Collective spin modes in chains of dipolarly interacting rectangular magnetic dots

We present a combined experimental and micromagnetic study of spin excitations in chains of dense magnetic dots. The samples consist of long chains of rectangular dots with rounded corners having lateral dimensions of 715 x 450 nm(2) and 1025 x 450 nm(2), respectively. Chains are composed of magnetic elements put side by side along either their major or minor axis with edge-to-edge separation below 100 nm. The frequency dispersion of the spin-wave excitations was measured by Brillouin light-scattering technique as a function of the transferred wave vector directed along the chains of dots and for an external magnetic field applied perpendicularly to the transferred wave vector in the dots plane. Evidence is given of collective excitations in the form of Bloch waves propagating through the chains characterized by magnonic energy bands. Micromagnetic calculations, performed by using the dynamical matrix method, enable us to satisfactorily reproduce the frequency dispersion of collective spin modes as well as to visualize the spatial profile of the dynamic magnetization inside the dots. We also propose a general rule to understand the frequency dispersion of collective modes starting from the relative phase of dynamic magnetization in the facing sides of adjacent dots