Magnetic vortex chirality determination via local hysteresis loops measurements with magnetic force microscopy

Abstract

Magnetic vortex chirality in patterned square dots has been investigated by means of a field-dependent magnetic force microscopy technique that allows to measure local hysteresis loops. The chirality affects the two loop branches independently, giving rise to curves that have different shapes and symmetries as a function of the details of the magnetisation reversal process in the square dot, that is studied both experimentally and through micromagnetic simulations. The tip-sample interaction is taken into account numerically, and exploited experimentally, to influence the side of the square where nucleation of the vortex preferably occurs, therefore providing a way to both measure and drive chirality with the present technique.

Figure 1. MFM images of two different squares at their positive ( + M_r) and negative (−M_r) remanent states.

In square “a” the chirality is inverted between the two remanent states, in square “b” it is preserved.

Figure 2. Local hysteresis loops: experimental (top row) and simulated (bottom row) results.

(a,c) MFM images constituted by the same profile acquired multiple times as a function of the applied magnetic field. (b,d) corresponding local hysteresis loops.

Figure 3. Simulated MFM images and local hysteresis loops of a square dot.

Dashed green lines represent the line scanned by the MFM tip. Top row: symmetric loops corresponding to inverted chirality (the vortex nucleates on the same side in both loop branches). Bottom row: asymmetric loops corresponding to preserved chirality (the vortex nucleates on opposite sides in the two loop branches). Red lines: first (descending) loop branch. Blue lines: second (ascending) loop branch.

Figure 4. Simulated (top row) and experimental (bottom row) local hysteresis loops.

Red lines: first (descending) loop branch. Blue lines: second (ascending) loop branch. The vertical axes report MFM “phase contrast” in arbitrary units, as the phase scale of the microscope does not require to be calibrated.

Figure 5. Simulated x and y components of the magnetisation of a square along two horizontal profiles, at 50 nm (lines, where the MFM tip performs the scan) and 750 nm (symbols) from the bottom edge.

The magnetic field generated by the tip is either neglected (blue colour) or taken into account (red colour) in the simulations. The green shaded area shows the region that is affected by the tip-sample interaction when the tip is close to the left margin of the square (beginning of the line scan and end of the respective retrace).

Figure 6. Probability of obtaining type I, II, III and IV local hysteresis loops as a function of the asymmetry between the two wells corresponding to the two different chirality states.

The experimentally observed probabilities lie in the shaded area.