544
E. Kamenetskii
inhomogeneous Maxwell equations [57, 70, 71]. It means that the ME fields appear
as the fields of axion electrodynamics. With such a unique topological structure
of ME near fields, two types of polaritons should be observed: right-handed ME
polaritons and left-handed ME polaritons. When an external microwave structure
is geometrically symmetrical, the two types of ME polaritons are indistinguishable. Otherwise, different microwave responses could be observed depending on the
direction of the bias magnetic field. When an external microwave structure contains
any elements with geometrical chirality, the right-hand and left-hand ME polaritons
becomes nondegenerate, and microwave responses depend on the direction of the
bias magnetic field. This fact was confirmed both numerically and experimentally
[56].
19.4 MDM Particles Inside Waveguides and Cavities
In microwaves, we are witnesses that long-standing research in coupling between
electrodynamics and magnetization dynamics noticeably reappear in recent studies
of strong magnon-photon interaction [72–76]. In a small ferromagnetic particle, the
exchange interaction can lead to the fact that a very large number of spins to lock
together into one macrospin with a corresponding increase in oscillator strength. This
results in strong enhancement of spin-photon coupling. In a structure of a microwave
cavity with a yttrium iron garnet (YIG) sphere inside, the avoided crossing in the
microwave reflection spectra verifies the strong coupling between the microwave
photon and the macrospin magnon. In these studies, the Zeeman energy is defined
by a coherent state of the macrospin-photon system when a magnetic dipole is in its
antiparallel orientation to the cavity magnetic field. Together with an analysis of the
strong coupling of the electromagnetic modes of a cavity with the fundamental Kittel
modes, coupling with non-uniform modes—the Walker modes—in a YIG sphere was
considered. In the microwave experiments, identification of the Walker modes in the
sphere was made based an effect of overlapping between the cavity and spin waves
due to relative symmetries of the fields [77, 78]. Nevertheless, the experimentally
observed effects of strong magnon-photon interaction, cannot be described properly
in terms of a single magnon-photon coupling process. In a view of these aspects, the
theory based on solving coupled Maxwell and Landau-Lifshitz-Gilbert equations
without making the conventional magnetostatic approximation have been suggested
[79, 80]. Currently, the studies of strong magnon-photon interaction are integrated
in a new field of research called cavity spintronics (or spin cavitronics) [81].
The coupling strength in the magnon-photon system is proportional to the probability of conversion of a photon to a magnon and vice versa. An effective way for
strong coupling is to confine both magnons and photons to a small (subwavelength)
region. Long-range spin transport in magnetic insulators demonstrates that the dipolar
interactions alone generate coherent spin waves on the scales that are much larger
than the exchange-interaction scales and, at the same time, much smaller than the
electromagnetic-wave scales. Because of symmetry breakings, the MDM ferrite disk,
E. Kamenetskii
inhomogeneous Maxwell equations [57, 70, 71]. It means that the ME fields appear
as the fields of axion electrodynamics. With such a unique topological structure
of ME near fields, two types of polaritons should be observed: right-handed ME
polaritons and left-handed ME polaritons. When an external microwave structure
is geometrically symmetrical, the two types of ME polaritons are indistinguishable. Otherwise, different microwave responses could be observed depending on the
direction of the bias magnetic field. When an external microwave structure contains
any elements with geometrical chirality, the right-hand and left-hand ME polaritons
becomes nondegenerate, and microwave responses depend on the direction of the
bias magnetic field. This fact was confirmed both numerically and experimentally
[56].
19.4 MDM Particles Inside Waveguides and Cavities
In microwaves, we are witnesses that long-standing research in coupling between
electrodynamics and magnetization dynamics noticeably reappear in recent studies
of strong magnon-photon interaction [72–76]. In a small ferromagnetic particle, the
exchange interaction can lead to the fact that a very large number of spins to lock
together into one macrospin with a corresponding increase in oscillator strength. This
results in strong enhancement of spin-photon coupling. In a structure of a microwave
cavity with a yttrium iron garnet (YIG) sphere inside, the avoided crossing in the
microwave reflection spectra verifies the strong coupling between the microwave
photon and the macrospin magnon. In these studies, the Zeeman energy is defined
by a coherent state of the macrospin-photon system when a magnetic dipole is in its
antiparallel orientation to the cavity magnetic field. Together with an analysis of the
strong coupling of the electromagnetic modes of a cavity with the fundamental Kittel
modes, coupling with non-uniform modes—the Walker modes—in a YIG sphere was
considered. In the microwave experiments, identification of the Walker modes in the
sphere was made based an effect of overlapping between the cavity and spin waves
due to relative symmetries of the fields [77, 78]. Nevertheless, the experimentally
observed effects of strong magnon-photon interaction, cannot be described properly
in terms of a single magnon-photon coupling process. In a view of these aspects, the
theory based on solving coupled Maxwell and Landau-Lifshitz-Gilbert equations
without making the conventional magnetostatic approximation have been suggested
[79, 80]. Currently, the studies of strong magnon-photon interaction are integrated
in a new field of research called cavity spintronics (or spin cavitronics) [81].
The coupling strength in the magnon-photon system is proportional to the probability of conversion of a photon to a magnon and vice versa. An effective way for
strong coupling is to confine both magnons and photons to a small (subwavelength)
region. Long-range spin transport in magnetic insulators demonstrates that the dipolar
interactions alone generate coherent spin waves on the scales that are much larger
than the exchange-interaction scales and, at the same time, much smaller than the
electromagnetic-wave scales. Because of symmetry breakings, the MDM ferrite disk,