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(Color) (a) Hysteresis loop of a Permalloy disk without defects (diameter: , thickness: , temperature: ) measured with micro-Hall magnetometry. The upper left inset shows a sketch of the disk in the vortex state with clockwise orientation of the magnetization. The dashed line illustrates the path of the vortex core perpendicular to the direction of , and the blue and red points mark the vortex core position at zero- and nonzero-magnetic field, respectively. The lower inset sketches the experimental setup. (b) Stray field hysteresis of a Permalloy disk (diameter: , thickness: , temperature: ) containing two antidots with distance . A similar particle is depicted in the scanning electron micrograph in the inset, also showing the direction of . The black lines are magnetization reversal loops covering the whole field range between the saturation fields at positive and negative . In contrast, the red curves are minor loops obtained by reversing the sweep direction before the sample is saturated.
(Color) The red hysteresis loop (left axis) is the same minor loop as shown in Fig. 1(b) measured at , the blue one (also left axis) was recorded from the same sample at . The switching fields drop from at to at . The calculated black line (diameter: , thickness: , right axis) closely matches the low-temperature data. The insets illustrate calculated remanent magnetization patterns of the metastable pinned vortex states for the vortex pinned to the left (upper inset) and to the right defect (lower inset).
(Color) Minor loops of Permalloy disks (diameter: , thickness: , temperature: ) containing three and four artificial pinning centers. is applied in the plane of the disks as indicated by arrows. (a) The three branches of the minor loop reflect pinning of the vortex core at different pinning sites. The blue hysteresis branch corresponds to pinning at the blue pinning site, etc. Double arrows represent reversible sections of the stray field curves, while single arrows show the direction of irreversible jumps. The antidots were separated by . (b) Four stable magnetic states can be found in a disk with four antidots separated by . Switching from plateau (i) to (ii) is accomplished by applying an external magnetic field between and . For clearness, the arrows were omitted.
Switching field as a function of the center to center distance . The points connected by lines are calculated ones (disk diameter: , thickness , defect diameter: ). The experimental data points (stars) agree well with the calculated switching fields.
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