Magnetic Vortex Dynamics in the Thick Ferromagnetic Nanoelement

Abstract

A magnetic vortex structure, which is formed in a ferromagnetic rectangular disk, circular disk, and elliptical disk, has attracted a lot of interest due to high thermal stability and structural rigidity among spatially non-uniform magnetization configuration. It consists of the in-plane curling magnetization configuration, which rotates either counterclockwise (CCW, c = +1) or clockwise (CW, c = -1), and out-of-plane magnetization configuration pointing either up (p = +1) or down (p = -1) which is called vortex core, i.e., it has energetically equivalent fourfold states. It has been known that the magnetic vortex is very stable and it is hard to be deformed by the dynamics of vortex core below the critical velocity. The magnetization distribution of the magnetic vortex is uniform along the thickness and most of studies using micromagnetic simulation employed two dimensional numerical calculation, i.e., the number of cell along the thickness is only one. The numerical simulation results are in a good agreement with experimental results when the thickness (< ~ 40 nm) is thin. However, the magnetization distribution of the magnetic vortex structure in the ground state is no longer uniform along the thickness when the thickness is relatively thick (> ~ 70 nm) and it causes a different dynamics compared to the magnetic vortex which is formed in thin ferromagnetic elements. This thesis treats the dynamics of the magnetic vortex structure under an in-plane rotating magnetic fields and an out-of-plane spin-polarized current by micromagnetic numerical simulations in relatively thick circular disk (> ~ 70 nm). Under an in-plane rotating magnetic fields, the dramatic time-varying deformation of vortex core during the gyration is observed in a relatively thick circular disk. Surprisingly, vortex core reversal does not occur although its velocity exceeds the critical velocity. Instead of vortex core reversals, the vortex core starts to tear up at the surface when the velocity of vortex core reaches some specific value as the amplitude of rotating magnetic fields increases more. When the magnetic vortex is driven by out-of-plane spin polarized dc current, it is well-known that the spin transfer torque (STT) does not influence eigenfrequency of magnetic vortex while a circumferential Oersted (OH) fields make shift of eigenfrequency. Accordingly, the energetically equivalent states of magnetic vortex are split by whether the in-plane magnetization is parallel to OH fields or not. However, in relatively thick circular disk, only STT can make shift of eigenfrequency of the magnetic vortex and it is dependent on chirality of magnetic vortex. Furthermore, each split state shows different dynamics. It is completely different from the dynamics of magnetic vortex driven by in-plane rotating magnetic fields. In case of vortex for c = -1, the vortex dynamics shows the vortex-antivortex mediated reversal is observed regardless of whether OH fields is included or not while it cannot be observed under in-plane rotating magnetic fields. However, vortex for c = +1 shows the difference for dynamics. Only STT cannot induce vortex core reversal. It shows non-linear dynamics instead of vortex core reversal, similar to the dynamics driven by rotating fields. The vortex core on the top surface is confined inside the small area while the vortex core on the bottom surface shows a large gyrotropic radius and undergo perturbation by vortex-antivortex pair. Interestingly, the vortex core reversal is observed when OH fields is included. However, it is achievable after chirality is reversed or both chirality and polarity are reversed simultaneously. When ac spin-polarized current is applied, the magnetic vortex shows an eigenmode, corresponding to the size oscillation of vortex core in the interior region analogous to the breathing mode of a magnetic skyrmion and radial mode of a magnetic vortex. When out-of-plane ac spin-polarized current is tuned to the eigenfrequency corresponding to the size oscillation of vortex core, ultrafast vortex core reversal can be achievable and the switching time is faster (< ~1 ns). During the reversal process, the antivortex-vortex, edge-soliton and the injection of Bloch point at the surface cannot be observed. Interestingly, in the interior region, the magnetic vortex is disconnected and Bloch-point pair is formed. One Bloch point moves into top surface and the other moves into bottom surface with removing the original vortex core. Each Bloch point is annihilated at the surface layer and the reversal process is complete. Finally, this thesis deal with a chaotic behavior in the formation of magnetic vortex structure. There is a fundamental hurdles to competitive magnetic-vortex-based memory device, chaos in the nucleation process. This thesis show comprehensive understandings on the deterministic chaos in the nucleation process of magnetic vortex in a nanodisk and we show that it can be manipulated simply by the breaking of the static- and dynamic-symmetries.