Preface
In this book, the reader will find a wide range of problems related to properties of
symmetry in the study of electromagnetic fields, materials, and the field-matter interactions. The book contains 19 chapters covering various aspects of these effects. The
chapters are written by international experts who have contributed to the advancement of science and engineering of the chirality, magnetism, and magnetoelectricity
in optical and microwave systems. What problems and challenges are analyzed and
discussed in the book? The fields of the studies are new and certain statements may
be disputable. The reader can see that current research leaves some questions open
to further discussion. Some chapters discuss similar issues from different physical
points of view. In this book, we aim to provide the reader with an overview of
the interdisciplinary research. Since many studies in these areas do not fit into a
well-established classification, we do not separate chapters into topical sections.
The most interesting physical phenomena arise from effects associated with
combinations of different types of symmetry and symmetry breakings. It is known
that chirality is a geometric property. An object is called chiral when it exists in two
enantiomeric forms, which can be superimposed only by a parity operation (mirror
image). Chirality properties can be observed both in material structures and in novel
types of engineered fields. It is also known that ferromagnetism breaks time-reversal
symmetry. The spin momentum of magnons is based on the time-reversal symmetry
breaking of the magnetic order. However, the magnetic dipole precession has neither
left-handed nor right-handed quality, that is to say, no chirality. Where from magnetic
symmetry can inherit chirality? One of the important issues is that magnetic symmetry
can derive chirality from the crystal structure. In magnetism, the curvilinear geometry
manifests Dzyaloshinskii–Moriya-like interaction. For magnons, the Dzyaloshinskii–Moriya interaction accounts for spin–orbit interaction and causes a nontrivial
topology.
The hybridization of magnetism and topology is a significant problem. It is
related to various topological structures of magnetic moments (spins), known as
spin textures. This is related also to the question of topological phases. Whereas the
topological phases were initially proposed for electron waves, then it became evident
for other types of waves. The topological phase is of particular importance for the
topologically nontrivial edge modes. Topological spin waves have been predicted to
v
In this book, the reader will find a wide range of problems related to properties of
symmetry in the study of electromagnetic fields, materials, and the field-matter interactions. The book contains 19 chapters covering various aspects of these effects. The
chapters are written by international experts who have contributed to the advancement of science and engineering of the chirality, magnetism, and magnetoelectricity
in optical and microwave systems. What problems and challenges are analyzed and
discussed in the book? The fields of the studies are new and certain statements may
be disputable. The reader can see that current research leaves some questions open
to further discussion. Some chapters discuss similar issues from different physical
points of view. In this book, we aim to provide the reader with an overview of
the interdisciplinary research. Since many studies in these areas do not fit into a
well-established classification, we do not separate chapters into topical sections.
The most interesting physical phenomena arise from effects associated with
combinations of different types of symmetry and symmetry breakings. It is known
that chirality is a geometric property. An object is called chiral when it exists in two
enantiomeric forms, which can be superimposed only by a parity operation (mirror
image). Chirality properties can be observed both in material structures and in novel
types of engineered fields. It is also known that ferromagnetism breaks time-reversal
symmetry. The spin momentum of magnons is based on the time-reversal symmetry
breaking of the magnetic order. However, the magnetic dipole precession has neither
left-handed nor right-handed quality, that is to say, no chirality. Where from magnetic
symmetry can inherit chirality? One of the important issues is that magnetic symmetry
can derive chirality from the crystal structure. In magnetism, the curvilinear geometry
manifests Dzyaloshinskii–Moriya-like interaction. For magnons, the Dzyaloshinskii–Moriya interaction accounts for spin–orbit interaction and causes a nontrivial
topology.
The hybridization of magnetism and topology is a significant problem. It is
related to various topological structures of magnetic moments (spins), known as
spin textures. This is related also to the question of topological phases. Whereas the
topological phases were initially proposed for electron waves, then it became evident
for other types of waves. The topological phase is of particular importance for the
topologically nontrivial edge modes. Topological spin waves have been predicted to
v