Magnetic normal modes in ferromagnetic nanoparticles: A dynamical matrix approach

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.