By means of a joint experimental and theoretical investigation, we propose an alternative way of describing band properties of collective spin waves (SWs) when considering their propagation direction across a magnonic crystal (in our case, a square antidot lattice, ADL): to build up an angular band diagram, in which frequency is plotted as a function of the angle of SW propagation. Similarly to conventional band diagrams, even in this case different dispersions of different modes give origin to allowed/forbidden bands, related not only to the specific in-plane angle at which they are considered, but also to the SW wavevector magnitude and the ADL constant. We performed Brilluoin light scattering (BLS) measurements on a Permalloy ADL (with a lattice constant of 440 nm), mounted on a two-axis goniometer, which allows us to choose a specific angle of incidence of light as well as to rotate the sample around the surface normal (azimuthal rotation). By changing these angles, it is possible to change the magnitude and/or the in-plane direction of the wavevector of light (and, as a consequence, of the detected SW) [1]. In Fig. 1, we show an example of angular band diagram for a SW with k=1.06×2π/a (corresponding to a light incidence angle of 40 degrees): full circles are the experimental data, lines are the dispersions calculated by means of the dynamical matrix method (DMM) [2]. As apparent in Fig. 1, a minimum gap between the most intense SW modes occurs close to φG=28 degrees: however, this value is critically dependent on the wavevector magnitude (and the lattice constant, if different ADLs are compared). We derive and prove this functional dependence with analitical considerations. We believe that this results are of interest for magnon-spintronic applications where a straight antenna on an ADL is used to emit SWs in any direction (omnidirectional SW emission). References: [1] G. Gubbiotti, F. Montoncello,S. Tacchi, M. Madami, G. Carlotti, L. Giovannini, J. Ding and A. O. Adeyeye, Applied Physics Letters 106, 262406 (2015). [2] L. Giovannini, F. Montoncello, and F. Nizzoli, Physical Review B 75, 024416 (2007).
Angular Band Diagrams for Multidirectional Spin Wave Propagation in Square Antidot Lattices
MONTONCELLO, Federico;GIOVANNINI, Loris;
2016
Abstract
By means of a joint experimental and theoretical investigation, we propose an alternative way of describing band properties of collective spin waves (SWs) when considering their propagation direction across a magnonic crystal (in our case, a square antidot lattice, ADL): to build up an angular band diagram, in which frequency is plotted as a function of the angle of SW propagation. Similarly to conventional band diagrams, even in this case different dispersions of different modes give origin to allowed/forbidden bands, related not only to the specific in-plane angle at which they are considered, but also to the SW wavevector magnitude and the ADL constant. We performed Brilluoin light scattering (BLS) measurements on a Permalloy ADL (with a lattice constant of 440 nm), mounted on a two-axis goniometer, which allows us to choose a specific angle of incidence of light as well as to rotate the sample around the surface normal (azimuthal rotation). By changing these angles, it is possible to change the magnitude and/or the in-plane direction of the wavevector of light (and, as a consequence, of the detected SW) [1]. In Fig. 1, we show an example of angular band diagram for a SW with k=1.06×2π/a (corresponding to a light incidence angle of 40 degrees): full circles are the experimental data, lines are the dispersions calculated by means of the dynamical matrix method (DMM) [2]. As apparent in Fig. 1, a minimum gap between the most intense SW modes occurs close to φG=28 degrees: however, this value is critically dependent on the wavevector magnitude (and the lattice constant, if different ADLs are compared). We derive and prove this functional dependence with analitical considerations. We believe that this results are of interest for magnon-spintronic applications where a straight antenna on an ADL is used to emit SWs in any direction (omnidirectional SW emission). References: [1] G. Gubbiotti, F. Montoncello,S. Tacchi, M. Madami, G. Carlotti, L. Giovannini, J. Ding and A. O. Adeyeye, Applied Physics Letters 106, 262406 (2015). [2] L. Giovannini, F. Montoncello, and F. Nizzoli, Physical Review B 75, 024416 (2007).I documenti in SFERA sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
