Discrete modes of a ferromagnetic stripe dipolarly coupled to a ferromagnetic film: a Brillouin light scattering study

Spin wave excitations in a magnetic structure consisting of a series of long permalloy stripes of a rectangular cross section magnetized along the stripe length and situated above a continuous permalloy film are studied both experimentally and theoretically. Stripes and continuous film are coupled by dipole-dipole interaction across 10 nm thick Cu spacers. Experimental measurements made using the Brillouin light scattering technique (with the light wavevector oriented along the stripe width) provide evidence for one dispersive spin wave mode associated with the continuous film and several discrete non-dispersive modes resonating within the finite width of the stripes.To interpret the experimental spectra, an analytic theory based on the spin wave formalism for finite-width magnetic stripes has been developed, achieving a good qualitative and partly quantitative description of the experimentally observed spin wave spectrum of the system. In particular, it is explained why the presence of a continuous magnetic film near the magnetic stripe leads to a substantial decrease of the frequencies of the discrete dipolar spin wave modes localized within the stripes. A more quantitative description of the measured frequencies and of the spatial profiles of the spin wave eigenmodes has been obtained by numerical calculations performed using a finite element method.