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 (HDMM) extended to periodic systems. The nanometric systems are composed by periodic square arrays of circular antidots (holes) embedded 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 H is applied along the y direction and perpendicularly to the Bloch wave vector K placed along the x direction in the sample plane. 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. These properties are those that characterize the 2D arrays of antidots as metamaterials [2]. In this way, the characteristic wavelength can be regarded as an effective wavelength λeff related to the scattering from the antidots of the given spin-wave mode. Interestingly, the effective wavelength, which can be defined for each mode of the spectrum, is not necessarily equal to the Bloch wavelength and, in the geometry studied, assumes either the value a or the value 2a. In the cases studied the ratio d /λeff <<1 for the whole range of Bloch wave vectors investigated. Correspondingly, also a small wave vector is introduced and important effective rules are derived. [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” in press in Photonics and Nanostructures - Fundamentals and Applications.
Effective quantities and effective rules in 2D ferromagnetic antidot lattices -- Presentazione orale by R. Zivieri - Conferenza internazionale
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 (HDMM) extended to periodic systems. The nanometric systems are composed by periodic square arrays of circular antidots (holes) embedded 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 H is applied along the y direction and perpendicularly to the Bloch wave vector K placed along the x direction in the sample plane. 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. These properties are those that characterize the 2D arrays of antidots as metamaterials [2]. In this way, the characteristic wavelength can be regarded as an effective wavelength λeff related to the scattering from the antidots of the given spin-wave mode. Interestingly, the effective wavelength, which can be defined for each mode of the spectrum, is not necessarily equal to the Bloch wavelength and, in the geometry studied, assumes either the value a or the value 2a. In the cases studied the ratio d /λeff <<1 for the whole range of Bloch wave vectors investigated. Correspondingly, also a small wave vector is introduced and important effective rules are derived. [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” in press in Photonics and Nanostructures - Fundamentals and Applications.I documenti in SFERA sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
