The effective properties of two-dimensional (2D) square arrays of antidots are studied according to micromagnetic and analytical calculations. Micromagnetic calculations were performed by using the Hamiltonian-based Dynamical Matrix Method extended to periodic systems. The nanometric systems are composed by periodic square arrays of circular antidots (holes) etched into a Permalloy ferromagnetic film. In the calculations the diameter d of the holes varies between 10 nm and 120 nm, the array periodicity is a = 800 nm and the thickness is L = 22 nm. The external field is applied in the plane of the system and perpendicularly to the Bloch wave vector. From the inspection of spatial profiles of collective modes it is possible to identify a characteristic wavelength which is commensurable with the periodicity a of the system [1]. Since collective modes are mainly affected by the finite size of the holes rather than the periodicity and since the characteristic wavelength is much larger than d, the dynamics is described in terms of effective properties and an effective medium approximation is used. In this way the characteristic wavelength can be regarded as an effective wavelength λeff related to the scattering from the antidots of the given collective mode and the 2D arrays of antidots behave as 2D metamaterials with holes acting as scattering point defects [2]. It is shown that the effective wavelength, defined for each spin-wave mode of the spectrum, is not necessarily equal to the Bloch wavelength λB and a general relation between the two wavelength is established. In the cases studied the ratio d /λeff <<1 for the whole range of Bloch wave vectors investigated. This condition would not be always fulfilled by replacing λeff with λB. Correspondingly, also a small wave vector is introduced and its relation with the Bloch wave vector is found. An effective rule involving the small wave vector and the dynamic magnetization is derived and its relation with the Bloch rule typical of periodic systems is established. A quantitative estimation of the effective ellipticity, expressed as the ratio between the in-plane and the out-of-plane component of the dynamic magnetization, for the most relevant mode of the spectrum is also given and is compared to that of the resonant Kittel mode of the continuous film. [1] R. Zivieri, Proceedings of Metamaterials ’2012, 6th International Congress on Advanced Electromagnetic Materials in Microwave and Optics (2012), 624-626. [2] R. Zivieri and L. Giovannini, “Metamaterial properties of ferromagnetic antidot lattices” Photonics and Nanostructures - Fundamentals and Applications 11, (2013) 191-202.
Effective description of magnonic mode dynamics in 2D ferromagnetic antidot lattices -- Presentazione orale by R. Zivieri -- Conferenza nazionale
ZIVIERI, Roberto
2013
Abstract
The effective properties of two-dimensional (2D) square arrays of antidots are studied according to micromagnetic and analytical calculations. Micromagnetic calculations were performed by using the Hamiltonian-based Dynamical Matrix Method extended to periodic systems. The nanometric systems are composed by periodic square arrays of circular antidots (holes) etched into a Permalloy ferromagnetic film. In the calculations the diameter d of the holes varies between 10 nm and 120 nm, the array periodicity is a = 800 nm and the thickness is L = 22 nm. The external field is applied in the plane of the system and perpendicularly to the Bloch wave vector. From the inspection of spatial profiles of collective modes it is possible to identify a characteristic wavelength which is commensurable with the periodicity a of the system [1]. Since collective modes are mainly affected by the finite size of the holes rather than the periodicity and since the characteristic wavelength is much larger than d, the dynamics is described in terms of effective properties and an effective medium approximation is used. In this way the characteristic wavelength can be regarded as an effective wavelength λeff related to the scattering from the antidots of the given collective mode and the 2D arrays of antidots behave as 2D metamaterials with holes acting as scattering point defects [2]. It is shown that the effective wavelength, defined for each spin-wave mode of the spectrum, is not necessarily equal to the Bloch wavelength λB and a general relation between the two wavelength is established. In the cases studied the ratio d /λeff <<1 for the whole range of Bloch wave vectors investigated. This condition would not be always fulfilled by replacing λeff with λB. Correspondingly, also a small wave vector is introduced and its relation with the Bloch wave vector is found. An effective rule involving the small wave vector and the dynamic magnetization is derived and its relation with the Bloch rule typical of periodic systems is established. A quantitative estimation of the effective ellipticity, expressed as the ratio between the in-plane and the out-of-plane component of the dynamic magnetization, for the most relevant mode of the spectrum is also given and is compared to that of the resonant Kittel mode of the continuous film. [1] R. Zivieri, Proceedings of Metamaterials ’2012, 6th International Congress on Advanced Electromagnetic Materials in Microwave and Optics (2012), 624-626. [2] R. Zivieri and L. Giovannini, “Metamaterial properties of ferromagnetic antidot lattices” Photonics and Nanostructures - Fundamentals and Applications 11, (2013) 191-202.I documenti in SFERA sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
