Quantized orbital angular momentums of dipolar magnons and magnetoelectric cavity polaritons

Magnons are viewed as local deviations from the ordered state. Usually, the spin magnetic moment of magnons is considered. In a 3D-confined structure of a magnetic insulator with magnetodipolar mode (MDM) oscillations, an orbital angular momentum (OAM) as well as a spin angular momentum (SAM) can be observed along a static magnetic field. In such a confined structure as quasi-2D ferrite disk, energy levels of MDM oscillations are quantized. Quantum confinement is characterized by a half-integer internal OAM, which is also associated with a circulating energy flow. The observation of MDM resonances in the 3D-confined structure of a magnetic insulator is due to the interaction of two subsystems: ferromagnetic and electric polarization orders. The coupling states of these two concurrent orders, caused by OAMs, are considered as magnetoelectric (ME) states. The fields in the vicinity of MDM resonators are characterized by simultaneous violation of time reversal and inversion symmetry. This plays a significant role in the problems of strong light-matter interaction regime and quantum atmosphere. The analysis of SAM and OAM in 3D-confined magnetic insulators becomes very important for the realization of ME meta-atomic structures. Current interest lies in considering such artificial systems as subwavelength ME quantum emitters of electromagnetic radiation.