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Magnetic vortex dynamics in the non-circular potential of a thin elliptic ferromagnetic nanodisk with applied fields

Department of Physics, Kansas State University, Manhattan, KS 66506 USA

Topical Section: Nanomaterials, nanoscience and nanotechnology

## Abstract    Full Text(HTML)    Figure/Table    Related pages

Spontaneous vortex motion in thin ferromagnetic nanodisks of elliptical shape is dominated by a natural gyrotropic orbital part, whose resonance frequency $\omega_G=\overline{k}/G$ depends on a force constant and gyrovector charge, both of which change with the disk size and shape and applied in-plane or out-of-plane fields. The system is analyzed via a dynamic Thiele equation and also using numerical simulations of the Landau-Lifshitz-Gilbert (LLG) equations for thin systems, including temperature via stochastic fields in a Langevin equation for the spin dynamics. A vortex is found to move in an elliptical potential with two principal axis force constants $k_x$ and $k_y$, whose ratio determines the eccentricity of the vortex motion, and whose geometric mean $\overline{k}=\sqrt{k_x k_y}$ determines the frequency. The force constants can be estimated from the energy of quasi-static vortex configurations or from an analysis of the gyrotropic orbits. $k_x$ and $k_y$ get modified either by an applied field perpendicular to the plane or by an in-plane applied field that changes the vortex equilibrium location. Notably, an out-of-plane field also changes the vortex gyrovector $G$, which directly influences $\omega_G$. The vortex position and velocity distributions in thermal equilibrium are found to be Boltzmann distributions in appropriate coordinates, characterized by the force constants.
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# References

1. Schneider M, Hoffmann H, Zweck J (2000) Lorentz microscopy of circular ferromagnetic permalloy nondisks. Appl Phys Lett 77: 2909.

2. Wysin GM, Figueiredo W (2012) Thermal vortex dynamics in thin circular ferromagnetic nanodisks. Phys Rev B 86: 104421.

3. Guslienko KY, Han XF, Keavney DJ, et al. (2006) Magnetic vortex core dynamics in cylindrical ferromagnetic dots. Phys Rev Lett 96: 067205.

4. Buchanan KS, Roy PE, Fradkin FY, et al. (2006) Vortex dynamics in patterned ferromagnetic ellipses. J Appl Phys 99: 08C707.

5. Wysin GM (2015) Vortex dynamics in thin elliptic ferromagnetic nanodisks. Low Temp Phys (Fiz Nizk Temp) 41: 788-800 (41: 1009?023).

6. Kireev VE, Ivanov BA (2003) Inhomogeneous states in a small magnetic disk with single-ion surface anisotropy. Phys Rev B 68: 104428.

7. Buchanan KS, Roy PE, Grimsditch M, et al. (2006) Magnetic-field tunability of the vortex translational mode in micron-sized permalloy ellipses: Experiment and micromagnetic modeling. Phys Rev B 74: 064404.

8. de Loubens G, Riegler A, Pigeau B, et al. (2009) Bistability of vortex core dynamics in a single perpendicularly magnetized nanodisk. Phys Rev Lett 102: 177602.

9. Fried JP, Fangohr H, Kostylev M, et al. (2016) Exchange-mediated, nonlinear, out-of-plane magnetic field dependence of the ferromagnetic vortex gyrotropic mode frequency driven by core deformation. Phys Rev B 94: 224407.

10. Thiele AA (1974) Applications of the gyrocoupling vector and dissipation dyadic in the dynamics of magnetic domains. J Appl Phys 45: 377.

11. García-Palacios JL, Lázaro FJ (1998) Langevin-dynamics study of the dynamical properties of small magnetic particles. Phys Rev B 58: 14937.

12. Wysin GM (2010) Vortex-in-nanodot potentials in thin circular magnetic dots. J Phys-Condens Mat 22: 376002.

13. Machado TS, Rappoport TG, Sampaio LC (2012) Vortex core magnetization dynamics induced by thermal excitation. Appl Phys Lett 100: 112404.