Full text loading...

^{1}and Sang-Koog Kim

^{1,a)}

### Abstract

The authors investigated the gyrotropic linear and nonlinear motions of a magnetic vortex in soft magnetic cylindrical nanodots under in-plane oscillating magnetic fields of different frequencies and amplitudes, by employing both micromagnetic simulations and the numerical solutions of Thiele’s equation of motion [Phys. Rev. Lett.30, 230 (1973)]. Not only noncircular elliptical vortex-core orbital trajectories in the linear regime but also complex trajectories including stadiumlike shape in the nonlinear regime were observed from the micromagnetic simulations and were in excellent agreement with the numerical solutions of the analytical equations of motion. It was verified that the numerical solutions of Thiele’s equation are promisingly applicable in order to predict and describe well such complex vortex gyrotropic linear and nonlinear motions in both the initial transient and later steady states. These results enrich the fundamental understanding of the linear and nonlinear motions of vortices in confined magnetic elements in response to oscillating driving forces.

The authors thank K. Y. Guslienko for fruitful discussions. This work was supported by Creative Research Initiatives (ReC-SDSW) of MOST/KOSEF.

### Key Topics

- Rotating flows
- 13.0
- Equations of motion
- 9.0
- Magnetic fields
- 8.0
- Micromagnetic simulations
- 7.0
- Numerical solutions
- 7.0

## Figures

(Color online) (a) Geometry and coordinates of the model Py nanodot along with the corresponding configurations at the indicated times. The top- and bottom-perspective snapshot images display the initial equilibrium and the dynamic MV states with the downward core orientation and counterclockwise in-plane rotation. The color and height of the surface indicate the in-plane and out-of-plane components, respectively. The spiral like black line on the right denotes the orbital trajectory of VC motion during the time period of with and . (b) Orbital trajectories of VC motions for the indicated and values. (c) The aspect ratio of the elliptical orbits vs for the case of . The red line indicates the case of ,^{21} where and are the lengths of the ellipse along the (perpendicular to the direction) and (along the direction) axes, respectively.

(Color online) (a) Geometry and coordinates of the model Py nanodot along with the corresponding configurations at the indicated times. The top- and bottom-perspective snapshot images display the initial equilibrium and the dynamic MV states with the downward core orientation and counterclockwise in-plane rotation. The color and height of the surface indicate the in-plane and out-of-plane components, respectively. The spiral like black line on the right denotes the orbital trajectory of VC motion during the time period of with and . (b) Orbital trajectories of VC motions for the indicated and values. (c) The aspect ratio of the elliptical orbits vs for the case of . The red line indicates the case of ,^{21} where and are the lengths of the ellipse along the (perpendicular to the direction) and (along the direction) axes, respectively.

(Color online) VC trajectories and their FFT powers under in-plane oscillating fields with various 's and 's, as noted. For comparison, the micromagnetic simulation results and the numerical solutions of the linearized equation of motion are shown in (a) and (b), respectively. The VC trajectories shown in the whole area of the dot were drawn during the time interval of , but in the upper left during , and in the lower right during 90–100, 94–100, and in order from the first to third column, respectively. The magnitudes of the FFT powers were normalized by the maximum value of each case.

(Color online) VC trajectories and their FFT powers under in-plane oscillating fields with various 's and 's, as noted. For comparison, the micromagnetic simulation results and the numerical solutions of the linearized equation of motion are shown in (a) and (b), respectively. The VC trajectories shown in the whole area of the dot were drawn during the time interval of , but in the upper left during , and in the lower right during 90–100, 94–100, and in order from the first to third column, respectively. The magnitudes of the FFT powers were normalized by the maximum value of each case.

(Color online) (a) Simulation results of the VC trajectories of the gyrotropic motion in different time periods as noted, and (b) the FFT power spectrum for the case of and . (c) Identification of the individual peaks (marked by colored regions) in the FFT power spectrum in (b). Each VC trajectory shown in the first row was obtained from the inverse FFTs of the frequency powers in each range of , , , and , as displayed by the color-coded regions in the frequency spectrum. The second row denotes the superposition of the filtered VC trajectories corresponding to the individual frequency regions.

(Color online) (a) Simulation results of the VC trajectories of the gyrotropic motion in different time periods as noted, and (b) the FFT power spectrum for the case of and . (c) Identification of the individual peaks (marked by colored regions) in the FFT power spectrum in (b). Each VC trajectory shown in the first row was obtained from the inverse FFTs of the frequency powers in each range of , , , and , as displayed by the color-coded regions in the frequency spectrum. The second row denotes the superposition of the filtered VC trajectories corresponding to the individual frequency regions.

(Color online) VC trajectories in different time periods as indicated, all of which were obtained from the numerical solutions of for the different values of , as noted above each case (column), for the same oscillating field parameters as in Fig. 3, i.e, and . The bottom row shows the FFT spectra corresponding to the VC motion in the time interval of . The FFT power spectra were normalized by the maximum value in each case.

(Color online) VC trajectories in different time periods as indicated, all of which were obtained from the numerical solutions of for the different values of , as noted above each case (column), for the same oscillating field parameters as in Fig. 3, i.e, and . The bottom row shows the FFT spectra corresponding to the VC motion in the time interval of . The FFT power spectra were normalized by the maximum value in each case.

Article metrics loading...

Commenting has been disabled for this content