Probing the Anharmonicity of the Potential Well for a Magnetic Vortex Core in a Nanodot

The anharmonicity of the potential well confining a magnetic vortex core in a nanodot is measured dynamically with a magnetic resonance force microscope (MRFM). The stray field of the MRFM tip is used to displace the equilibrium core position away from the nanodot center. The anharmonicity is then inferred from the relative frequency shift induced on the eigenfrequency of the vortex core translational mode. An analytical framework is proposed to extract the anharmonic coefficient from this variational approach. Traces of these shifts are recorded while scanning the tip above an isolated nanodot, patterned out of a single crystal FeV film. We observe a $+10\%$ increase of the eigenfrequency when the equilibrium position of the vortex core is displaced to about one-third of its radius. This calibrates the tunability of the gyrotropic mode by external magnetic fields.

Figure 1

(a) Side and (b) top views of the experimental setup: The stray field of a MRFM tip is used to displace the static position ${\mathit{X}}_0$ of the vortex core. The magnetic vortex state is shown in a bivariate color map of $\mathit{m}=\mathit{M}/M_s$ ($\mathrm{\text{amplitude phase}}\leftrightarrow \mathrm{\text{luminance hue}}$). The insets are microscopy images of the magnetic tip and disk sample.

Figure 2

Density plot showing the experimentally measured variation of the eigenfrequency of the gyrotropic mode upon a lateral displacement, ${\delta }_x$, of the MRFM tip at fixed ${\delta }_y=0$ and nominal ${\delta }_z=3.0$. A red-blue color map shows the sign of the force acting on the cantilever. The arrows indicate where the change of polarity occurs.

Figure 3

(a) Trajectory of the vortex core ${\mathit{X}}_0=(X_0,Y_0)$ during an implicit lateral scan of the tip ${\delta }_x\in [-8,+8]$ at three different heights ${\delta }_z$. (b) Norm of the displacement vector, $|{\mathit{X}}_0|$, as a function of the tip position ${\delta }_x$.

Figure 4

(a) Plot of the relative variation of eigenfrequency of the gyrotropic mode as a function of $|{\mathit{X}}_0|$. A fit by a parabola yields $\lambda =0.5\pm 0.15$. The crosses are the results of micromagnetic simulation. (b) Relative variation of the eigenfrequency as a function of ${\delta }_x$. The lines show the analytically predicted behavior for a vanishing (0) and finite (0.5) anharmonic coefficient.