Bistability of Vortex Core Dynamics in a Single Perpendicularly Magnetized Nanodisk

Microwave spectroscopy of individual vortex-state magnetic nanodisks in a perpendicular bias magnetic field $H$ is performed using a magnetic resonance force microscope. It reveals the splitting induced by $H$ on the gyrotropic frequency of the vortex core rotation related to the existence of the two stable polarities of the core. This splitting enables spectroscopic detection of the core polarity. The bistability extends up to a large negative (antiparallel to the core) value of the bias magnetic field $H_r$, at which the core polarity is reversed. The difference between the frequencies of the two stable rotational modes corresponding to each core polarity is proportional to $H$ and to the ratio of the disk thickness to its radius. Simple analytic theory in combination with micromagnetic simulations give a quantitative description of the observed bistable dynamics.

Figure 1

(a) The cantilever frequency, proportional to $M_z$, the vertical component of the static magnetization of the $R_1=130\mathrm{nm}$ NiMnSb nanodisk, as a function of the perpendicular bias magnetic field $H$. Inset: Detection scheme: The vortex gyrotropic mode is sensed through the dipolar force induced on the spherical Fe probe. (b) Nanodisk excitation spectrum in the saturated regime ($|H|>H_s$) recorded at 7.5 GHz. (c) Excitation spectra in the vortex (unsaturated) state ($|H|<H_s$).

Figure 2

Frequency of the lowest excitation mode in a magnetic disk as a function of the perpendicular bias magnetic field for two sizes: (a) $R_1=130\mathrm{nm}$ and (b) $R_2=520\mathrm{nm}$. Dark blue (light red) dots are experimental points corresponding to the field variation starting from large positive (negative) values. Solid lines are theoretical predictions from Eq. (1) for $|H|>H_s$ and from Eq. (2) for $|H|<H_s$.

Figure 3

(a) Numerically calculated field dependence of the static magnetization of the NiMnSb disk (thickness $t=43.75\mathrm{nm}$, radius $R=100\mathrm{nm}$): the hysteretic behavior of the static magnetization $M_z$ averaged over the disk volume (dashed loop) and over the vortex core (solid loop). The insets show the spatial distribution of $M_z$ at four progressively decreasing values of $H$. (b) Resonance locus calculated by the 3D micromagnetic code (dots) along with the analytical model (solid lines).