Phase-field Simulation Of The Magnetic Vortex In Ferromagnetic Materials

A real-space phase-field model, which explicitly includes the coupling between magnetization and mechanical strain, is applied to simulate the properties of magnetic vortex under the effect of normal strain and shear strain in Fe1-xGax alloy nanodot. The simulation results reveal that the strain along the axis of the nanodot has little effect on the magnitude and distribution of the in-plane magnetization while affects the out-of-plane magnetization much more obviously. To be specific, the magnitude of the out-of-plane magnetization increases with the increment of tensile strain while decreases with the rising of compressive strain. It is also found that the vortex polarity of the nanodot in Fe81Ga29 can be switched by torsion when the sign of the torsion is opposite to that of vortex chirality, whereas switching does not take place if the sign of torsion is the same as that of vortex chirality. Since the sign of magnetoelastic constant λ111 of Fe74.3Ga25.7 and Fe71Ga29 Fe81Ga29 is opposite to that of Fe81Ga29, thus, only when the torsion direction is the same as that of vortex chirality could the polarity be switched.To reduce the magnitude of the critical shear strain γc that induces the polarity switching of magnetic vortex, the above three kinds of Fe1-xGax alloy with various exchange stiffness constants are also considered. The results demonstrate that the value of magnetostrictive constant λ111 and the exchange stiffness constant Aex has a great effect on the magnitude of γc, i.e. yc decreases with the increase of γ111 or the decrease of Aex. This is because the magneto-elastic coupling, gradient and magnetic energies, which involve an intriguing interplay of magnetization, strain and demagnetization, play the decisive roles in the polarity switching. The critical shear strain in Fe71Ga29 is one order smaller than that of the Fe81Ga19 nanodot, which suggests another way to control vortex polarity by mechanical torsion other than magnetic field and electric current. The responses of magnetic vortices in three different geometrical nanodots, i.e., cylinder, hexagonal prism and cubic, under the effect of torsion are also investigated. The results demonstrate that the section shape of the model has a strong influence on the magnitude of critical torsion angle φc which triggers the polarity reversal process. Compared with the vortex in cylinder, the vortices in hexagonal prism and cuboid have much smaller φc. Especially that the magnitude of φc in cuboid is nearly half of that in the cylinder and this may open up the possibility of the magnetic vortex to be applied in magneto-elastic sensors.A novel intrinsic Dzyaloshinskii-Moriya interaction, which arises from the spin-orbit coupling due to the lack of inversion symmetry at surfaces,has been discovered to play a significant role for magnetic vortex. In this paper, the ferromagnetic phase-field model is extended by taking the DMI into consideration. The vortices in different thin films under the effect of various DM constants are simulated. The results demonstrate that the DM interaction has an obvious effect on the structure of the vortex. To be specific, the DMI would induce an out-of-plane magnetization on the edge of the model and enlarge the size of the core. The magnitude of the out-of-plane magnetization at the core and the edge would grow with the increase of Dzyaloshinskii-Moriya constant.