A micromagnetic study of the band structure of a three-dimensional magnonic crystal formed by a periodic array of cobalt cylindrical dots partially etched into a permalloy film 16 nm thick is performed. The periodicity of the system is a = 600 nm, the dot diameter is d = 310 nm and the dot thickness is L = 8 nm. The studied geometry is with an external field H along the y axis and with the Bloch wave vector K along the x axis in the plane of the system. The used micromagnetic approach, called dynamical matrix method, is generalized to study the dynamical properties of periodic binary permalloy/cobalt systems. The dispersion of the most representative frequency modes, the DEnBZPy and the DEnBZCo, respectively, with n = 1,2,…has been calculated (DE stands for Damon-Eshbach and BZ for Brillouin zone) up to the 5BZ. The DEnBZPy modes have amplitudes spreading mainly inside the Py film with maxima either in the horizontal channels or in the horizontal rows containing Co dots. Instead, the DEnBZCo modes are either mainly localized in the Co dots or along the horizontal rows containing Co dots. At edges of nBZs there is the opening of band gaps caused by Bragg diffraction, because of the magnetic contrast between Py and Co. According to numerical calculations we have found that the band gap amplitude of DEnBZPy at the edge of the 1BZ is about 0.3 GHz and reduces with increasing band index apart from a slight increase at the edge of the 4BZ showing a behavior similar to the one found for extended modes in a 2D antidot lattice [1]. Also band widths follow a similar trend showing a decrease of their amplitudes from about 1.8 GHz for 1BZ to about 1 GHz for 5BZ. Moreover, we have found that the perturbation which produces the band gaps is proportional to the quantity of Co. Also the portion of Co dot above the Py surface plays an important role in increasing the band gap amplitude. This work was partially supported by MIUR-PRIN 2010-11 Project2010ECA8P3 “DyNanoMag”. [1] R. Zivieri, S. Tacchi, F. Montoncello, L. Giovannini, F. Nizzoli, M. Madami, G. Gubbiotti, G. Carlotti, S. Neusser, G. Duerr, and D. Grundler, Phys. Rev. B 85, 012403 (2012).
Magnonic modes in three-dimensional permalloy/cobalt binary systems -- Presentazione orale by R. Zivieri -- Conferenza internazionale
MALAGO', Perla;ZIVIERI, Roberto;GIOVANNINI, Loris
2013
Abstract
A micromagnetic study of the band structure of a three-dimensional magnonic crystal formed by a periodic array of cobalt cylindrical dots partially etched into a permalloy film 16 nm thick is performed. The periodicity of the system is a = 600 nm, the dot diameter is d = 310 nm and the dot thickness is L = 8 nm. The studied geometry is with an external field H along the y axis and with the Bloch wave vector K along the x axis in the plane of the system. The used micromagnetic approach, called dynamical matrix method, is generalized to study the dynamical properties of periodic binary permalloy/cobalt systems. The dispersion of the most representative frequency modes, the DEnBZPy and the DEnBZCo, respectively, with n = 1,2,…has been calculated (DE stands for Damon-Eshbach and BZ for Brillouin zone) up to the 5BZ. The DEnBZPy modes have amplitudes spreading mainly inside the Py film with maxima either in the horizontal channels or in the horizontal rows containing Co dots. Instead, the DEnBZCo modes are either mainly localized in the Co dots or along the horizontal rows containing Co dots. At edges of nBZs there is the opening of band gaps caused by Bragg diffraction, because of the magnetic contrast between Py and Co. According to numerical calculations we have found that the band gap amplitude of DEnBZPy at the edge of the 1BZ is about 0.3 GHz and reduces with increasing band index apart from a slight increase at the edge of the 4BZ showing a behavior similar to the one found for extended modes in a 2D antidot lattice [1]. Also band widths follow a similar trend showing a decrease of their amplitudes from about 1.8 GHz for 1BZ to about 1 GHz for 5BZ. Moreover, we have found that the perturbation which produces the band gaps is proportional to the quantity of Co. Also the portion of Co dot above the Py surface plays an important role in increasing the band gap amplitude. This work was partially supported by MIUR-PRIN 2010-11 Project2010ECA8P3 “DyNanoMag”. [1] R. Zivieri, S. Tacchi, F. Montoncello, L. Giovannini, F. Nizzoli, M. Madami, G. Gubbiotti, G. Carlotti, S. Neusser, G. Duerr, and D. Grundler, Phys. Rev. B 85, 012403 (2012).I documenti in SFERA sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
