Because of confinement phenomena, semiconductor quantum dots show typical atomic properties such as discrete energy levels and shell structures. The energy eigenstates are described based on the Schrödinger-like equation for the electronic envelope wavefunctions. From the point of view of fundamental studies, the reduction of dimensionality in microwave ferrites brings into play new effects, which should be described based on the quantized picture and demonstrate, as a fact, the properties of artificial atomic structures. The intermediate position of magnetic-dipolar (or magnetostatic) oscillations in ferrite samples between 'pure' electromagnetic and spin-wave (exchangeinteraction) processes reveals the very special behaviour of geometrical effects. In view of recent studies on the local-field effects for subwavelength systems, some aspects of magnetic-dipolar oscillations in a normally magnetized ferrite disc should be reconsidered based on macroscopically quantized methods. The purpose of this paper is to develop macroscopically quantized phenomenological models for magnetostatic-wave ferrite discs based on the Schrödinger-like equation.

There has been a surge of interest in the subwavelength confinement of electromagnetic fields. It is well known that, in optics, subwavelength confinement can be obtained from surface plasmon (quasielectrostatic) oscillations. In this article, we propose to realize subwavelength confinement in microwaves by using dipolarmode (quasimagnetostatic) magnon oscillations in ferrite particles. Our studies of interactions between microwave electromagnetic fields and small ferrite particles with magnetic-dipolar-mode (MDM) oscillations show strong localization of electromagnetic energy. MDM oscillations in a ferrite disk are at the origin of topological singularities resulting in Poynting vector vortices and symmetry breakings of the microwave near fields. We show that new subwavelength microwave structures can be realized based on a system of interacting MDM ferrite disks. Wave propagation of electromagnetic signals in such structures is characterized by topological phase variations. Interactions of microwave fields with an MDM ferrite disk and MDM-disk arrays open a perspective for creating engineered electromagnetic fields with unique symmetry properties.

In 1948 Tellegen ͓Philips Res. Rep. 3, 81 ͑1948͔͒ suggested that an assembly of the lined up electric-magnetic dipole twins can construct a new type of an electromagnetic material. Until now, however, the problem of creation of the Tellegen medium is a subject of strong discussions. An elementary symmetry analysis makes questionable an idea of a simple combination of two ͑electric and magnetic͒ dipoles to realize local materials with the Tellegen particles as structural elements. In this paper we show that in search of sources with local junctions of the electrical and magnetic properties one cannot rely on the induced parameters of small electromagnetic scatterers. No near-field electromagnetic structures and no classical motion equations for point charges give a physical basis for realization of sources with a local junction of the electrical and magnetic properties. We advance a hypothesis that local magnetoelectric ͑ME͒ particles should be physical objects with eigenmode oscillation spectra and nonclassical symmetry breaking effects. Our studies convincingly prove this assumption. We show that a quasi-two-dimensional ferrite disk with magnetic-dipolar-mode oscillations is characterized by unique symmetry features with topological phases resulting in appearance of the ME properties. An entire ferrite disk can be characterized as a combined system with the eigenelectric and eigenmagnetic moments. The fields near such a particle are distinguished by special symmetry properties. The questions raised in this paper give new insights into a problem of realization of local ME composites.

PACS. 03.65.-w -Quantum mechanics. PACS. 85.35.Be -Quantum well devices (quantum dots, quantum wires, etc.). PACS. 76.50.+g -Ferromagnetic, antiferromagnetic, and ferrimagnetic resonances; spin-wave resonance.Abstract. -We show that magnetic-dipolar-mode oscillations in a normally magnetized ferromagnetic disk have typical atomic properties like discrete-energy levels. Because of the discreteenergy eigenstates of such oscillations resulting from structural confinement, one can describe the oscillating system as a collective motion of quasiparticles -the light magnons. We calculate the energy levels in a magnetic quantum well and the effective masses of the light magnons.Introduction. -Semiconductor quantum dots are manmade structures in which electrons are confined in all three spatial directions similar to the physical situation in atoms. As they show typical atomic properties like discrete-energy levels and shell structures, they are often referred to as artificial atoms [1]. This provides various implementations of solid-state systems based on semiconductor quantum dots. It is interesting that confinement phenomena for magnetic dipolar modes in a normally magnetized ferrite disk may also show typical atomic properties like discrete-energy levels. Such wave processes reveal very special behaviors of the geometrical effects. As a starting point for this statement, we call the reader's attention to the fundamental difference between the experimental absorption spectra for magnetostatic (MS) modes in the sphere-shaped [2] and the disk-shaped ferrite resonators [3]. The δ-functional character of the multiresonance spectra, that one can see in the case of a ferrite disk resonator, leads to the clear conclusion that the energy of a source of a DC bias magnetic field is absorbing "by portions" or discretely, in other words. On the contrary, the spectrum of a ferrite sphere does not show a series of sharp field-dependent resonances and is characterized by very few and much "spreading" absorption peaks.The MS-mode characterization in ferrite samples looks as a relatively straightforward and old problem in magnetism. Nevertheless, some aspects of such oscillations should be reconsidered in view of macroscopically quantized methods. In the last years, there has been a renewed interest in the high-frequency dynamic properties of finite-size magnetic structures. In a series of recent publications, confinement phenomena of high-frequency magnetization dynamics in magnetic particles have been the subject of much experimental and theoretical

Magnetic-dipolar-mode (MDM) oscillations in a quasi-2D ferrite disc show unique dynamical symmetry properties resulting in the appearance of topologically distinct structures. Based on the magnetostatic (MS) spectral problem solutions, in this paper we give evidence for eigen-MS power-flow-density vortices in a ferrite disc. Due to these circular eigen-power flows, the MDMs are characterized by MS energy eigenstates. It becomes evident that the reason for stability of the vortex configurations in saturated ferrite samples is completely different from the nature of stability in magnetically soft cylindrical dots. We found a clear correspondence between analytically derived MDM vortex states and numerically modeled electromagnetic vortices in quasi-2D ferrite discs.