The magnetic normal modes of nanometric magnetic disks are calculated using a recently developed, hybrid micromagnetic method. The method is based on the subdivision of a particle into small cells and the development of a “dynamical matrix” that contains the restoring torques acting on the magnetization of each cell. The method includes dipolar, Zeeman, and exchange interactions. The results of these calculations are used to interpret the spin wave spectra measured by Brillouin scattering in an array of nanometric Permalloy™ disks over a wide range of applied fields encompassing both the vortex and saturated states.

We present a method to compute the magnetic normal modes of a ferromagnetic particle. The method is a hybrid of micromagnetic simulations and a “dynamical matrix” approach similar to that used for vibrational studies. We use the method to calculate the normal modes of an Fe parallelepiped and compare the results with the modes recently extracted from a purely micromagnetic simulation. The results of the two approaches are in excellent agreement. We discuss the pros and cons of both approaches. We also present information on standing waves with wave vector perpendicular to the applied field and on a family of modes localized at the particle ends.

The dispersion curves of collective spin-wave excitations in a magnonic crystal consisting of a square array of interacting saturated nanodisks have been measured by Brillouin light scattering along the four principal directions of the first Brillouin zone. The experimental data are successfully compared to calculations of the band diagram and of the Brillouin light scattering cross section, performed through the dynamical matrix method extended to include the dipolar interaction between the disks. We found that the fourfold symmetry of the geometrical lattice is reduced by the application of the external field and therefore equivalent directions of the first Brillouin zone are characterized by different dispersion relations of collective spin waves. The dispersion relations are explained through the introduction of a bidimensional effective wave vector that characterizes each mode in this magnonic metamaterial.

Brillouin light scattering (BLS) spectra have been measured in arrays of cylindrical Permalloy dots with elliptical cross section, $200\mathrm{nm}$ wide, $15\mathrm{nm}$ thick, and eccentricities from 1 to 3. Several spin modes are observed and their frequencies tracked as a function of the direction of the applied $1.5\mathrm{kOe}$ magnetic field $\mathit{H}$. The experimental data are interpreted within the framework of the recently introduced dynamical matrix method to calculate spin excitations in magnetic particles. We find that the mode frequencies strongly depend on the eccentricity of the dots and on the direction of the applied field. For fields along the principal axes the solutions can be classified into: (i) modes localized near the particle ends, (ii) modes with nodal lines perpendicular to $\mathit{H}$ (backwardlike modes), (iii) modes with nodal lines parallel to $\mathit{H}$ (Damon-Eshbach-like modes) and (iv) modes with both parallel and perpendicular nodal lines. In cases where the frequencies of two modes in different families are similar, some hybridization between the modes is observed. For $\mathit{H}$ along nonsymmetry directions only the modes of type (i) remain reasonably well defined, other modes can at best be described as hybrids of modes in the above categories. Determining which of the modes is active in BLS experiments leads to excellent agreement with the experimental results.

Miniaturization of magnonic devices for wave-like computing requires emission of short-wavelength spin waves, a key feature that cannot be achieved with microwave antennas. In this paper, we propose a tunable source of short-wavelength spin waves based on highly localized and strongly pinned magnetic domain walls in ferroelectric-ferromagnetic bilayers. When driven into oscillation by a microwave spin-polarized current, the magnetic domain walls emit spin waves with the same frequency as the excitation current. The amplitude of the emitted spin waves and the range of attainable excitation frequencies depend on the availability of domain wall resonance modes. In this respect, pinned domain walls in magnetic nanowires are particularly attractive. In this geometry, spin wave confinement perpendicular to the nanowire axis produces a multitude of domain wall resonances enabling efficient spin wave emission at frequencies up to 100 GHz and wavelengths down to 20 nm. At high frequency, the emission of spin waves in magnetic nanowires becomes monochromatic. Moreover, pinning of magnetic domain wall oscillators onto the same ferroelectric domain boundary in parallel nanowires guarantees good coherency between spin wave sources, which opens perspectives towards the realization of Mach-Zehnder type logic devices and sensors.

We have developed a theory for the determination of the collective spin-wave modes of regular arrays of magnetic particles, taking into account the dipolar interaction among particles. The frequencies and profiles of the spin modes of arrays of permalloy cylindrical particles with different interparticle separation have been calculated with a numerical implementation of this model, using a three-dimensional representation of the magnetic particles in their actual nonuniform fundamental state. The results show a very good agreement with recently published experimental data, and allow us to discuss the dispersion curves and some relevant properties of the Brillouin light-scattering intensity from spin modes in periodic arrays.