Magnetic antidot to dot crossover in Co and Py nanopatterned thin films

The crossover from antidot to dot magnetic behavior on arrays patterned in a ferromagnetic thin film has been achieved by modifying only the geometry. A series of antidot arrays has been fabricated on cobalt with fixed diameter $d$ and by reducing the period of the array $p$ from $p\gg d$ to $p<d$. A dramatic change in the coercivity dependence with $p$, correlated with a significant modification in the magnetic domain structure observed by x-ray photoemission electron microscopy, evidences the crossover. An intermediate regime has been found between the superdomain structure present in antidot arrays and the array of astroid-state noncorrelated dots. The study has been reproduced for a different ferromagnetic material, permalloy, and supported by micromagnetic simulations.

Figure 1

Left: Definition of the geometrical parameters of the arrays: $p$, $d$, $d_{\mathrm{eff}}$, and $\lambda$. Orange color represents the magnetic material, while black areas are nonmagnetic holes with diameter $d$, and grey areas are the holes with effective diameter $d_{\mathrm{eff}}$. Right: Scheme of the astroid-shaped dots formed by the intersection of the holes in the dot ($D$) regime, where $p<d_{\mathrm{eff}}$.

Figure 2

SEM images of some of the arrays in Series 1, with $p$ = (a) 105, (b) 120, (c) 200, and (d) 500 nm. The inset in (b) shows a zoomed-out and ${52}^{\circ }$ tilted SEM image of the array with $p=120$ nm, in which the parameters $d$, $d_{\mathrm{ext}}$, and $p$ are indicated. In the arrays with small $p$, silicon etched from the substrate redeposit over the neighboring holes, causing the antidot diameter to seem smaller, as is the case in (a), where some of the antidots have been almost filled up with Si redeposit.

Figure 3

Low magnification bright field TEM images of arrays in Series 2-Co with (a) $p$ = 500 nm and (b) $p$ = 175 nm. Dashed squares in (a, b) hallmark the areas in which the chemical mapping at Figs. 4 and 5 has been performed. (c) High resolution TEM image of $p$ = 500 nm.

Figure 4

STEM-EDX chemical mapping of the array in Series 2-Co with $p=500$ nm in the region around one of the holes, as hallmarked in Fig. 3. (a) High-angle annular dark-field (HAADF) imaging in which the diameters $d$, $d_{\mathrm{ext}}$, and $d_{\mathrm{eff}}$ are indicated. Integrated x-rays intensity maps in (b) Co-K, (c) Si-K, and (d) Ga-K are composed with blue, red, and green colors in an RGB color map in (e).

Figure 5

STEM-EDX chemical mapping of the array in Series 2-Co with $p=175$ nm in the region between two holes, as hallmarked in Fig. 3. (a) HAADF image. Integrated x-rays intensity maps in (b) Co-K, (c) Si-K, and (c) Ga-K are composed with blue, red, and green colors in a RGB color map in (e).

Figure 6

Series 1. $H_C$ vs $p$. Red, green, and blue colors represents D, INT, and AD regimes, respectively. The black line is the fit of $\Delta H_C\propto 1/\lambda$, giving a fitting value for $d_{\mathrm{eff}}=114\pm 4$ nm. Dashed horizontal line indicates the coercivity of the unpatterned film, which is 14 Oe. In the inset, $H_C$ is plotted as a function of $1/\lambda$.

Figure 7

Series 1: XPEEM images of the unpatterned film, and the arrays of $p$ = (a) 500, (b) 400, (c) 300, (d) 200, (e) 150, (f) 140, (g) 130, (h) 120, and (i) 105 nm. In a zoom the astroid-like shape of the dots formed by the intersection of the antidots can be apreciated. Blue and red colors in the images mean magnetization projection along the MSD pointing up and down, respectively. White color corresponds to magnetization either zero or perpendicular to the MSD. A superdomain is encircled in (d). A blue, green, or red frame surrounding each image indicates whether it belongs to the antidot (AD), intermediate (INT), or dot (D) regime.

Figure 8

AD regime. Left: XMCD images of the array with $p=200$ nm, belonging to the AD regime, with MSD vertical (up), and ${45}^{\circ }$ tilted (down). Right: $\theta$ map of the magnetization angle.

Figure 9

INT regime. Left: XMCD images of the array with $p=120\mathrm{nm}$, belonging to the INT regime, with MSD vertical (up), and ${45}^{\circ }$ tilted (down). Right: $\theta$ map of the magnetization angle.

Figure 10

AD regime. $\theta \left(r\right)$ linescans in the array with $p=200$ nm, which belong to the AD regime. Experimental $\theta \left(r\right)$ along lines 1 and 2 indicated in Fig. 8 have been plotted as open squares and circles, respectively. Simulated $\theta \left(r\right)$ along lines 1 and 2 indicated in Fig. 15 are plotted as dashed and continuous lines, respectively. Circles on top of the graph represent the antidot positions. Holes with $d$ are plotted in dark grey and the FIB damaged ring with $d_{\mathrm{eff}}$ in light grey.

Figure 11

INT regime. $\theta \left(r\right)$ linescans in the array with $p=120$ nm, which belong to the INT regime. Experimental $\theta \left(r\right)$ along the line indicated in Fig. 9 has been plotted as open squares. The simulated linescan along the line indicated in Fig. 15 is plotted as a continuous line. Circles on top of the graph represent the antidot positions. Holes with $d$ are plotted in dark grey and the FIB damaged ring with $d_{\mathrm{eff}}$ in light grey.

Figure 12

Series 2: $H_C$ dependence on $p$ of the antidot arrays on Co and Py are plotted as solid squares and open circles, respectively. The blue, green, and red colors represent data belonging to the AD, INT, and D regimes, respectively. In the inset, $H_C$ vs ${\lambda }^{-1}$ is plotted, showing a linear trend for $p$ above the crossover. The function $\Delta H_C\propto 1/\lambda$, with the obtained $d_{\mathrm{eff}}$ value [35], is plotted as solid and dashed black lines for cobalt and permalloy, respectively.

Figure 13

$H_C$ of simulated arrays of antidots with $d=$ 80 nm (squares), 90 nm (circles), 100 nm (triangles), 110 nm (rhombs), and 120 nm (stars), as a function of $\lambda$. Experimental values for Series 1 are plotted as open squares for comparison. The data belonging to the antidot, intermediate, and D regimes are represented with blue, green, and red colors, respectively. In the inset the same data set is plotted vs ${\lambda }^{-1}$.

Figure 14

Values of $H_C^{\max }$ and $p_{\max }$ as a function of $d$ for $H_C$ curves of different diameters. The linear fit of $p_{\max }$ vs $d$ confirms that the $H_C^{\max }$ allways occurs for $p=d+12.3$ nm.

Figure 15

Simulated $\theta$ maps of the magnetization angle of antidot arrays with $d=110$ nm belonging to the (a) AD and (b) INT regimes, with $p=200$ and 120 nm, respectively. (c) $\theta$ map of the remanent state of a dot of the D regime array with $p=d=110$ nm. (d) Colorscale of $\theta$.