Abstract
We found resonantly excited precession motions of a three-dimensional vortex core in soft magnetic nanospheres and controllable precession frequency with the sphere diameter 2R, as studied by micromagnetic numerical and analytical calculations. The precession angular frequency for an applied static field HDC is given as ωMV = γeffHDC, where γeff = γ〈mΓ〉 is the effective gyromagnetic ratio in collective vortex dynamics, with the gyromagnetic ratio γ and the average magnetization component 〈mΓ〉 of the ground-state vortex in the core direction. Fitting to the micromagnetic simulation data for 〈mΓ〉 yields a simple explicit form of 〈mΓ〉 ≈ (73.6 ± 3.4)(lex/2R)2.20±0.14, where lex is the exchange length of a given material. This dynamic behavior might serve as a foundation for potential bio-applications of size-specific resonant excitation of magnetic vortex-state nanoparticles, for example, magnetic particle resonance imaging.
Highlights
For the vortex-state spheres (40 nm ≤ 2R ≤ 1 20 nm), the precession frequency of a vortex core showed a strong variation with 2R, as can be expressed by fMV =HDC, where γeff(< γ) is the effective gyromagnetic ratio, which is variable with the sphere diameter
In order to gain physical insight into the fMV = (γ/2π)〈 mΓ〉 HDC relation obtained from the micromagnetic simulations, we analytically derived vortex-core precession dynamics in nanospheres
By micromagnetic numerical calculations, the resonantly excited precession motion of a vortex core in nanospheres and its size-dependent precession frequency, and its physical origin, based on the size effect on the effective gyromagnetic ratio in collective spin dynamics analytically derived
Summary
For the vortex-state spheres (40 nm ≤ 2R ≤ 1 20 nm), the precession frequency of a vortex core showed a strong variation with 2R, as can be expressed by fMV = (γeff/2π)HDC, where γeff(< γ) is the effective gyromagnetic ratio, which is variable with the sphere diameter. In order to quantitatively elucidate the γeff-versus-2R relation, we plotted the value of f/HDC as a function of 2R, as compared with the average magnetization component over the sphere volume in the vortex-core orientation,〈 mΓ〉 , both of which were obtained from the micromagnetic simulations.
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