Observation of the dynamic modes of a magnetic antivortex using Brillouin light scattering

The dynamic behavior of magnetic antivortices stabilized in patterned pound-key-like microstructures was studied using microfocus Brillouin light scattering (micro-BLS) at frequencies above the gyrotropic mode $\left(>1\mathrm{GHz}\right)$. Micro-BLS spectra obtained as a function of the frequency of a driving microwave field show an intricate spectrum for the antivortex state for an in-plane driving field. Spatial mode profiles for the strongest antivortex resonance frequencies, obtained for samples in the antivortex as well as the single domain states, show that while the symmetry of one of the observed resonances is relatively insensitive to the spin configuration, the antivortex exhibits a unique mode profile for the other. A comparison with micromagnetic simulations shows that the frequency and symmetry of the latter are consistent with one of the antivortex azimuthal modes. Furthermore, the simulations show that this mode involves coupling between the antivortex spin excitations and propagating spin waves in the structure legs, which may be useful for high-wave-number spin-wave generation.

Figure 1

MFM images of two 37-nm-thick Permalloy structures superimposed on a diagram of a waveguide to illustrate the experimental geometry. The upper left intersection in structure (a) is saturated parallel to the dynamic field $h \left(\mathrm{Sa}{\mathrm{t}}_{\parallel }\right)$ while the hourglass-like MFM contrast in the lower right intersection indicates that this intersection contains a single AV $\left(\mathrm{A}{\mathrm{V}}_1\right)$. Structure (b) has an AV in the upper left intersection $\left(\mathrm{A}{\mathrm{V}}_2\right)$ and is saturated perpendicular to $h$ in the lower right intersection $\left(\mathrm{Sa}{\mathrm{t}}_{\perp }\right)$. The white arrows indicate the direction of the magnetization.

Figure 2

BLS intensity as a function of $f_P$ measured within the intersection regions of the pound-key-like structures. Data are shown for intersections in the AV, $\mathrm{Sa}{\mathrm{t}}_{\parallel }$, and $\mathrm{Sa}{\mathrm{t}}_{\perp }$ states. The inset illustrates the position of the laser spot (shaded green spot), which is displaced from the center of the intersection towards one of the outer legs. The dashed lines at 3.4 and 5.9 GHz show the frequencies at which spatial scans were obtained (Fig. 3).

Figure 3

BLS intensity as a function of position for a 2D grid of $10\times 10$ points obtained over intersections in the (b), (c) AV, (e), (f) $\mathrm{Sa}{\mathrm{t}}_{\parallel }$, and (h), (i) $\mathrm{Sa}{\mathrm{t}}_{\perp }$ states, where $h$ is applied in-plane, along the diagonal, as illustrated in Fig. 2. The diagrams (a), (d), and (g) show the scan region (shaded in green), which is slightly larger than the intersection, and the white arrows illustrate the direction of the magnetization for each state. The dark and light gray shading on the diagrams and beside each of the BLS plots is used to identify the outer and inner legs of the structure, respectively, with respect to the scan region. BLS scans are shown for each state for $f_P=3.4\mathrm{GHz}$ in the middle column [(b), (e), and (h)] and $f_P=5.9\mathrm{GHz}$ in the right column [(c), (f), and (i)].

Figure 4

(a) Frequency spectra and (b)–(m) spatially resolved modes obtained from micromagnetic simulations for intersections that are in the AV (left) and $\mathrm{Sa}{\mathrm{t}}_{\parallel }$ (right) states in response to an in-plane magnetic field pulse applied along the structure diagonal. The frequency spectra shown in (a) represent the amplitude of the Fourier transform of the time-dependent out-of-plane component of the magnetization $M_z$ in each cell, averaged over a $200\times 200\mathrm{n}{\mathrm{m}}^2$ subregion within the intersection (locations marked by squares in the inset). In the inset, the dark and light shading indicates outer vs inner legs of the structure, respectively, and the white arrows illustrate the spin configurations. The mode maps (b)–(m) show the normalized spectral amplitude of $M_z$ for a $3\times 3\mu {\mathrm{m}}^2$ region centered on the intersection.