Figure 1 shows the typical SEM images of Co antidot arrays with pore diameters of 1.3 and 6.2 μ m. Here, Fig. 1a shows the evidence the high hexagonal order in the antidot arrays, which mirrors the former positions of the voids between the spheres. As shown in Fig. 1b, each edge of hexagonal pore is nearly 3.1 μ m, which is just half of the hole diameter (≈ 6.2 μ m). The antidot arrays exhibit regularly hexagonal macropores and good uniformity in both the size and the distance between the pores. A specially magnified cell of Co antidot arrays is shown in Fig. 1c, where mean hole diameter (≈ 1.3 μ m) and typical interhole distance (≈ 360 nm) are presented. This result indicates that the mean interhole distance to the diameters of corresponding PS particles is about 1/4. Similar results have been observed in the other samples prepared with the same procedure, showing the generality of the geometric characteristics. In this article, when the sputtering power is suitable, the Co atoms can pitch in the interface of the adjoining microspheres along the tangential direction, which results in the hexagonal holes.

Fig.1

	Figure Option ViewDownloadNew Window
	Fig.1 Highly ordered Co antidot arrays with pore diameter about 1.3 μ m a, 6.2 μ m b, c magnification of a displaying mean hole dimension and the angle-to-angle distances

The hole depth of Co antidot arrays is measured by AFM imaging. As shown in Fig. 2, the mean hole depth of the 1.3 μ m and the sample is about 35 nm, and the regular hexagonal holes are confirmed again. Furthermore, the depth values are nearly constant for different samples, indicating that all the samples are approximately the same thickness.

Fig.2

	Figure Option ViewDownloadNew Window
	Fig.2 a AFM image of Co antidot arrays with pore diameter about 1.3 μ m, b the same image was converted into a three-dimensional perspective

Figure 3 reveals the XRD spectrum of continuous Co film of the same thickness. Only two diffraction peaks correspond to the (111) and (110) of Co can be found in the pattern. The (111) peak is dominate, implying the obviously preferred orientation in Co grains of the antidot arrays. The average crystallite size D of Co can be given by Scherrer’ s equation ^[19]:

D=0.89λ /β cosθ , (1)

where λ is the X-ray wavelength and β is the full width at half maximum (FWHM) of a diffraction peak at 2θ corrected for instrumental broadening. From Eq. (1), the estimated crystallite size of Co is about 17 nm.

Fig. 3

	Figure Option ViewDownloadNew Window
	Fig. 3 XRD pattern of the continuous Co film

The magnetic properties of the Co antidot arrays are measured at room temperature, and the typical results are indicated in Fig. 4. The H_‖ represents the external magnetic field parallel to the surface of the Co antidot arrays, and the H _⊥ perpendicular to the surface of the arrays. It can be found that the value of the remanence of H_‖ is 9.5 Am²/kg, which is as much as 10 times greater than that of H_⊥. At the same time, the value of magnetization appears to be saturate at 306.7 A/m for H_‖ orientation. In contrast, the magnetization is difficult to saturate throughout the period in the case of H _⊥ orientation. Moreover, the same tendency also is found to the other samples. Therefore, it is confirmed that the easily magnetized direction is parallel to the surface of the samples and the Co antidot array has obvious magnetic anisotropy.

Fig. 4

	Figure Option ViewDownloadNew Window
	Fig. 4 Hysteresis hoops of the Co antidot arrays with pore diameter about 1.3 μ m. The H‖ represents the direction of magnetic field applied parallel to the surface of Co antidot arrays and the H ⊥ perpendicular to Co antidot arrays

In order to investigate the effect of the pore diameter on the magnetic properties, the change of the coercivity and squareness at H_‖ orientation as a function of the pore diameter is summarized in Fig. 5. Since the intervals of the pore diameters are close to micron scale, the dependence of the coercivity and squareness on the pore diameter is well observed. The coercivity decreases from 51.4 to 29.8 A/m, and the squareness decreases from 0.84 to 0.75 with increasing pore diameter from 1.3 to 6.2 μ m. As indicated in Fig. 6, the values of coercivity and squareness of the Co films are the lowest, 0.9 and 0.31 A/m, respectively. It should be noted that when the pore size is in the range of 1.3-6.2 μ m, the squareness values of the samples are close to the optimum value from media noise viewpoint ^[20].

Fig. 5

	Figure Option ViewDownloadNew Window
	Fig. 5 Change of the coercivity (H) and squareness (M r/M s) at H‖ orientation with the pore diameter

Fig. 6

	Figure Option ViewDownloadNew Window
	Fig. 6 Hysteresis hoops of the Co films at H‖ orientation

The difference of coercivity and squareness between continuous film and antidot arrays maybe comes from the shape anisotropies introduced by the hexagonal holes. For the case of Co film, the magnetic properties are mainly determined by the magnetocrystalline anisotropy, which makes the magnetic moment be along its easy-axis direction ^[21]. While in Co 2D antidot arrays, the patterning-induced shape anisotropies will make the magnetic moments be around the each edge of the hexagonal holes to decrease the demagnetization energy. This effect is similar to that the antidot pinned the magnetic moment ^{[22, 23]}. Thus, we assume that the magnetic properties of Co 2D antidot arrays will be determined by the interplay between the intrinsic magnetocrystalline anisotropy and pinning of the hexagonal holes. In this case, only when the applied field is strong enough, the magnetic moment can be reversed to the direction of external field. Moreover, in the antidot arrays, the reversible component of magnetization may be much lower than that of continues films. Accordingly, the values of coercivity and squareness of Co 2D antidot arrays are much higher than those of Co continues films.

Figure 7 illustrates a geometric model used to define the in-plane structural parameters of Co 2D antidot arrays with hexagonal holes. The fundamental building block of the antidot arrays is equilateral triangle, which side length is the diameter of the corresponding PS particles (d). According to Fig. 1, the interhole distance (a) and the radius of hexagonal macropore (r) are d/4 and 3d/8, respectively. Therefore, the area of formed array surface surrounded by the triangle is (37 3d² )/256 corresponding the area of the triangle surface 3d² /4 3d2/4, so the ratio of both areas is a constant and equals to 0.578, no matter how much the pore diameter is. Therefore, the number of the hexagonal holes decreases while the amount of Co is thought to keep constant with the increase in the pore diameter. As a result, with the increase in the pore diameter, the pinning effect becomes increasingly weak due to the decrease in the shape anisotropies. This behavior leads to the situation of decreased number of the magnetic moments around the antidot and increased reversible component of magnetization. Therefore, both the coercivity and the squareness decrease with increasing pore diameter of Co 2D antidot arrays.

Fig. 7

	Figure Option ViewDownloadNew Window
	Fig. 7 Structure model of Co 2D antidot arrays with hexagonal holes, where d is defined as the diameter of the corresponding PS particles, r is the radius of the hexagonal macropore, and a is the interhole distance