Collective spin excitations in bi-component magnonic crystals consisting of bi-layer Permalloy/Fe nanowires

In the developing field of magnonics, it is very important to achieve tailoring of spin wave propagation by both a proper combination of materials with different magnetic properties and their nanostructuring on the submicrometric scale. With this in mind, we have exploited deep ultraviolet lithography, in combination with the tilted shadow deposition technique, to fabricate arrays of closely spaced bilayer nanowires (NWs), with separation d = 100 nm and periodicity a = 440 nm, having bottom and top layers made of permalloy and iron, respectively. The NWs have either a "rectangular" cross section (bottom and upper layers of equal width) or an "L-shaped" cross section (upper layer of half width). The frequency dispersion of collective spin wave excitations in the above bilayered NW arrays has been measured by the Brillouin light-scattering technique while sweeping the wave vector perpendicularly to the wire length over three Brillouin zones of the reciprocal space. For the rectangular NWs, the lowest-frequency fundamental mode, characterized by a quasiuniform profile of the amplitude of the dynamic magnetization across the NW width, exhibits a sizable and periodic frequency dispersion. A similar dispersive mode is also present in L-shaped NWs, but the mode amplitude is concentrated in the thin side of the NWs. The width and the center frequency of the magnonic band associated with the above fundamental modes have been analyzed, showing that both can be tuned by varying the external applied field. Moreover, for the L-shaped NWs it is shown that there is also a second dispersive mode, at higher frequency, characterized by an amplitude concentrated in the thick side of the NW. These experimental results have been quantitatively reproduced by an original numerical model that includes a two-dimensional Green's function description of the dipole field of the dynamic magnetization and interlayer exchange coupling between the layers.