Geodesic
Coupled dynamics of magnetic vortexes in a three-layer thin conductive permalloe nanodisc
Čelâbinskij fiziko-matematičeskij žurnal, Tome 5 (2020) no. 2, pp. 161-173

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The dynamics of two magnetic vortices in the presence of a spin-polarized current is investigated. A magnetic conducting nanostructure in the form of a three-layer conducting cylinder of small diameter 120 nm is considered. A thick magnetic layer of permalloy has a thickness of 15 nm, an intermediate non-magnetic layer has a thickness of 10 nm, and a thin magnetic layer of permalloy has a thickness of 4 nm. The dynamics of magnetostatically coupled vortices were numerically calculated using the generalized Landau — Lifshitz equation and the SpinPM software package for a micromagnetic simulation. Vortex trajectories for three different dynamic modes are constructed and studied. For the case of low currents, this is the regime of damped oscillations of magnetic vortices. For the case of small currents, this is an important for practical applications regime of stationary coupled oscillations of magnetic vortices. At the initial moment of motion, a strongly nonlinear mode of motion is observed. Then the trajectory of movement goes to an expanding spiral and reaches its maximum value. Both vortices then move around the circle with the same frequency and different radii. Upon the exit of the vortex core to the edge of the disk in the thick and thin layers, the formation of the $C$-structure of the vortex state was observed. For high currents, when a current value is greater than a certain critical value, a new dynamic mode is realized, the "departure" of the vortex from a thin layer. In a thick layer, after a "departure" of a vortex in a thin layer, the vortex performs stationary oscillations with a frequency and a radius approximately equal to the values obtained for the case of a single vortex.
Keywords: generalized Landau — Lifshitz equation, nonlinear dynamics, magnetic nanostructure, magnetic vortex, $C$-structure of vortex states. 
@article{CHFMJ_2020_5_2_a7,
     author = {E. G. Ekomasov and S. V. Stepanov and M. I. Fakhretdinov and G. I. Antonov and A. E. Ekomasov and K. A. Zvezdin},
     title = {Coupled dynamics of magnetic vortexes in a three-layer thin conductive permalloe nanodisc},
     journal = {\v{C}el\^abinskij fiziko-matemati\v{c}eskij \v{z}urnal},
     pages = {161--173},
     publisher = {mathdoc},
     volume = {5},
     number = {2},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHFMJ_2020_5_2_a7/}
}
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E. G. Ekomasov; S. V. Stepanov; M. I. Fakhretdinov; G. I. Antonov; A. E. Ekomasov; K. A. Zvezdin. Coupled dynamics of magnetic vortexes in a three-layer thin conductive permalloe nanodisc. Čelâbinskij fiziko-matematičeskij žurnal, Tome 5 (2020) no. 2, pp. 161-173. http://geodesic.mathdoc.fr/item/CHFMJ_2020_5_2_a7/