Development of vortex state in circular magnetic nanodots: Theory and experiment

We compare magnetic reversal of nanostructured circular magnetic dots of different sizes. This comparison is based on superconducting quantum interference device (SQUID) magnetometry, neutron scattering, Monte Carlo simulation, and analytical calculations and is quantified using a parameter which characterizes the variation in the hysteresis curve width. Below a critical dot diameter, the magnetic reversal occurs by coherent rotation and above that diameter, the reversal occurs by formation of a magnetic vortex. The vortex-core diameter is controlled by competing magnetic energy contributions. For 20-nm-thick Fe dots, the values of the critical diameter (58–60 nm) and the vortex core (16–19 nm) are in very good agreement between the different experimental and theoretical methods: neutron scattering, SQUID magnetometry, Monte Carlo simulations, and analytical calculations.

Figure 1

(Color online) Hysteresis loops for 43- (squares) and 65- (circles) nm-diameter, 20-nm-thick Fe dots at 10 K, and virgin curve (empty circles) for the 65 nm dots: (a) experimental data (after Ref. 14); (b) Monte Carlo simulations for the same conditions.

Figure 2

(Color online) Ratio of the loop width at coercivity to the width at half saturation as a function of the dot diameter for 600 Monte Carlo steps (after Ref. 14).

Figure 3

(Color online) (a) Scanning electron microscope image of the sample fabricated for neutron-scattering experiment. (b) Distribution of the dot diameters. Average diameter $65\pm 8\text{nm}$.

Figure 4

(Color online) Ratio of the loop width at coercivity to the width at half saturation for a 65 nm diameter dot as a function of number of MCS.

Figure 5

Magnetic configurations during the switching process for different dot diameters: (a) $D=55\text{nm}$, (b) $D=65\text{nm}$, and (c) $D=67\text{nm}$.

Figure 6

(Color online) Energies during the field reversal for a 60 nm (dashed red line) and a 65 nm dot (continuous blue line): (a) total magnetic energy during the reversal, (b) internal energy. Letters identify different regimes as explained in the text. Internal energy has been shifted to zero value and expressed in arbitrary units.

Figure 7

(Color online) Out-of-plane magnetization (corresponding to the vortex core) in units of $M_s$ by using two different theoretical methods: (a) Monte Carlo simulation and (b) analytical calculation using Eq. (5) with $L=20\text{nm}$ and $l_{ex}=3.7\text{nm}$.