Fourier Transform Imaging of Spin Vortex Eigenmodes

Thin-circular lithographically defined magnetic elements with a spin vortex configuration are excited with a short perpendicular magnetic field pulse. We report the first images of excited magnetic eigenmodes up to third order, obtained by means of a phase sensitive Fourier transform imaging technique. Both axially symmetric and symmetry breaking azimuthal eigenmodes are observed. We observe strong oscillations of the magnetization in the central part of the magnetic elements. The experimental data are in good agreement with micromagnetic simulations.

Figure 1

Temporal evolution of the precessional motion. $M_z(t)-M_z(t=0)$is imaged as a function of the time elapsed after the magnetic field pulse. Notice that some images show a central spot which is clearly distinguishable from the surroundings. This feature will be discussed in connection with Fig. 5.

Figure 2

Fourier transform of the axially symmetric eigenmodes. FT of Fig. 1 at each location results in a Fourier spectrum with five resonances (width: $\approx 1\mathrm{G}\mathrm{H}\mathrm{z}$). In (a)–(c): Fourier amplitude (left) and Fourier phase (right) at resonance for modes with radial symmetry. Their frequencies are $2.8\mathrm{G}\mathrm{H}\mathrm{z}$ (a), $3.9\mathrm{G}\mathrm{H}\mathrm{z}$ (b) and $4.5\mathrm{G}\mathrm{H}\mathrm{z}$ (c). (a) has the largest spectral weight, i.e., it is dominating the motion and is responsible for the overall periodicity apparent from Fig. 1. The left hand side of the images reports the results of our micromagnetic simulation; the right hand side are the experimental data. Because of our finite spatial resolution the experimental images extend over the border of the disk.

Figure 3

Nonaxially symmetric modes. (a) on the left the amplitude and on the right the phase of the mode with $1.5\mathrm{G}\mathrm{H}\mathrm{z}$ is displayed. (b) Back transforming the images in (a) produces a temporal sequence similar to the one in Fig. 1, but containing only the mode under investigation. Three images of this sequence also available as animated online movie [12], are given in (b). Time interval between middle (right) and left image:150 (360) ps. This mode consists of four regions, oscillating in pairs in phase. (c): On the left the amplitude and on the right the phase of a mode with $1.9\mathrm{G}\mathrm{H}\mathrm{z}$. This mode has only one in-plane node dividing a region of roughly equal Fourier amplitude but roughly opposite phase. (d) Back transformation of the images in (c) produces the temporal evolution of this mode, illustrated by three images (time interval between the middle (right) image and the left image: 120 (270) ps and available as an animated movie online [12]. This mode consists of two regions divided by a node and oscillating with opposite phase.

Figure 4

Circularly polarized mode. (a) The single-node nonaxially symmetric mode in a $4\mu \mathrm{m}$ disk, occurring at $2.5\mathrm{G}\mathrm{H}\mathrm{z}$. The node is more pronounced on one side, where the $\pi$-phase jump is also clearly visible. (b) The back transformed temporal sequence (see also online animated movie [12]) is given in (b). The time interval between the middle (right) and left images is 80 (160) ps. (c) The single-node nonaxially symmetric mode in a $3\mu \mathrm{m}$ disk occurs at $2.8\mathrm{G}\mathrm{H}\mathrm{z}$. The node is weak and the phase (right) changes gradually along a trajectory surrounding the core center. Correspondingly, the temporal sequence obtained by back transformation — given in (d) after a time interval of 125 and 250 ps and also available online as an animated movie [12] — consists of a bright-dark doublet rotating around the disk center.

Figure 5

The core region. Top: plot of the coordinates of the central part with respect to the geometrical image center ($X=0,Y=0$), in units of $\mu \mathrm{m}$. Bottom: the continuous line indicates the average signal over the disk, and provides us with a check of the zero line (dotted), obtained from the nonmagnetic surroundings. The triangles give the strength of the magnetization surrounding the core, as derived from line scans of the images of the type indicated. The circles give the strength of the magnetization in the core region, which is seen to become negative and positive. The signal also deviates systematically from the zero line expected for axially symmetric dipolar modes. The data from the line scans shown are marked with arrows.