PMC

(a) Vortex core velocity just before switching. The gyrofield of the moving vortex is proportional to this velocity. Because of the important contribution of the spin wave background, this quantity is not a constant at GHz excitation and shows strong differences between CW and CCW excitation. (b) Excitation time until switching occurs in a logarithmic colour scale. At sufficiently high amplitudes, switching takes on the order of one period of the excitation frequency, resulting in a widening of the resonances and a dominance of the mode (n=1, m=+1).

This sketch shows the origin of the out-of-plane magnetization near the vortex core and illustrates the origin of the observed asymmetry in the 'dip' formation for CW versus CCW spin-wave excitation. To the left, the basic shape of the vortex core and the bipolar amplitude of the spin wave are shown. The magnetization change as a result of the gyrofield of the moving vortex core differs for CW and CCW rotation senses (middle sketches). The resulting structures (right sketches) agree qualitatively with results from the micromagnetic simulations as shown in , and .

Switching only occurs if the senses of rotation (CW or CCW) of both the external field and the eigenmode (green arrows) are the same. At the left hand side, the sub-GHz frequency gyromode is illustrated. The right hand side shows the azimuthal spin wave modes at much higher (GHz) frequencies, characterized by the radial mode number n and the azimuthal mode number (m=±1), denoting the sense of rotation of the eigenmode. In vortex structures, the symmetry is broken by the out-of-plane component of the core, and thus, a frequency splitting is observed between (m=−1) and (m=+1) modes.

The frames show the time evolution of the out-of-plane magnetization for a vortex up during the application of in-plane rotating magnetic fields. Only the inner part of the sample is shown. The size of the black bar corresponds to a length of 200 nm. The left frame corresponds to the relaxed ground state (phase angle 0°). The two rows oppose counter rotating modes at a frequency of 5.0 GHz for the (m=−1) mode and 6.2 GHz for the (m=+1) mode at the same azimuthal angle of the external field. The blue arrows in the middle indicate this angle for the corresponding frame.

The out-of-plane magnetization of the central part extracted from the 1.6-μm disc before the core reversal. (a) A section of 300 nm in diameter showing the excited azimuthal spin wave modes as well as the 'dip'. The dynamics of modes with the same rotation sense are similar in the number of 'dips' and in their phase relation to the vortex core. This is indicated by the arrows below the snapshots. The difference between oppositely rotating modes are the result of the symmetry breaking due to the gyrofield. (b) For comparison the central part of the same structure with 500 nm in diameter is given, excited at the gyrotropic resonance. This results in a much larger trajectory of the core and the 'dip'. The black bars correspond to a lateral size of 100 nm in both cases (a, b).

The legend (c) shows microscopy images of X-ray transmission through the inner part (150 nm×150 nm) of the sample indicating the vortex core polarity (white: vortex up; black: vortex down) before and after a field burst. The phase diagrams show the points (excitation amplitude versus frequency) where vortex core reversal from up to down was observed in the experiments (a) and the simulations (b). Rotating in-plane magnetic field bursts with an amplitude B₀, a frequency f and a duration of 24 periods have been applied. As indicated in the legend of the top panel with the recorded X-ray images (c), the blue triangles with a dot in the middle indicate vortex core switching only after a CW rotating field burst, whereas red triangles indicate switching only after a CCW field burst. Black dots indicate no switching for either rotation sense. The minima in the switching threshold with differing sense of rotation correspond to the resonance frequencies of the excited azimuthal spin wave modes with the same sense of rotation as sketched in the middle of the figure. The modes are identified with the help of the phases derived from a local fast Fourier transform of the simulated out-of-plane magnetization of the sample with 1.62 μm in diameter as shown in the inset to the right of the bottom panel (d).