Energy scheme of magnetostatically coupled vortices in nano-disks.

We have investigated theoretically the dynamics of vortices in a square lattice system with various combinations of vortex core polarizations in the lattice. The vortex core polarizations play an important role in determining the rotational dynamics of the vortices. In the orderly polarized vortex lattice, their dynamical properties can be represented by the dispersion curves and the density of states. These properties can be designed by choosing the combinations of the vortex core polarizations. From our analysis, we can speculate on the following phenomena: A randomly polarized vortex lattice should reveal the localization behavior in the rotational motion of the vortices in the real space as a consequence of various superposition of ferromagnetic type I and antiferromagnetic type II domains. On the analogy of the lattice vibration of a coupled diatomic lattice, the vortex lattice with two kinds of disks is expected to exhibit eigenfrequency gap in the dispersion curve. Furthermore the localization mode can be controlled since we can design a defective lattice. Finally, the above expected results encourages us to fabricate an electromagnetic wave guide in the artificial crystal of the magnetic vortex system, which should be similar to the two-dimensional photonic crystal.