Spin excitation spectrum in a magnetic nanodot with continuous transitions between the vortex, Bloch-type skyrmion, and Néel-type skyrmion states

Abstract

We study spin-wave excitations in a circular ferromagnetic nanodot in different inhomogeneous, topologically non-trivial magnetization states, specifically, vortex and skyrmion states. Gradual change in the strength of the out-of-plane magnetic anisotropy and the Dzyaloshinskii-Moriya exchange interaction leads to continuous phase transitions between different stable magnetic configurations and allows for mapping of dynamic spin modes in and between the vortex, Bloch-type skyrmion and Néel-type skyrmion states. Our study elucidates the connections between gyrotropic modes, azimuthal spin waves and breathing modes in various stable magnetization states and helps to understand the rich spin excitation spectrum on the skyrmion background.

Eigenmodes of Néel skyrmions in ultrathin magnetic films

“…The simulations corroborate the recentlyformulated classification of the three fundamental Néel skyrmion eigenmodes, 35 and also confirm the experimental energy hierarchy of these modes in GaV 4 S 8 . 36 Of particular interest is the observation that the three modes exhibit drastically different magnetic-field dependences across the skyrmionlattice to isolated-skyrmion phase transition.…”

“…Mruczkiewicz et al recently formulated a classification of the fundamental breathing, CCW and CW eigenexcitations based on their azimuthal and radial mode indices (m = 0, n = 0), (m = +1, n = 0) and (m = 1, n = 1), respectively. 35 Noteworthily, the numbers of radial nodes n, and the rotation senses of the simulated modes, namely m = 0 (breathing; absence of rotation), +1 (CCW) and 1 (CW), are consistent with the classification. Figure 3 shows that the dynamic magnetization and phase profiles of the CW mode exhibit a node along the radial direction of the skyrmion, while the profiles of the other two excitations are devoid of such nodes.…”

Collective magnetic skyrmion gyrotropic modes in a dot chain

“…Three low frequency (GHz range) excitation modes (clockwise, counterclockwise rotating modes, and breathing mode) were found in the collective spectra of the skyrmion lattices [10][11][12][13], and several gyrotropic and SW modes were found in the spectra of individual skyrmions in magnetic nanodots [14][15][16][17][18]. The physical origin of these modes is still actively discussed [14,16]. Currently the most of researchers converge in opinion that the number of gyrotropic and high frequency SW modes depends on the skyrmion dimensions and physical mechanisms favoring the skyrmion state.…”

“…Currently the most of researchers converge in opinion that the number of gyrotropic and high frequency SW modes depends on the skyrmion dimensions and physical mechanisms favoring the skyrmion state. Namely, one gyrotropic mode is realized in the skyrmions stabilized by DMI in utrathin dots [14,[16][17][18]. It was shown that in FeGe circular dots [14] the high intensity mode with lowest frequency is the gyrotropic mode.…”

Динамика Магнитных Скирмионов В Наноточках

“…Различия частот CW и CCW мод были определены на основе численных расчетов в 2012 г. [11], однако интерпретация спектров магнитных скирмионов, наблюдаемых эксперименталь-но [12][13][14][15], а также рассчитанных методами микромаг-нитной симуляции [17][18][19][20][21], до сих пор является предме-том активных научных дискуссий. Авторы работы [14] связывают асимметрию мод с гиротропными осцилляци-ями скирмиона, в экспериментах [15,16] обнаружены две низкочастотные моды, исследования [12,13,[17][18][19][20][21] ука-зывают на наличие одной гиротропной моды в спектре возбуждений магнитных скирмионов.…”