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Direct imaging of phase relation in a pair of coupled vortex oscillators
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http://aip.metastore.ingenta.com/content/aip/journal/adva/2/4/10.1063/1.4771683
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Figures

Image of FIG. 1.

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FIG. 1.

Micromagnetic simulation of the stray field during the vortex gyration outside a square. (a) The amplitude of the stray field along the center line in positive x direction at a distance 2d/l from the center of the structure is shown for three core positions (solid, dashed, and dotted lines). The corresponding core deflections in negative x, positive x, and positive y direction are illustrated in the insets via the magnetization pattern using the same color code as in (b) where arrows outside the square indicate the direction of the stray field and arrows inside the square mark the magnetization direction in the domains for a core deflection in negative x direction. The x and y components of the stray field during one cycle for a distance 2d/l = 2.2 are plotted against each other in (c). For comparison, the gray dashed line indicates the shape of a rotational field with constant amplitude. Black dots mark the stray fields corresponding to vortex core deflections along the x and y axis.

Image of FIG. 2.

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FIG. 2.

(a) Scanning-electron micrograph of a pair of permalloy squares. Striplines are deposited on top of both squares I and II. (b) X-ray images of the center part (400 nm× 400 nm) of a square at different time steps during one period of gyration. (c) Vortex-core trajectory in square I during harmonic excitation with 160 MHz. The black and the gray symbols mark the deflection in x and y direction determined from the x-ray images, respectively.

Image of FIG. 3.

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FIG. 3.

Vector diagrams indicating the phase relation between the vortex cores in a harmonically excited pair of permalloy squares for different frequencies of the excitation signal. Only the core in the first element (I) is directly excited via an alternating rf field of a strip line. The time-dependent trajectories (red symbols for element I and blue symbols for element II) are determined via scanning-transmission x-ray microscopy (STXM). The two elements have same chiralities (see STXM image in the top row) and opposite core polarizations. A red vector points to the reference position of the core in element I and a blue vector points to the position of the core in element II at the same time step.

Image of FIG. 4.

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FIG. 4.

Vector diagrams corresponding to Fig. 3 but for elements that have opposite chiralities (see STXM image in the top row). No trajectories are shown for f = 200 MHz since the time resolution of the setup is highly limited at this frequency.

Image of FIG. 5.

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FIG. 5.

Schematic illustration of the relative orientations of the effective magnetic moments during coupled vortex gyrations in a pair of ferromagnetic squares with opposite core polarizations at the low-frequency and at the high-frequency mode for the case of (a) same chiralities and (b) opposite chiralities. Black arrows mark the magnetization directions in the corresponding domains of the Landau pattern. Red and blue arrows show the effective magnetic moment of element I and element II, respectively. The dashed green arrows indicate the sense of gyration in the particular element. For each mode, the relative configurations at four different time steps during one period of gyration are shown.

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/content/aip/journal/adva/2/4/10.1063/1.4771683
2012-12-05
2014-04-20

Abstract

We study the magnetization dynamics in a stray-field coupled pair of ferromagnetic squares in the vortex state. Micromagnetic simulations give an idea of the mediating stray field during vortex gyration. The frequency-dependent phase relation between the vortices in the spatially separated squares is studied using time-resolved scanning transmission x-ray microscopy while one element is harmonically excited via an alternating magnetic field. It is shown that the normal modes of coupled vortex-core motion can be understood as an attractive (low-frequency) and a repulsive (high-frequency) mode of the effective magnetic moments of the microstructures.

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Scitation: Direct imaging of phase relation in a pair of coupled vortex oscillators
http://aip.metastore.ingenta.com/content/aip/journal/adva/2/4/10.1063/1.4771683
10.1063/1.4771683
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