Two-dimensional arrays of interacting magnetic elements have recently received increased interest in the field of magnonics. These systems, indeed, can support propagation of collective spin excitations, whose dispersion is characterised by the presence of allowed magnonic states and ranges of forbidden frequencies (band gaps), related to the appearance of Brillouin Zones (BZ) induced by the artificial periodicity of the pattern geometry. Nevertheless, detailed investigation of the spin-wave band structure in two-dimensional (2D) systems is still lacking. Here, Brillouin Light Scattering (BLS) has been used to study the spin-wave band structure of a dense array of Permalloy cylindrical dots, 50 nm thick, having a diameter of 600 nm and interdot separation of 55 nm. BLS measurements were carried out applying the magnetic field H=1000 Oe in the sample plane along the side of the square matrix and varying both the magnitude and in-plane direction of the transferred wave vector k. This allowed us to map the major symmetry directions of the first BZ: the Y (along which, k is perpendicular to H), the X (along which, k is parallel to H ), the YM and the XM directions (along which, k has both a component parallel and perpendicular to H). We found that a few modes show an oscillating behaviour, while other modes are stationary waves. This indicates that, due to the dynamical dipolar interdot coupling, a few modes propagate through the array as a Bloch wave, characterized by a periodicity induced by the pattern symmetry. In order to interpret the measurements, the band diagram of this system has been calculated by using the dynamical matrix method, which was extended to include the dipolar interaction in an infinite 2-D array of dots and to allow the calculation of the whole set of eigenvalues/eigenvectors at any given point in the reciprocal space [1]. The agreement with the measured diagram is very good. Considerations of general validity on the dispersion and cross section of modes with different symmetry are finally given. This work was supported by the European Community's Seventh Framework Programme (FP7/2007-2013) under Grant Agreement n°228673 (MAGNONICS) and n°233552 (DYNAMAG).
Spin-wave band diagram in a 2-D magnonic crystal consisting of interacting permalloy disks
MONTONCELLO, Federico;GIOVANNINI, Loris;NIZZOLI, Fabrizio;ZIVIERI, Roberto;
2011
Abstract
Two-dimensional arrays of interacting magnetic elements have recently received increased interest in the field of magnonics. These systems, indeed, can support propagation of collective spin excitations, whose dispersion is characterised by the presence of allowed magnonic states and ranges of forbidden frequencies (band gaps), related to the appearance of Brillouin Zones (BZ) induced by the artificial periodicity of the pattern geometry. Nevertheless, detailed investigation of the spin-wave band structure in two-dimensional (2D) systems is still lacking. Here, Brillouin Light Scattering (BLS) has been used to study the spin-wave band structure of a dense array of Permalloy cylindrical dots, 50 nm thick, having a diameter of 600 nm and interdot separation of 55 nm. BLS measurements were carried out applying the magnetic field H=1000 Oe in the sample plane along the side of the square matrix and varying both the magnitude and in-plane direction of the transferred wave vector k. This allowed us to map the major symmetry directions of the first BZ: the Y (along which, k is perpendicular to H), the X (along which, k is parallel to H ), the YM and the XM directions (along which, k has both a component parallel and perpendicular to H). We found that a few modes show an oscillating behaviour, while other modes are stationary waves. This indicates that, due to the dynamical dipolar interdot coupling, a few modes propagate through the array as a Bloch wave, characterized by a periodicity induced by the pattern symmetry. In order to interpret the measurements, the band diagram of this system has been calculated by using the dynamical matrix method, which was extended to include the dipolar interaction in an infinite 2-D array of dots and to allow the calculation of the whole set of eigenvalues/eigenvectors at any given point in the reciprocal space [1]. The agreement with the measured diagram is very good. Considerations of general validity on the dispersion and cross section of modes with different symmetry are finally given. This work was supported by the European Community's Seventh Framework Programme (FP7/2007-2013) under Grant Agreement n°228673 (MAGNONICS) and n°233552 (DYNAMAG).I documenti in SFERA sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
