Magnetic vortex formation and gyrotropic mode in nanodisks

Abstract

The superparamagnetic limit imposes a restriction on how far the miniaturization of electronic devices can reach. Recently it was shown that magnetic thin films with nanoscale dimensions can exhibit a vortex as its ground state. The vortex can lower its energy by developing an out-of-plane magnetization perpendicular to the plane of the film, the z direction, which can be “up” or “down.” Because the vortex structure is very stable this twofold degeneracy opens up the possibility of using a magnetic nanodisk as a bit of memory in electronic devices. The manipulation of the vortex and a way to control the core magnetization is a subject of paramount importance. Recent results have suggested that the polarity of a vortex core could be switched by applying a pulsed magnetic field in the plane of the disk. Another important effect induced by an external magnetic field due to the component out-of-plane in vortex-core is the gyrotropic mode. The gyrotropic mode is the elliptical movement around the disk center executed by the vortex-core under the influence of a magnetic field. In the present work we used numerical simulations to study the ground state as well as the dynamical behavior of magnetic vortices in thin nanodisks. We have considered a model where the magnetic moments interact through exchange (−J∑S⃗i⋅S⃗j) and dipolar potentials {D∑[S⃗i⋅S⃗j−3(S⃗i⋅r̂ij)×(S⃗j⋅r̂ij)]/rij3}. We have investigated the conditions for the formation of the vortex-core with and without an out-of-plane magnetization as a function of the strength of the dipole interaction D and of the size and thickness of the magnetic nanodisk. Our results were consistent with the existence of two vortex phases separated by a crossover line [(Dc−D)α]. We have observed that Dc does not depend on the radius of nanodisk but depends on its thickness. The exponent α was found to be α≈0.55(2). The gyrotropic motion is studied by applying an external magnetic field parallel to the plane of the magnetic nanodisk. Our results show that there is a minimum value for the modulus of the out-of-plane vortex-core magnetization, from which we can excite the gyrotropic mode. This minimum value depends on the thickness of the nanodisk. This result suggest that an experimental way to improve the stability of the process of switching may be through the thickness control. We also observed that the gyrotropic mode frequency increases with the aspect ratio, which is in qualitatively accordance with theoretical and experimental results. Finally, we present theoretical results for Permalloy nanodisks obtained from our model, which are also in good agreement with experimental results.