Band structure and properties of vortex modes in a 2-D magnonic crystal‎

Magnonic crystals are artificial materials with periodic modulation of the magnetic properties that have ‎recently received large interest from the scientific community. Indeed, the possibility of tuning the ‎propagating properties, speed and allowed/forbidden band width of magnetic collective excitations with ‎an external field has attracted special attention on these systems. However, while in the saturated case ‎the band diagram has been extensively investigated [1], only a few incomplete studies on collective ‎modes in the vortex state have been reported [e.g. Ref. 2]. Here we present a thorough investigation on ‎this subject: employing the dynamical matrix method [3], we performed calculations on a squared 2D ‎lattice of dots in the vortex state, varying the in-plane wavevector components to investigate the first ‎Brillouin zone. We computed the dispersion relations for gyrotropic, azimuthal and radial modes (Fig. 1). ‎Dynamics in vortex states is a complex matter, since the coupling is mainly due to the fluctuations of the ‎magnetization, which is a second order effect, but is more interesting because a slight change of the ‎external field can have dramatic consequences on the information carriers (“magnons”), which can be ‎slowed down even to zero speed: in this way information could be stored or delivered with little energy ‎effort within the same device, which operates either as a memory or a waveguide. We discuss the ‎dynamical coupling of modes with different cell wavefunctions, the corresponding mode dispersion and ‎bandwidth, the effects of interdot coupling on the circular polarization on the modes, the Brillouin Light ‎Scattering cross section of the principal modes. The investigation extends also to vortex states in ‎presence of a nonzero applied field, where the vortex core is no more in the center of the disk, and to ‎the corresponding symmetry breaking in the dispersion relations. This work was supported by the ‎European Community's Seventh Framework Programme (FP7/2007-2013) under Grant Agreement ‎n°233552 (DYNAMAG).‎ ‎[1] S. Tacchi, F. Montoncello, M. Madami, G. Gubbiotti, G. Carlotti, L. Giovannini, R. Zivieri , F. Nizzoli, S. ‎Jain, A. O. Adeyeye, and N. Singh, Physical Review Letters, in press (2011). ‎[2] A. Yu. Galkin, B. A. Ivanov and C. E. Zaspel, Physical Review B, 74, 144419 (2006). ‎[3] L. Giovannini, F. Montoncello, and F. Nizzoli, Physical Review B 75, 024416 (2007).