. These findings are illustrated by applying the theoretical framework to two distinct experiments: a magnetic sphere placed in a three-dimensional resonator, and a rectangular, magnetic prism placed on a two-dimensional resonator. The theory provides comprehensive understanding of the overall behaviour of strongly coupled systems and it can be easily modified for a variety of other systems.

The cross-integration of spin-wave and superconducting technologies is a promising method for creating novel hybrid devices for future information processing technologies to store, manipulate, or convert data in both classical and quantum regimes. Hybrid magnon–polariton systems have been widely studied using bulk Yttrium Iron Garnet (Y3Fe5O12, YIG) and three-dimensional microwave photon cavities. However, limitations in YIG growth have, thus far, prevented its incorporation into CMOS compatible technologies, such as high-quality factor superconducting quantum technology. To overcome this impediment, we have used Plasma Focused Ion Beam (PFIB) technology—taking advantage of precision placement down to the micrometer scale—to integrate YIG with superconducting microwave devices. Ferromagnetic resonance has been measured at milliKelvin temperatures on PFIB-processed YIG samples using planar microwave circuits. Furthermore, we demonstrate strong coupling between superconducting resonators and YIG ferromagnetic resonance modes by maintaining reasonably low loss while reducing the system down to the micrometer scale. This achievement of strong coupling on-chip is a crucial step toward fabrication of functional hybrid quantum devices from spin-wave and superconducting components.