Resonantly excited precession motion of three-dimensional vortex core in magnetic nanospheres

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.

Resonant vortex-core reversal in magnetic nano-spheres as robust mechanism of efficient energy absorption and emission

“…As reported in ref. 13 , the value of 〈 m Λ 〉 varies markedly with 2 R in vortex-state spheres (〈 m Λ 〉 = 1 for single-domain spheres). In the present results, it was quite noticeable that the core reversal’s frequency is a function of both 〈 m Λ 〉 and H AC .…”

“…In the numerical calculation, we used 〈 m Λ 〉 = 73.6( l ex /2 R ) 2.20 with l ex the exchange length ( l ex ~ 5.3 nm for Py), as reported in ref. 13 . For the given material Py, f rev is therefore a function of both H AC and 2 R for the vortex-state spheres, but only of H AC for the single-domain spheres (i.e., 〈 m Λ 〉 = 1), independently of the particle size, as shown in the inset of Fig.…”

“…Although the vortex-core precession in nano-spheres and its frequency dependence on particle size and the strength of the DC field have already been reported (see ref. 13 ), the vortex-core reversal and its underlying physics have as yet remained (until the present work) unexplored. The simulation and analytical numerical calculations in the present work revealed that the core-reversal frequency changes significantly with the AC field strength for a given particle diameter.…”

“…As shown in ref. 13 , the vortex core in nano-spheres is found to exhibit a unique precession motion around the direction of an externally applied static field, and, further, the precession frequency is determined by the sphere size as well as the static field strength. The core precession thus can be excited with low-power consumption when the frequency of an externally applied AC magnetic field is tuned to the eigenfrequency of the core-precession mode, though the mechanism is completely different from that of vortex-core gyration in planar thin-film dots.…”

“…Such novel dynamics as the mechanism 3 4 5 , criterion 6 7 8 9 10 11 , and physical origin 4 8 11 of the core reversals are well established in case of planar thin-film disks. As for soft-magnetic nano-spheres, our previous papers 12 13 reported that they bear specific spiral magnetizations around a uniformly magnetized core region, the so-called vortex core, in cases where the particle diameter is larger than single-domain size but smaller than multiple-domain size. In our earlier work 12 , we demonstrated successful fabrication of spherical Permalloy (Py) nanoparticles and conformed vortex-state magnetization configurations using the electron holography measurement technique.…”