Effect of the Geometry of an Yttrium Iron Garnet Film on the Spin-Wave Dispersion Relation

Abstract

In the last couple of years spintronics gained much attention as a research area. The reason for this is that spintronics signal processing devices could replace conventional electronic devices. As of lately, spin waves carrying spin currents in magnetic insulators like yttrium iron garnet (YIG) have been studied. For example, there has been research on a YIG film with an external magnetic field and motivated by the results we will verify it. Furthermore we will consider holes in the film to obtain new results. In our thesis we will use the Holstein-Primakoff transformation to find the dispersion relation of a Hamiltonian, considering the exchange and dipole-dipole interaction. We will do this via numerical simulations. To lower the computational time we will use the Ewald summation for the dipole-dipole interaction. Furthermore, we shall give a motivation on why the Ewald summation gives reliable results and why it lowers the computational time. Our results show that there are bandgaps in our dispersion relation, which were also found experimentally in Wang et al. If we neglect the exchange interaction we found a similar shape as well. The results we obtained could be used to develop ways to control spin waves in magnetic insulators.