Band-gap Structures Of Two-dimensional Magnonic Crystals With Nesting Complex Lattices

Magnonics is a new field of modern magnetism,and it is considered to be a subfield of modern solid-state physics.Magnonics combines wave and magnetism,and its main purpose is to study the behavior of spin waves in nanostructured elements.In essence,the spin wave is a reordering of magnetization in a material which is caused by the precession of the magnonic moment.Magnetic moment comes from the orbital and the spin moment of the electron.The most common is that this spin moment results in a net magnonic moment.Just like photonic crystal is a kind of periodic composite materials with different dielectric constants,and phononic crystal is the composite functional material arranged periodically by different elastic materials.In the field of magnetic materials,the analogues of photonic crystals and phononic crystals are called magnonic crystals.Magnonic crystal is an artificial microstructure composite material composed of two or more kinds of magnetic materials.It mainly consists of two parts.The continuous phase is the basis,and the discontinuous phase is the scatterer.The scattereres have many shapes,such as square,rectangle,oval and others.The propagation of spin waves in magnonic crystals can be inhibited,which is the formation of the spin wave band gap.Only spin waves with frequencies greater than the band gap can propagate through the composite medium,which results in the selective property of the propagation of spin waves.This property has great application prospects in the microwave field.Since the wavelength of the spin wave in magnonic crystal is shorter than the wavelength of the electromagnetic wave with the same frequency in the photonic crystal,the magnonic crystal is an excellent candidate material for manufacturing the micr-or nano-scaled waves device.The advantage of artificial micro-structured composites lies in the flexibility of manual design,so that the "cuttability" of the band gap structure can be realized in the magnetic composite materials.The transmission characteristics of waves in crystals can be completely determined by its dispersion relations(structures),so the research of band structures is very important,and this research is mainly the task of the theoretical calculation of material science,and spin wave in magnonic crystal is also the same.A large number of studies have been done on the structure of magnonic crystals and the dispersion relation of the simple lattice.In this thesis,the simple lattice is broken through,a model of two-dimensional magnonic crystals with nesting complex lattice is proposed on the basis of previous works of our group.Firstly,each single cylinder called scaterer in a simple lattice has been replaced with an array of small iron rods,and the structure of sacterers is more subtle.So,the models of two-dimensional magnonic crystals with nesting complex square or triangular lattices are proposed.And then,the expression of structural factor of two-dimensional nesting complex lattice is derived,which is the theoretical foundation of the successful application the plane wave expansion method.The plane wave expansion method in the field of artificial crystal has extensive application in band calculation whether in two-or three-dimensional magnonic crystal,especial for the numerical calculation of spin wave dispersion relation,field distribution of defect modes and others.At last,the band gap structures of two kinds of nesting are calculated by using the plane wave expansion method,and the results are compared with those of the simple lattice,respectively.The contrasting results show that the nested grid has more advantages.The detail is discussed in the below.In conclusion,the nested composited lattices can provide an approach or ways for the design of artificial composite materials based on the magnonic crystals.