ABSTRACT
In this chapter, the authors explains about stable magnetic configuration and spin-wave excitations in small two-dimensional magnetic dots. They describe quite simple and very effective method to explore the magnetic configuration and the spin-wave spectrum in nanodots without simulations. The authors discuss the in-plane vortex state: its stability and spin-wave normal modes versus the dipolar-to-exchange interaction ratio, the size and shape of the system, and the symmetry of the lattice from which it has been cut. Two types of interaction are most common in magnetic systems, namely dipolar and exchange interactions, and these two differ significantly from each other. Dynamical matrix diagonalization gives the spectrum of so-called normal modes or standing waves. Normal modes are collective harmonic oscillations of the system about a local energy minimum, where all spins precess with the same frequency, the natural frequency of the system.
