Application of the dynamical matrix approach to the investigation of spin excitations in nanometric dots

The dynamical matrix method, which has been recently introduced for spin mode calculations in magnetic nano-dots, is reviewed. The method is a hybrid of micro-magnetic simulations (i.e. the dot is approximated out of small cells) and an eigenvalue/eigenvector approach, which requires the computation of a matrix, whose elements represent the torque acting on each cell. We apply this method to calculate the normal modes of dots of different shape (parallelepipeds, disks, ellipses and rings), material (Fe, Permalloy) and magnetization state (saturated, vortex, with and without external field). In each case, the equilibrium configuration is preliminarily computed and then used to perform the dynamical calculation, which yields the eigenvalues (frequencies) and eigenvectors (profiles) of the spin modes. The modes are classified according to the orientation of the nodal lines with respect to the local magnetization, and are investigated in their frequency dependence on the wave-vector, nodal number and applied field. Many physical features are discussed, such as the existence of localized modes in saturated dots, the hybridization between modes, the interaction of modes with the out-of-plane vortex core in cylindrical dots, the dependence of the mode frequency on the eccentricity in elliptical dots.