Classification of super domains and super domain walls in permalloy antidot lattices

We study the remanent domain configurations of rectangular permalloy antidot lattices over a range of lattice parameters. The influence of antidot diameter, antidot spacing, and aspect ratio of the lattice on the remanent domain configuration are investigated by magnetic force microscopy and supported by micromagnetic simulations. In the remanent state, areas of cells with the same orientation of average magnetization form magnetic super domains separated by super domain walls (SDWs). Two types of SDWs are identified. The first type is characterized by low stray field energy, is linear, and expands over many lattice constants. In contrast, the second type shows high stray field energy and is situated at kinks of low energy SDWs. Its width can vary from a minimum of two lattice cells up to several lattice constants, depending on the lattice parameters. The occurrence and structure of these two types of SDWs as functions of lattice parameters are classified and discussed in terms of the interplay of stray field and exchange energy.

Figure 1

(a) Schematic diagram of the permalloy antidot lattice and the domain distributions in one cell. (b) Two possible orientations of $m_{\mathit{av}}$ in experimental conditions. (c) HE-SDW in the $x$ direction. (d) LE-SDW in the $y$ direction.

Figure 2

Remanent-state MFM images of the lattice: $d$ $=$ 80 nm, $S_x$ $=$ 350 nm, and $S_y$ $=$ 300 nm. Solid circles indicate the positions of antidots. Dashed lines and dotted rectangular frames indicate the LE-SDWs (L) and HE-SDWs (H), respectively.

Figure 3

The spin configurations of the lattice with $d$ $=$ 80 nm, $S_x$ $=$ 350 nm, and $S_y$ $=$ 300 nm (a) and close-ups of SD (b), LE-SDW (c), and HE-SDW (d) obtained numerically. HE-SDWs are indicated by rectangular frames in (a) and (d). LE-SDW is indicated by the dashed line in (c).

Figure 4

Remanent-state MFM images of the lattices with a scan size of 5 × 5 μm${}^2$ (left side) and 2 × 2 μm${}^2$ (right side). Solid circles and dotted circles indicate the positions of antidots. Dashed lines and dotted rectangular frames indicate the LE-SDWs and HE-SDWs, respectively.

Figure 5

Different occurrences of HE-SDWs as a function of $S_x$, $S_y$, and $d$ $=$ 60 (a), 80 (b), and 100 (c) nm. Shaded regions indicate the occurrence of HE-SDWs. Open circles indicate the lattices where no HE-SDWs are found; half-filled circles (red part) indicate the lattices with narrow HE-SDWs; and filled circles (blue part) indicate the lattices with extended HE-SDWs. The right panels show two typical MFM images of the lattices with extended HE-SDWs and narrow HE-SDWs, corresponding to the filled (blue) and half-filled (red) circles, respectively.

Figure 6

(a) Sketch of distribution of energy in an extended HE-SDW in the lattice with a small $d$. (b) Change of energy sections in an extended HE-SDW and a narrow HE-SDW in the lattice with a large $d$. The overall orientations of magnetization in different energy sections are indicated by black arrows.

Figure 7

(a) and (b) Two consecutive MFM images of the lattice with $d$ $=$ 80 nm, $S_x$ $=$ 350 nm, and $S_y$ $=$ 300 nm. HE-SDWs that disappeared (1), whose widths were increased (2), and whose widths shrank (3) are indicated by arrows. (c) Schematic diagram of the change of a HE-SDW in the section marked by dotted rectangular in (b) during five consecutive MFM scans, as indicated by different colors online. Cells that were occupied with sections of a HE-SDW during 26 scans are indicated by circled $+$ signs. (d) Histogram of the change in width (ΔW) of extended HE-SDWs (unchanged HE-SDWs are not included) from each scan during 26 consecutive MFM scans. The dashed line indicates a Gaussian fitting curve.