Spin-wave Resonant Frequency Of Magnetic Thin Films And MMagnetic Nanobelts

By using the Heisenberg model,and through the utilization of the linear spin-wave approximation and Green's function technique,the spin-wave resonance(SWR)frequency in a magnetic bilayer film,triple-layer film and magnetic nanobelt have been studied.And the effects of surface and the interface anisotropies,interfacial exchange coupling and magnetic field on the SWR frequency also have been studied.The study of course extended to the effects of the magnetic nanobelt,the bulk anisotropy,up-and down-surface anisotropy,side surface anisotropy,and edge anisotropy on the SWR frequency of the magnetic nanobelts as well.The SWR frequencies of a triple-layer film are different from those of a bilayer film.And the SWR frequencies of a film with an antiferromagnetic interface coupling are also different from that of a film with a ferromagnetic interface coupling.As for a bilayer or triple-layer film with a ferromagnetic interface,all of the SWR frequencies will increase with the increasing of the surface anisotropy,interface anisotropy,interfacial coupling and magnetic field.The effect of ferromagnetic interfacial coupling on the SWR frequencies(m=1)is small.And the different interfacial coupings can lead to different effects of interface anisotropy on the SWR frequencies.The SWR frequencies will decrease as the thickness of the film increases.As for a bilayer or triple-layer film with an antiferromagnetic interfacial coupling,all of the SWR frequencies will increase as the interface anisotropy and antiferromagnetic interfacial coupling increase.As the surface anisotropy increases,the SWR frequencies of two modes will increase,while other two modes remain unchanged.The antiferromagnetic interfacial coupling does not affect the effect of interface anisotropy on the SWR frequencies.As for a bilayer film,when the magnetic field increases,the SWR frequencies of two modes will also increase but that of other two modes will decrease.While for a triple-layer,when the magnetic field increases,the SWR frequencies of three modes increase,and that of other one modes will decrease.And as the thickness of a film increases,the SWR frequencies of three modes will decrease.When the interfacial coupling is larger,the SWR frequencies of other one modes will increase as the thickness of a film increases.For a magnetic nanobelt,all of the SWR frequencies will increase when bulk anisotropy,up-and down-surface anisotropy,side surface anisotropy and edge anisotropy increase.The effects of bulk anisotropy and up-and down-surface anisotropy on the SWR frequencies are greater than that of side surface anisotropy and edge anisotropy.When the spin quantum number increases,the effect of bulk anisotropy,up-and down-surface anisotropy,side surface anisotropy and edge anisotropy on the SWR frequencies will increase.