Asymmetric frequency dispersions of equivalent spin wave modes measured along symmetry directions of a hexagonal magnonic crystal

Magnonic crystals have been receiving special attention in front-line research on magnetism and magnetic materials because of their outstanding physical properties and potential technological applications: in particular, the collective mode propagation can be easily controlled in these systems by an external field. This gives the possibility of tuning, from one side, the width and the frequency range of the allowed/forbidden spin wave bands and, from the other, the group velocity of the spin waves so that information could be stored or delivered with little effort within the same device, which can operate either as a memory or a waveguide. In this paper, we report a Brillouin light scattering (BLS) investigation on a hexagonal array of Permalloy interacting disks, fabricated via etched nanosphere lithography technique. BLS spectra were measured in the Voigt configuration for two different orientation of the applied magnetic field, i.e., parallel and perpendicular to the direction of adjacent dots [1]. Measurements highlight the occurrence of non-monotonic dispersions, with maximum/minimum occurring inside the first Brillouin zone. The dynamical matrix method [2] was used to interpret the experimental results, and the thorough understanding of all dispersions, in all their complexity, was found straightforward within the effective wavevector model [3]. Asymmetry of mode propagation is considered a challenging feature of these systems: equivalent modes can propagate in different directions with different bandwidth and different group velocity, and in some cases different dispersion slope: this means that they can carry different binary digits, a crucial property useful, for example, in spin-logic devices. This work was supported by the European Community's Seventh Framework Programme (FP7/2007-2013) under Grant Agreement n. 228673 (MAGNONICS) and by MIUR-PRIN 2010-11 Project 2010ECA8P3 "DyNanoMag". References: [1] F. Montoncello, L. Giovannini, S. Tacchi, M. Madami, G. Gubbiotti, G. Carlotti, E. Sirotkin, E. Ahmad, F. Y. Ogrin and V. V. Kruglyak, Applied Physics Letters 102, 202411 (2013). [2] L. Giovannini, F. Montoncello and F. Nizzoli, Physical Review B 75, 024416 (2007). [3] S. Tacchi, F. Montoncello, M. Madami, G. Gubbiotti, G. Carlotti, L. Giovannini, R. Zivieri, F. Nizzoli, S. Jain, A. O. Adeyeye and N. Singh, Phys. Rev. Lett. 107, 127204 (2011).